{"id":9737,"date":"2026-07-25T20:21:56","date_gmt":"2026-07-25T11:21:56","guid":{"rendered":"https:\/\/sasamath.com\/blog\/?page_id=9737"},"modified":"2026-07-26T23:19:32","modified_gmt":"2026-07-26T14:19:32","slug":"math-abstraction-02-implicit-era","status":"publish","type":"page","link":"https:\/\/sasamath.com\/blog\/mathematical-abstraction\/math-abstraction-02-implicit-era\/","title":{"rendered":"\ucd08\uae30 \uc218\ud559\uc5d0\uc11c\uc758 \uc554\ubb35\uc801 \ucd94\uc0c1\ud654"},"content":{"rendered":"<p><!-- \uc218\ud559\uc801 \ucd94\uc0c1\ud654 2\ud3b8: \uc554\ubb35\uc801 \ucd94\uc0c1\ud654\uc758 \uc2dc\ub300 --><\/p>\n<div class=\"math-abs-series\">\n<p>\uc591 \ub2e4\uc12f \ub9c8\ub9ac\uc640 \uc0ac\uacfc \ub2e4\uc12f \uac1c\uc5d0\uc11c \ub3d9\uc77c\ud55c \u2018\ub2e4\uc12f\u2019\uc744 \uc54c\uc544\ubcf4\ub294 \uc77c\uc740 \uc624\ub298\ub0a0 \ub108\ubb34\ub098 \ub2f9\uc5f0\ud574 \ubcf4\uc778\ub2e4. <a href=\"..\/math-abstraction-01-essence\/\">1\ubd80<\/a>\uc5d0\uc11c \uc81c\uc2dc\ud55c \uad00\uc810\uc73c\ub85c \ub9d0\ud558\uba74, \uc774\ub54c \uc6b0\ub9ac\ub294 \ub300\uc0c1\uc758 \uc885\ub958\ub97c \uace0\ub824\uc5d0\uc11c \uc81c\uc678\ud558\uace0 \uc218\ub7c9\ub9cc\uc744 \ubcf4\uc874\ud55c\ub2e4. <!-- \ub2e4\ub9cc \uc774\ub7ec\ud55c \ucca0\ud559\uc801 \ubd84\uc11d\uc744 \uace7\ubc14\ub85c \uc120\uc0ac\uc2dc\ub300 \uc0ac\ub78c\ub4e4\uc758 \uc2e4\uc81c \uc2ec\ub9ac \uc0c1\ud0dc\uc5d0 \ub300\ud55c \uc99d\uac70\ub85c \ubc14\uafb8\uc5b4\uc11c\ub294 \uc548 \ub41c\ub2e4. \ub0a8\uc544 \uc788\ub294 \ud1a0\ud070\uacfc \uc218 \ud45c\uae30\ub294 \uc0ac\ub78c\ub4e4\uc774 \ubb34\uc5c7\uc744 \uae30\ub85d\ud558\uace0 \uc5b4\ub5bb\uac8c \uacc4\uc0b0\ud588\ub294\uc9c0\ub294 \ubcf4\uc5ec\uc8fc\uc9c0\ub9cc, \uadf8\ub4e4\uc774 \uba38\ub9bf\uc18d\uc5d0\uc11c \u2018\ucd94\uc0c1\ud654\u2019\ub77c\ub294 \uc870\uc791\uc744 \uc790\uac01\ud588\ub294\uc9c0\uae4c\uc9c0 \uc9c1\uc811 \uc99d\uc5b8\ud558\uc9c0\ub294 \uc54a\uae30 \ub54c\ubb38\uc774\ub2e4<a class=\"math-abs-series-ref\" title=\"Overmann, K. A. (2018). Updating the \u201cabstract\u2013concrete\u201d distinction in ancient Near Eastern numbers. Cuneiform Digital Library Journal, 2018(1), 1\u201322.\" href=\"#ref-Overmann2018\">[Overmann2018, \u00a7\u00a71\u20133]<\/a>. --><\/p>\n<p><a href=\"..\/math-abstraction-01-essence\/\">1\ubd80<\/a>\uc5d0\uc11c\ub294 \ucd94\uc0c1\ud654\ub97c \u2018\ub300\uc0c1\uc5d0\uc11c \ud2b9\uc815\ud55c \uc131\uc9c8\uc5d0 \uc8fc\ubaa9\ud558\uace0 \ub098\uba38\uc9c0\ub97c \uace0\ub824\uc5d0\uc11c \uc81c\uc678\ud558\uc5ec \uc0c8\ub85c\uc6b4 \uac1c\ub150\uc774\ub098 \ub300\uc0c1\uc744 \uaddc\uc815\ud558\ub294 \uc870\uc791\u2019\uc73c\ub85c \uc124\uba85\ud588\ub2e4. \ub3d9\uce58\ub958\ub97c \uc774\uc6a9\ud55c \ud604\ub300\uc801 \uad6c\uc131\uacfc \u2018\ucd94\uc0c1\uc5d0 \uc758\ud55c \uc815\uc758\u2019\uc5d0 \ub300\ud55c \ub17c\ub9ac\uc801 \ubd84\uc11d\uc740 \uc8fc\ub85c 19\uc138\uae30 \uc774\ud6c4\uc5d0 \uc815\uad50\ud574\uc84c\uc9c0\ub9cc, \uc11c\ub85c \ub2e4\ub978 \ub300\uc0c1\uc744 \uac19\uc740 \uc218\ub85c \uc138\uac70\ub098 \uac1c\ubcc4 \ub3c4\ud615\uc744 \ud1b5\ud574 \uc77c\ubc18 \uba85\uc81c\ub97c \ub17c\uc99d\ud558\ub294 \uc2e4\ucc9c\uc740 \ud6e8\uc52c \uc624\ub798\ub418\uc5c8\ub2e4<a class=\"math-abs-series-ref\" title=\"Mancosu, P. (2016). Abstraction and Infinity. Oxford University Press. Publisher page.\" href=\"#ref-Mancosu2016\">[Mancosu2016, Chs. 1\u20132]<\/a>. \uc774\uc81c\ubd80\ud130 \uba87 \ud3b8\uc5d0 \uac78\uccd0 \uc0b4\ud3b4\ubcfc \uc9c8\ubb38\uc740 \ud558\ub098\uc774\ub418, \uc138 \uce35\uc704\ub97c \uad6c\ubd84\ud574\uc57c \ud55c\ub2e4. \ucd94\uc0c1\uc801\uc778 \uc2e4\ucc9c\uc740 \uc5b8\uc81c \ub098\ud0c0\ub0ac\ub294\uac00? \uadf8 \uc2e4\ucc9c\uc744 \ucca0\ud559\uc801\uc73c\ub85c \uc124\uba85\ud558\ub824\ub294 \uc774\ub860\uc740 \uc5b8\uc81c \ub098\ud0c0\ub0ac\ub294\uac00? \uadf8\ub9ac\uace0 \ucd94\uc0c1\ud654\ub97c \uc218\ud559\uc758 \uba85\uc2dc\uc801\uc778 \ubc29\ubc95\uc73c\ub85c \ud1b5\uc81c\ud558\uae30 \uc2dc\uc791\ud55c \ub54c\ub294 \uc5b8\uc81c\uc778\uac00?<\/p>\n<p>\ub530\ub77c\uc11c \uace0\ub300\uc5d0 \ub300\ud55c \ub2f5\uc744 \ub2e8\uc21c\ud788 \u2018\uc544\ubb34\ub3c4 \uc54c\uc9c0 \ubabb\ud588\ub2e4\u2019\ub77c\uace0 \ud560 \uc218\ub294 \uc5c6\ub2e4. \ud2b9\ud788 \ud50c\ub77c\ud1a4\uacfc \uc544\ub9ac\uc2a4\ud1a0\ud154\ub808\uc2a4\ub294 \uc218\ud559\uc801 \ub300\uc0c1\uacfc \uac10\uac01\uc801 \uc0ac\ubb3c\uc758 \uad00\uacc4\ub97c \ubd84\uba85\ud788 \ub17c\uc758\ud588\ub2e4. \uc774 \uae00\uc5d0\uc11c \ub9d0\ud558\ub294 <span class=\"defined\">\u2018\uc554\ubb35\uc801 \ucd94\uc0c1\ud654\u2019<\/span>\ub780 \uace0\ub300\uc778\uc774 \ucd94\uc0c1\uc801 \uc0ac\uace0\ub97c \uc804\ud600 \uc790\uac01\ud558\uc9c0 \ubabb\ud588\ub2e4\ub294 \uc2ec\ub9ac\ud559\uc801 \uc8fc\uc7a5\uc774 \uc544\ub2c8\ub77c, \uacc4\uc0b0\uacfc \uc99d\uba85\uc758 \uad00\ud589\uc774 \uc624\ub298\ub0a0\uacfc \uac19\uc740 \uba85\uc2dc\uc801 \ud615\uc2dd \uaddc\uce59\uc73c\ub85c \uc644\uc804\ud788 \uc815\ub9ac\ub418\uc5b4 \uc788\uc9c0\ub294 \uc54a\uc558\ub2e4\ub294 \ubd84\uc11d\uc801 \ud45c\ud604\uc774\ub2e4. \uc774 \uc81c\ud55c\ub41c \uc758\ubbf8\uc5d0\uc11c \uc148\ub3cc\uacfc \uc218 \ud45c\uae30, \uc808\ucc28 \uc911\uc2ec\uc758 \ubb38\uc81c \ubb38\ud5cc, \uadf8\ub9ac\uc2a4\uc758 \uc99d\uba85\uc744 \ucc28\ub840\ub85c \uc0b4\ud3b4\ubcf8 \ub4a4, \uc720\ud074\ub9ac\ub4dc \u201c\uc6d0\ub860\u201d 1\uad8c \uba85\uc81c 1\uc758 \uad50\uc810 \uac00\uc815\uacfc 0, \uc74c\uc218\uc758 \uc11c\ub85c \ub2e4\ub978 \uc218\uc6a9\uc0ac\ub97c \uc0ac\ub840\ub85c \uac80\ud1a0\ud55c\ub2e4.<\/p>\n<h4>\uc148\ub3cc\uc5d0\uc11c \uc218\ub85c<\/h4>\n<p>\uc11c\uc544\uc2dc\uc544 \uc5ec\ub7ec \uc720\uc801\uc5d0\uc11c\ub294 \uc6d0\ubfd4, \uacf5, \uc6d0\ubc18, \uc6d0\uae30\ub465 \ub4f1\uc73c\ub85c \ube5a\uc740 \uc791\uc740 \uc810\ud1a0 \ubb3c\uccb4\uac00 \ucd9c\ud1a0\ub418\uba70, \uc77c\ubd80 \uc720\ud615\uc740 \uae30\uc6d0\uc804 8\ucc9c\ub144\uae30\uae4c\uc9c0 \uac70\uc2ac\ub7ec \uc62c\ub77c\uac04\ub2e4. \uace0\uace0\ud559\uc790 \ub4dc\ub2c8\uc988 \uc288\ub9cc\ud2b8-\ubca0\uc138\ub77c\ud2b8(Denise Schmandt-Besserat)\ub294 \uc774 \ubb3c\uccb4\ub4e4\uc744 \ubb3c\ud488\uacfc \uc218\ub7c9\uc744 \uae30\ub85d\ud55c <span class=\"defined\">\ud1a0\ud070<\/span>(token) \uccb4\uacc4\ub85c \ud574\uc11d\ud558\uace0, \ud1a0\ud070, \uc9c4\ud759 \ubd09\ud22c, \uc218\ub7c9 \uc778\uc0c1, \uc6d0\uc2dc \uc124\ud615\ubb38\uc790 \uc0ac\uc774\uc758 \uacc4\ubcf4\ub97c \uc81c\uc548\ud588\ub2e4<a class=\"math-abs-series-ref\" title=\"Schmandt-Besserat, D. (1984). Before numerals. Visible Language, 18(1), 48\u201360.\" href=\"#ref-SchmandtBesserat1984\">[SchmandtBesserat1984]<\/a><a class=\"math-abs-series-ref\" title=\"Schmandt-Besserat, D. (1992). Before Writing (2 vols.). University of Texas Press. Google Books.\" href=\"#ref-SchmandtBesserat1992\">[SchmandtBesserat1992]<\/a>. \uadf8\ub7ec\ub098 \ubaa8\ub4e0 \uc18c\ud615 \uc810\ud1a0 \ubb3c\uccb4\uac00 \uac19\uc740 \uae30\ub2a5\uc744 \ud588\ub294\uc9c0, \uac01 \ubaa8\uc591\uc774 \uc5b8\uc81c\ub098 \ubb3c\ud488 \ud55c \ub2e8\uc704\uc640 \uc5c4\uaca9\ud55c \uc77c\ub300\uc77c \ub300\uc751\uc744 \uc774\ub8e8\uc5c8\ub294\uc9c0, \ubcf5\uc7a1\ud55c \ud1a0\ud070\uc774 \ubb38\uc790 \uae30\ud638\uc758 \uc9c1\uc811\uc801\uc778 \uc120\uc870\uc600\ub294\uc9c0\ub294 \uacc4\uc18d \ub17c\uc758\ub418\uace0 \uc788\ub2e4<a class=\"math-abs-series-ref\" title=\"Bennison-Chapman, L. E. (2019). Reconsidering \u201ctokens\u201d: The Neolithic origins of accounting or multifunctional, utilitarian tools? Cambridge Archaeological Journal, 29(2), 233\u2013259.\" href=\"#ref-BennisonChapman2019\">[BennisonChapman2019]<\/a>.<\/p>\n<p>[\ub4dc\ub2c8\uc988 \uc288\ub9cc\ud2b8-\ubca0\uc138\ub77c\ud2b8\uac00 1970\ub144\ub300\ubd80\ud130 \uc804\uac1c\ud55c \ud1a0\ud070 \uc5f0\uad6c\ub294 \ub450 \uad8c\uc9dc\ub9ac \uc800\uc11c <i>Before Writing<\/i>(1992)\uc5d0 \uc9d1\ub300\uc131\ub418\uc5b4 \uc788\ub2e4. \ub2e4\ub9cc \uc544\ub798\uc758 \ub2e8\uacc4\uc801 \uc11c\uc220\uc740 \uadf8\uc758 \uc601\ud5a5\ub825 \uc788\ub294 \ud574\uc11d \ubaa8\ud615\uc774\uc9c0, \uc138\ubd80\uae4c\uc9c0 \ud569\uc758\ub41c \ub2e8\uc120\uc801 \uc5f0\ub300\uae30\ub294 \uc544\ub2c8\ub2e4<a class=\"math-abs-series-ref\" title=\"Schmandt-Besserat, D. (1992). Before Writing (2 vols.). University of Texas Press. Google Books.\" href=\"#ref-SchmandtBesserat1992\">[SchmandtBesserat1992]<\/a><a class=\"math-abs-series-ref\" title=\"Overmann, K. A. (2018). Updating the \u201cabstract\u2013concrete\u201d distinction in ancient Near Eastern numbers. Cuneiform Digital Library Journal, 2018(1), 1\u201322.\" href=\"#ref-Overmann2018\">[Overmann2018]<\/a>.]<\/p>\n<p>\uc288\ub9cc\ud2b8-\ubca0\uc138\ub77c\ud2b8\uc758 \ubaa8\ud615\uc5d0\uc11c \ud1a0\ud070\uc740 \uc2e4\uc81c \ubb3c\ud488\uc744 \ub300\uc2e0\ud558\uc5ec \uc218\ub7c9\uc744 \ubb3c\ub9ac\uc801\uc73c\ub85c \uc870\uc791\ud560 \uc218 \uc788\uac8c \ud55c\ub2e4. \uc608\ucee8\ub300 \uc5b4\ub5a4 \uc720\ud615\uc758 \ud1a0\ud070 \ub2e4\uc12f \uac1c\ub97c \uc62e\uaca8 \uc591 \ub2e4\uc12f \ub9c8\ub9ac\uc758 \uac70\ub798\ub97c \ub098\ud0c0\ub0bc \uc218 \uc788\uc5c8\uc744 \uac83\uc774\ub2e4. \uc774\ub54c \uae30\ub85d \ub9e4\uccb4\uac00 \ubb3c\ud488 \uc885\ub958\uc640 \uacc4\ub7c9 \ub9e5\ub77d\uc5d0 \uae34\ubc00\ud788 \ubb36\uc5ec \uc788\uc5c8\ub2e4\ub294 \uc810\uc740 \uc911\uc694\ud558\ub2e4. <!-- \uadf8\ub7ec\ub098 \uc5ec\uae30\uc11c \u2018\ub2e4\uc12f\uc774\ub77c\ub294 \ub3c5\ub9bd\ub41c \uc218 \uac1c\ub150\uc774 \uc874\uc7ac\ud558\uc9c0 \uc54a\uc558\ub2e4\u2019\uace0 \uacb0\ub860 \ub0b4\ub9b4 \uc218\ub294 \uc5c6\ub2e4. \uce90\ub7f0\ub9ac \uc624\ubc84\uba3c(Karenleigh Overmann)\uc740 \uc218\uac00 \uad6c\uccb4\uc801 \uc0ac\ubb3c\uc744 \uac00\ub9ac\ud0ac \ub54c\uc5d0\ub3c4 \uc218\ub7c9 \uad00\uacc4 \uc790\uccb4\ub294 \ucd94\uc0c1\uc801\uc774\uba70, \ucd08\uae30 \uc218 \uac1c\ub150\uc740 \ube44\ucd94\uc0c1\uc801\uc774\uc5c8\ub2e4\uae30\ubcf4\ub2e4 \uc190\uac00\ub77d, \ud1a0\ud070, \uae30\ud638 \uac19\uc740 \ubb3c\uc9c8\uc801 \uc7a5\uce58\uc640 \uacb0\ud569\ub418\uc5b4 \uc788\uc5c8\ub2e4\uace0 \ube44\ud310\ud55c\ub2e4<a class=\"math-abs-series-ref\" title=\"Overmann, K. A. (2018). Updating the \u201cabstract\u2013concrete\u201d distinction in ancient Near Eastern numbers. Cuneiform Digital Library Journal, 2018(1), 1\u201322.\" href=\"#ref-Overmann2018\">[Overmann2018, \u00a7\u00a74\u20136]<\/a>. \uc720\ubb3c\uc740 \ud45c\uc0c1\uc758 \ubb3c\uc9c8\uc801 \ud615\uc2dd\uc744 \ubcf4\uc5ec\uc8fc\uc9c0\ub9cc, \ub9d0\ub85c \ud45c\ud604\ub418\uc5c8\uc744 \uc218 \uac1c\ub150\uc758 \uc804\ubd80\ub97c \ubcf4\uc874\ud558\uc9c0\ub294 \uc54a\ub294\ub2e4. --><\/p>\n<p>\uae30\uc6d0\uc804 4\ucc9c\ub144\uae30 \ud6c4\ubc18\uc758 \uba54\uc18c\ud3ec\ud0c0\ubbf8\uc544\uc5d0\uc11c\ub294 \ud1a0\ud070\uc744 \ub123\uc5b4 \ubd09\uc778\ud55c \uc18d\uc774 \ube48 \uc810\ud1a0 \ubd09\ud22c(<i>bulla<\/i>), \uadf8 \ud45c\uba74\uc758 \uc778\uc0c1, \uc218\ub7c9\uc744 \uae30\ub85d\ud55c \uc810\ud1a0\ud310\uc774 \ud568\uaed8 \ud655\uc778\ub41c\ub2e4. \ud1a0\ud070\uc744 \ub20c\ub7ec \ud45c\uc2dc\ud55c \uc790\uad6d\uc774 \ub0a9\uc791\ud55c \uc810\ud1a0\ud310\uc758 \uae30\ud638\ub85c \ubc14\ub00c\uc5c8\ub2e4\ub294 \uc124\uba85\uc740 \ud1a0\ud070 \uac00\uc124\uc758 \ud575\uc2ec\uc774\ub2e4. <!-- \uadf8\ub7ec\ub098 \ubaa8\ub4e0 \ub2e8\uacc4\uac00 \ud558\ub098\uc758 \ud544\uc5f0\uc801\uc778 \uacc4\uc5f4\ub85c \uc774\uc5b4\uc84c\ub2e4\uace0 \ub2e8\uc815\ud558\uae30\ubcf4\ub2e4, \uc5ec\ub7ec \uae30\ub85d \uae30\uc220\uc774 \ud589\uc815 \ud658\uacbd\uc5d0\uc11c \uacb9\uce58\uace0 \ubcc0\ud615\ub418\uc5c8\ub2e4\uace0 \ubcf4\ub294 \ud3b8\uc774 \uc548\uc804\ud558\ub2e4<a class=\"math-abs-series-ref\" title=\"Schmandt-Besserat, D. (1992). Before Writing (2 vols.). University of Texas Press. Google Books.\" href=\"#ref-SchmandtBesserat1992\">[SchmandtBesserat1992]<\/a><a class=\"math-abs-series-ref\" title=\"Nissen, H. J., Damerow, P., &amp; Englund, R. K. (1993). Archaic Bookkeeping: Early Writing and Techniques of Economic Administration in the Ancient Near East (P. Larsen, Trans.). University of Chicago Press. Google Books.\" href=\"#ref-Nissen1993\">[Nissen1993, Chs. 1\u20133]<\/a>. --> <!-- \ub610\ud55c \uba54\uc18c\ud3ec\ud0c0\ubbf8\uc544\uc758 \uc6d0\uc2dc \uc124\ud615\ubb38\uc790\ub294 \ud604\uc874 \uc790\ub8cc \ub300\ubd80\ubd84\uc774 \ubc30\uae09, \ub178\ub3d9, \ubb3c\ud488 \uad00\ub9ac\uc640 \uad00\ub828\ub41c\ub2e4\ub294 \uc810\uc5d0\uc11c \ud68c\uacc4\uc640 \ubc00\uc811\ud558\uc9c0\ub9cc, \uc774\uac83\uc744 \uace7 \u2018\uc778\ub958\uc758 \ubaa8\ub4e0 \ubb38\uc790\uac00 \ud55c \ud68c\uacc4 \uc7a5\ubd80\uc5d0\uc11c \ud0c4\uc0dd\ud588\ub2e4\u2019\ub294 \uba85\uc81c\ub85c \ud655\ub300\ud560 \uc218\ub294 \uc5c6\ub2e4. \uc774\uc9d1\ud2b8, \uc911\uad6d, \uba54\uc18c\uc544\uba54\ub9ac\uce74 \ub4f1\uc5d0\uc11c\ub294 \ubb38\uc790\uac00 \ub3c5\ub9bd\uc801\uc73c\ub85c \uc0dd\uaca8\ub09c \uac83\uc73c\ub85c \uc5f0\uad6c\ub418\uae30 \ub54c\ubb38\uc774\ub2e4<a class=\"math-abs-series-ref\" title=\"Woods, C. (Ed.). (2010). Visible Language: Inventions of Writing in the Ancient Middle East and Beyond. Oriental Institute of the University of Chicago. Official PDF.\" href=\"#ref-Woods2010\">[Woods2010]<\/a>. --><\/p>\n<p>\uc6b0\ub8e8\ud06c\uc758 \uc6d0\uc2dc \uc124\ud615\ubb38\uc790 \ubb38\uc11c\uc5d0\uc11c\ub294 \uc218\ub7c9\uc744 \ub098\ud0c0\ub0b4\ub294 \uae30\ud638\uc640 \uc148\uc758 \ub300\uc0c1, \ubb3c\ud488\uc744 \ub098\ud0c0\ub0b4\ub294 \uae30\ud638\uac00 \ud45c\uae30\uc0c1 \uad6c\ubd84\ub41c\ub2e4. \ud558\ub098\uc758 \uc218\ub7c9 \uae30\ud638\ub97c \ubb3c\ud488 \uae30\ud638\uc640 \uacb0\ud569\ud558\ub294 \ubc29\uc2dd\uc740 \ubc18\ubcf5\ub41c \ubb3c\ud488 \uadf8\ub9bc\ub9cc\uc73c\ub85c \uc218\ub7c9\uc744 \ub098\ud0c0\ub0b4\ub294 \ubc29\uc2dd\ubcf4\ub2e4 \uacbd\uc81c\uc801\uc774\uba70, \uc218\ub7c9\uc744 \uc5ec\ub7ec \ub9e5\ub77d\uc5d0\uc11c \uc7ac\uc0ac\uc6a9\ud560 \uc218 \uc788\uac8c \ud55c\ub2e4<a class=\"math-abs-series-ref\" title=\"Nissen, H. J., Damerow, P., &amp; Englund, R. K. (1993). Archaic Bookkeeping: Early Writing and Techniques of Economic Administration in the Ancient Near East (P. Larsen, Trans.). University of Chicago Press. Google Books.\" href=\"#ref-Nissen1993\">[Nissen1993, Chs. 4\u20136]<\/a>. \uc774\uac83\uc740 \uc218 \ud45c\uc0c1\uc758 \uc911\uc694\ud55c \ubcc0\ud654\uc774\ub2e4. \ub2e4\ub9cc \uc5b4\ub290 \ud55c \uc810\ud1a0\ud310\uc744 \u2018\uc5ed\uc0ac\uc0c1 \ucc98\uc74c \ub2e4\uc12f\uc774 \uc591\uc5d0\uc11c \ubd84\ub9ac\ub41c \uc21c\uac04\u2019\uc73c\ub85c \ud2b9\uc815\ud560 \uc218\ub294 \uc5c6\ub2e4. \ub9d0\ub85c \ub41c \uc218\uc0ac\uc640 \ud1a0\ud070 \uad00\ud589\uc740 \ubb38\ud5cc\ubcf4\ub2e4 \uc55e\uc130\uc744 \uc218 \uc788\uace0, \ud45c\uae30\uc0c1\uc758 \ubd84\ub9ac\uc640 \uc778\uc9c0\uc801 \ucd94\uc0c1\ud654\uac00 \ub3d9\uc77c\ud55c \uc0ac\uac74\ub3c4 \uc544\ub2c8\uae30 \ub54c\ubb38\uc774\ub2e4<a class=\"math-abs-series-ref\" title=\"Overmann, K. A. (2018). Updating the \u201cabstract\u2013concrete\u201d distinction in ancient Near Eastern numbers. Cuneiform Digital Library Journal, 2018(1), 1\u201322.\" href=\"#ref-Overmann2018\">[Overmann2018]<\/a>.<\/p>\n<p>\ucd08\uae30 \ubb38\uc11c\uc5d0\ub294 \ud558\ub098\uc758 \ubcf4\ud3b8\uc801 \uc218 \uccb4\uacc4\uac00 \uc544\ub2c8\ub77c, \uc138\ub294 \ub300\uc0c1\uacfc \uc7ac\ub294 \uc591\uc5d0 \ub530\ub77c \ub2ec\ub77c\uc9c0\ub294 10\uc5ec \uac1c, \ud754\ud788 \uc57d 13\uac1c\ub85c \ubd84\ub958\ub418\ub294 \uc218, \uacc4\ub7c9 \uccb4\uacc4\uac00 \uc4f0\uc600\ub2e4. \uc0ac\ub78c, \ub3d9\ubb3c, \uac00\uacf5\ud488\ucc98\ub7fc \ub0b1\uac1c\ub85c \uc138\ub294 \ub300\uc0c1, \uace1\ubb3c\uc758 \ubd80\ud53c, \ud1a0\uc9c0 \uba74\uc801, \uc2dc\uac04 \ub4f1\uc5d0 \uc11c\ub85c \ub2e4\ub978 \uacc4\uc5f4\uc774 \uc801\uc6a9\ub418\uc5c8\uace0, \uac19\uc740 \ubaa8\uc591\uc758 \uae30\ud638\ub3c4 \uccb4\uacc4\uc5d0 \ub530\ub77c \uac12\uc774 \ub2ec\ub77c\uc9c8 \uc218 \uc788\uc5c8\ub2e4<a class=\"math-abs-series-ref\" title=\"Nissen, H. J., Damerow, P., &amp; Englund, R. K. (1993). Archaic Bookkeeping: Early Writing and Techniques of Economic Administration in the Ancient Near East (P. Larsen, Trans.). University of Chicago Press. Google Books.\" href=\"#ref-Nissen1993\">[Nissen1993, pp. 25\u201335]<\/a>. \ub530\ub77c\uc11c \uc218\ub7c9 \uae30\ud638\uc640 \ubb3c\ud488 \uae30\ud638\uac00 \ubd84\ub9ac\ub418\uc5c8\ub2e4\ub294 \uc0ac\uc2e4\uacfc \ubaa8\ub4e0 \ub300\uc0c1\uc5d0 \ud1b5\uc6a9\ub418\ub294 \ud558\ub098\uc758 \uc21c\uc218 \uc218 \uccb4\uacc4\uac00 \ud655\ub9bd\ub418\uc5c8\ub2e4\ub294 \uc8fc\uc7a5\uc740 \uad6c\ubd84\ud574\uc57c \ud55c\ub2e4.<\/p>\n<p>[\ud55c\uc2a4 \ub2c8\uc13c(Hans J. Nissen), \ud398\ud130 \ub2e4\uba54\ub85c(Peter Damerow), \ub85c\ubca0\ub974\ud2b8 \uc5e5\uae00\ub8ec\ud2b8(Robert K. Englund)\uc758 <i>Archaic Bookkeeping<\/i>(1993)\uc740 \uc6d0\uc2dc \uc124\ud615\ubb38\uc790\uc758 \ud589\uc815 \ubb38\uc11c\uc640 \ubcf5\uc218\uc758 \uc218 \uccb4\uacc4\ub97c \ubd84\uc11d\ud55c\ub2e4. \ud1a0\ud070\uc5d0\uc11c \ubb38\uc790\ub85c \uc774\uc5b4\uc9c0\ub294 \uc9c4\ud654 \uc11c\uc0ac\uc758 \uc138\ubd80 \uc0ac\ud56d, \ud2b9\ud788 \uc9c4\ud759 \ubd09\ud22c\uc640 \ud3c9\ud310 \uc0ac\uc774\uc758 \uc778\uacfc\uad00\uacc4\uc5d0\ub294 \ud559\uacc4\uc758 \uc774\uacac\uc774 \uc788\uc73c\uba70, \ud1a0\ud070 \uac00\uc124 \uc790\uccb4\ub3c4 \uc218\uc815\uacfc \ube44\ud310\uc758 \ub300\uc0c1\uc774 \ub418\uc5b4 \uc654\ub2e4<a class=\"math-abs-series-ref\" title=\"Nissen, H. J., Damerow, P., &amp; Englund, R. K. (1993). Archaic Bookkeeping: Early Writing and Techniques of Economic Administration in the Ancient Near East (P. Larsen, Trans.). University of Chicago Press. Google Books.\" href=\"#ref-Nissen1993\">[Nissen1993]<\/a><a class=\"math-abs-series-ref\" title=\"Bennison-Chapman, L. E. (2019). Reconsidering \u201ctokens\u201d: The Neolithic origins of accounting or multifunctional, utilitarian tools? Cambridge Archaeological Journal, 29(2), 233\u2013259.\" href=\"#ref-BennisonChapman2019\">[BennisonChapman2019]<\/a>.]<\/p>\n<p>\ud1a0\ud070 \uac00\uc124\uc744 \uc774 \uae00\uc758 \ucd94\uc0c1\ud654 \uad00\uc810\uc5d0\uc11c \uc7ac\uad6c\uc131\ud558\uba74 \ub2e4\uc74c\uacfc \uac19\uc740 \u2018\ubc30\uc81c\uc758 \uc5f0\uc1c4\u2019\ub97c \uc0dd\uac01\ud574 \ubcfc \uc218 \uc788\ub2e4. \uc774\uac83\uc740 \uc720\ubb3c\ub9cc\uc73c\ub85c \uc785\uc99d\ub41c \uc2ec\ub9ac \ub2e8\uacc4\uac00 \uc544\ub2c8\ub77c, \uae30\ub85d \ub9e4\uccb4\uc758 \ubcc0\ud654\ub97c \uc124\uba85\ud558\uae30 \uc704\ud55c \ud574\uc11d \ubaa8\ud615\uc774\ub2e4.<\/p>\n<ul>\n<li>\uc2e4\uc81c \ubb3c\ud488 \ub300\uc2e0 \ud1a0\ud070\uc744 \uc870\uc791\ud558\uba74 \ubb3c\ud488\uc758 \ub9ce\uc740 \ubb3c\ub9ac\uc801 \uc131\uc9c8\uc744 \ubb34\uc2dc\ud558\uace0 \uae30\ub85d\uc5d0 \ud544\uc694\ud55c \uc720\ud615\uacfc \uc218\ub7c9\uc744 \ubcf4\uc874\ud560 \uc218 \uc788\ub2e4.<\/li>\n<li>\uc785\uccb4 \ud1a0\ud070 \ub300\uc2e0 \uc810\ud1a0 \ud45c\uba74\uc758 \uc778\uc0c1\uc774\ub098 \uae30\ud638\ub97c \uc0ac\uc6a9\ud558\uba74 \ud1a0\ud070 \uc790\uccb4\ub97c \ubcf4\uad00\ud558\uc9c0 \uc54a\uace0\ub3c4 \uc815\ubcf4\ub97c \uc804\ub2ec\ud560 \uc218 \uc788\ub2e4.<\/li>\n<li>\uc218\ub7c9 \uae30\ud638\uc640 \ubb3c\ud488 \uae30\ud638\ub97c \uc870\ud569\ud558\uba74 \ub3d9\uc77c\ud55c \uc218\ub7c9 \ud45c\uc0c1\uc744 \uc11c\ub85c \ub2e4\ub978 \ub300\uc0c1\uacfc \uacb0\ud569\ud560 \uc218 \uc788\ub2e4.<\/li>\n<\/ul>\n<p>\uc774 \ubcc0\ud654\ub4e4\uc744 \ucd94\ub3d9\ud55c \uc911\uc694\ud55c \ubc30\uacbd\uc5d0\ub294 \ucc3d\uace0 \uc7ac\uace0, \ubc30\uae09, \ub178\ub3d9\uacfc \uacc4\uc57d\uc744 \uad00\ub9ac\ud574\uc57c \ud588\ub358 \ud589\uc815\uc801 \ud544\uc694\uac00 \uc788\uc5c8\ub2e4. \uadf8\ub7ec\ubbc0\ub85c \uba54\uc18c\ud3ec\ud0c0\ubbf8\uc544 \uc790\ub8cc\ub294 \uc2e4\uc6a9\uc801 \uae30\ub85d \ud65c\ub3d9\uc774 \uc218 \ud45c\uc0c1\uc758 \uc77c\ubc18\ud654\ub97c \ucd09\uc9c4\ud55c \uac15\ub825\ud55c \uc0ac\ub840\ub2e4<a class=\"math-abs-series-ref\" title=\"Nissen, H. J., Damerow, P., &amp; Englund, R. K. (1993). Archaic Bookkeeping: Early Writing and Techniques of Economic Administration in the Ancient Near East (P. Larsen, Trans.). University of Chicago Press. Google Books.\" href=\"#ref-Nissen1993\">[Nissen1993]<\/a><a class=\"math-abs-series-ref\" title=\"Woods, C. (Ed.). (2010). Visible Language: Inventions of Writing in the Ancient Middle East and Beyond. Oriental Institute of the University of Chicago. Official PDF.\" href=\"#ref-Woods2010\">[Woods2010]<\/a>. <!-- \ub2e4\ub9cc \uc774\ub97c \u2018\uc778\ub958 \ucd5c\ucd08\uc758 \ucd94\uc0c1\ud654\u2019\ub77c\uace0 \ubd80\ub974\uac70\ub098, \uadf8 \uc774\uc804 \uc0ac\ub78c\ub4e4\uc774 \ucd94\uc0c1\uc801 \uc218\ub97c \uc804\ud600 \uac16\uc9c0 \uc54a\uc558\ub2e4\uace0 \ub9d0\ud558\ub294 \uac83\uc740 \ud604\uc7ac\uc758 \uc99d\uac70\ub97c \ub118\uc5b4\uc120\ub2e4<a class=\"math-abs-series-ref\" title=\"Overmann, K. A. (2018). Updating the \u201cabstract\u2013concrete\u201d distinction in ancient Near Eastern numbers. Cuneiform Digital Library Journal, 2018(1), 1\u201322.\" href=\"#ref-Overmann2018\">[Overmann2018]<\/a>. --><\/p>\n<h4>\uc808\ucc28\uc758 \uc218\ud559<\/h4>\n<p>\uace0\ub300 \uc774\uc9d1\ud2b8\uc640 \ubc14\ube4c\ub85c\ub2c8\uc544\uc758 \uc5ec\ub7ec \uc218\ud559 \ubb38\ud5cc\uc740 \ubb38\uc81c\uc640 \uc218\uce58, \uc218\ud589\ud560 \uacc4\uc0b0 \uc808\ucc28, \ub54c\ub85c\ub294 \uac80\uc0b0\uc744 \uc911\uc2ec\uc73c\ub85c \uad6c\uc131\ub418\uc5b4 \uc788\ub2e4. <!-- \uc774 \ubb38\ud5cc \uc591\uc2dd\uc744 \ud604\ub300\uc758 \uc815\uc758\u2013\uc815\ub9ac\u2013\uc99d\uba85 \ud615\uc2dd\uacfc \uad6c\ubd84\ud560 \uc218\ub294 \uc788\uc9c0\ub9cc, \u2018\uc2e4\uc6a9 \uc9c0\uce68\uc11c\u2019\ub77c\ub294 \uc774\uc720\ub9cc\uc73c\ub85c \uc774\ub860\uc801 \uc0ac\uace0\ub098 \uc815\ub2f9\ud654\uac00 \uc804\ud600 \uc5c6\uc5c8\ub2e4\uace0 \ub2e8\uc815\ud574\uc11c\ub294 \uc548 \ub41c\ub2e4. --> \ub0a8\uc740 \ubb38\uc11c\ub294 \ud2b9\uc815\ud55c \uc11c\uae30\uad00 \uad50\uc721\uacfc \uae30\ub85d \uc7a5\ub974\uac00 \ubb34\uc5c7\uc744 \uae00\ub85c \ub0a8\uacbc\ub294\uc9c0\ub97c \ubcf4\uc5ec\uc8fc\uae30 \ub54c\ubb38\uc774\ub2e4<a class=\"math-abs-series-ref\" title=\"Imhausen, A. (2016). Mathematics in Ancient Egypt: A Contextual History. Princeton University Press.\" href=\"#ref-Imhausen2016\">[Imhausen2016, Chs. 3\u20135]<\/a><a class=\"math-abs-series-ref\" title=\"H\u00f8yrup, J. (2002). Lengths, Widths, Surfaces: A Portrait of Old Babylonian Algebra and Its Kin. Springer.\" href=\"#ref-Hoyrup2002\">[H\u00f8yrup2002, Ch. 5]<\/a>.<\/p>\n<p>\ub9b0\ub4dc \uc218\ud559 \ud30c\ud53c\ub8e8\uc2a4(Rhind Mathematical Papyrus)\ub294 \ud604\uc7ac\uc758 \uc5f0\ub300 \ucd94\uc815\uc73c\ub85c \ub300\uccb4\ub85c \uae30\uc6d0\uc804 16\uc138\uae30 \uc911\uc5fd\uc5d0 \ud544\uc0ac\ub41c \ubb38\ud5cc\uc774\uba70, \uc11c\uae30\uad00 \uc544\uba54\uc2a4(Ahmes)\ub294 \ub354 \uc624\ub798\ub41c \uc790\ub8cc\ub97c \uc62e\uacbc\ub2e4\uace0 \uc801\uc5c8\ub2e4. \uc774 \ubb38\ud5cc\uc5d0\ub294 80\uc5ec \uac1c\uc758 \ubb38\uc81c\uac00 \uc218\ub85d\ub418\uc5b4 \uc788\ub2e4<a class=\"math-abs-series-ref\" title=\"Chace, A. B., Bull, L., Manning, H. P., &amp; Archibald, R. C. (1927). The Rhind Mathematical Papyrus: British Museum 10057 and 10058 (Vol. I). Mathematical Association of America. Public-domain PDF.\" href=\"#ref-Chace1927\">[Chace1927, pp. 19\u201321]<\/a><a class=\"math-abs-series-ref\" title=\"Imhausen, A. (2016). Mathematics in Ancient Egypt: A Contextual History. Princeton University Press.\" href=\"#ref-Imhausen2016\">[Imhausen2016, Ch. 4]<\/a>. \ubb38\uc81c 24\ub294 \u201c\uc5b4\ub5a4 \uc591\uacfc \uadf8 7\ubd84\uc758 1\uc744 \ub354\ud558\uba74 19\uac00 \ub41c\ub2e4\u201d\ub294 \ubb38\uc81c\ub2e4. \uc544\uba54\uc2a4\ub294 \uba3c\uc800 \uadf8 \uc591\uc744 7\uc774\ub77c\uace0 \uac00\uc815\ud574 \ud569 8\uc744 \uc5bb\uace0, 8\uacfc 19\uc758 \ube44\uc728\ub85c \uac00\uc815\uac12\uc744 \uc870\uc815\ud558\uc5ec \ub2f5 \\(16+\\frac12+\\frac18\\)\uc744 \uad6c\ud55c \ub4a4 \uacb0\uacfc\ub97c \ud655\uc778\ud55c\ub2e4<a class=\"math-abs-series-ref\" title=\"Chace, A. B., Bull, L., Manning, H. P., &amp; Archibald, R. C. (1927). The Rhind Mathematical Papyrus: British Museum 10057 and 10058 (Vol. I). Mathematical Association of America. Public-domain PDF.\" href=\"#ref-Chace1927\">[Chace1927, Problem 24]<\/a>. \ud604\ub300 \uc218\ud559\uc0ac\ub294 \uc774\ub7f0 \uc720\ud615\uc744 <span class=\"defined\">\uac70\uc9d3\uc704\uce58\ubc95<\/span>(false position; regula falsi)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4.<\/p>\n<p>\ud30c\ud53c\ub8e8\uc2a4\uc5d0\ub294 \\(x+x\/7=19\\)\uc758 \uc77c\ubc18\ud574\ub97c \ubb38\uc790\uc2dd\uc73c\ub85c \uc4f0\uac70\ub098 \uc808\ucc28\uc758 \ud0c0\ub2f9\uc131\uc744 \uc720\ud074\ub9ac\ub4dc\uc2dd \uc5f0\uc5ed \uc99d\uba85\uc73c\ub85c \uc81c\uc2dc\ud558\ub294 \ub300\ubaa9\uc740 \uc5c6\ub2e4. <!-- \uadf8\ub807\ub2e4\uace0 \u2018\uadfc\uac70 \uc5c6\uc774 \uae30\uacc4\uc801 \uba85\ub839\ub9cc \ub098\uc5f4\ud588\ub2e4\u2019\uace0 \ub9d0\ud558\uae30\ub3c4 \uc5b4\ub835\ub2e4. --> \uacc4\uc0b0\uc758 \uc120\ud0dd\uacfc \uac80\uc0b0\uc740 \ub2f5\uc774 \uc870\uac74\uc744 \ub9cc\uc871\ud568\uc744 \ubcf4\uc5ec\uc8fc\uba70, \uad6c\uccb4\uc801\uc778 \uc218\uce58 \uc0ac\ub840\ub294 \uc808\ucc28\ub97c \uac00\ub974\uce58\ub294 \uc5ed\ud560\uc744 \ud55c\ub2e4. <!-- \uc6b0\ub9ac\uac00 \ub9d0\ud560 \uc218 \uc788\ub294 \uac83\uc740 \uc77c\ubc18\uc131\uc774 \ud604\ub300\uc758 \uae30\ud638 \uacf5\uc2dd\uc774\ub098 \ubcc4\ub3c4\uc758 \uc99d\uba85 \ubb38\uc7a5\uc73c\ub85c \ud45c\ud604\ub418\uc9c0 \uc54a\uc558\ub2e4\ub294 \uc810\uc774\uc9c0, \uc11c\uae30\uad00\uc774 \ub2e4\ub978 \uc218\uce58\uc5d0\ub3c4 \ud1b5\ud558\ub294 \ubc29\ubc95\uc744 \ubab0\ub790\ub2e4\ub294 \uc810\uc774 \uc544\ub2c8\ub2e4. --><\/p>\n<p>\uace0\ubc14\ube4c\ub85c\ub2c8\uc544 \uc2dc\ub300\uc758 \uc810\ud1a0\ud310 BM 13901\uc740 \uc815\uc0ac\uac01\ud615\uc758 \ubcc0\uacfc \ub113\uc774\uc5d0 \uad00\ud55c 24\uac1c\uc758 \ubb38\uc81c\ub97c \uccb4\uacc4\uc801\uc73c\ub85c \ubcc0\uc8fc\ud55c\ub2e4. \uccab \ubc88\uc9f8 \ubb38\uc81c\ub294 \u201c\ub113\uc774\uc640 \ud55c \ubcc0\uc744 \ub354\ud558\uba74 \\(0;45\\)\u201d\uac00 \ub41c\ub2e4\ub294 \ub0b4\uc6a9\uc774\uba70, \ud604\ub300 \ubd84\uc218\ub85c\ub294 \\(\\frac34\\)\uc774\ub2e4<a class=\"math-abs-series-ref\" title=\"H\u00f8yrup, J. (2002). Lengths, Widths, Surfaces: A Portrait of Old Babylonian Algebra and Its Kin. Springer.\" href=\"#ref-Hoyrup2002\">[H\u00f8yrup2002, pp. 41\u201345]<\/a>. \ud55c \ubcc0\uc744 \\(x\\)\ub77c\uace0 \ub193\ub294 \ud604\ub300\uc2dd \ubc88\uc5ed\uc5d0\uc11c\ub294<br \/>\n\\[<br \/>\nx^2+x=\\frac34<br \/>\n\\]<br \/>\n\uc774\uc9c0\ub9cc, \uc6d0\ubb38\uc5d0\ub294 \ubb38\uc790 \\(x\\)\ub098 \ud604\ub300\uc801 \uc758\ubbf8\uc758 \ubc29\uc815\uc2dd\uc774 \uc5c6\ub2e4. \ub610\ud55c \ud604\ub300\uc2dd \\(x\\)\ud56d\uc5d0 \ud574\ub2f9\ud558\ub294 \uae38\uc774\ub294 \uc6d0\ubb38\uc758 \uc808\ucc28\uc5d0\uc11c \ud3ed\uc774 1\uc778 \uc9c1\uc0ac\uac01\ud615\uc73c\ub85c \ubc14\ub00c\uc5b4 \ub113\uc774\uc640 \uacb0\ud569\ub418\ubbc0\ub85c, \uc774 \uc2dd\uc740 \ucc28\uc6d0\uc774 \ub2e4\ub978 \uc591\uc744 \ubb34\uc2ec\ucf54 \ub354\ud55c \uc6d0\uc2dd\uc744 \uadf8\ub300\ub85c \uc62e\uae34 \uac83\uc774 \uc544\ub2c8\ub77c \uae30\ud558\uc801 \uc808\ucc28\ub97c \uc555\ucd95\ud55c \ubc88\uc5ed\uc774\ub2e4<a class=\"math-abs-series-ref\" title=\"H\u00f8yrup, J. (2002). Lengths, Widths, Surfaces: A Portrait of Old Babylonian Algebra and Its Kin. Springer.\" href=\"#ref-Hoyrup2002\">[H\u00f8yrup2002, pp. 41\u201345]<\/a>.<\/p>\n<p>[\uc6d0\ub798 \uc810\ud1a0\ud310\uc758 \uc218 \\(0;45\\)\ub294 60\uc9c4\ubc95\uc5d0\uc11c \\(45\/60=3\/4\\)\uc744 \ub73b\ud55c\ub2e4. \uc544\ub798\uc758 \ubd84\uc218\uc640 \ubc29\uc815\uc2dd\uc740 \ub3c5\uc790\ub97c \uc704\ud55c \ud604\ub300\uc2dd \ubc88\uc5ed\uc774\uba70, \uace0\ub300 \uc11c\uae30\uad00\uc774 \ub3d9\uc77c\ud55c \uae30\ud638 \ub300\uc218 \uccb4\uacc4\ub97c \uc0ac\uc6a9\ud588\ub2e4\ub294 \ub73b\uc774 \uc544\ub2c8\ub2e4<a class=\"math-abs-series-ref\" title=\"H\u00f8yrup, J. (2002). Lengths, Widths, Surfaces: A Portrait of Old Babylonian Algebra and Its Kin. Springer.\" href=\"#ref-Hoyrup2002\">[H\u00f8yrup2002, pp. 9\u201312, 41\u201345]<\/a>.]<\/p>\n<p>\uc808\ucc28\ub97c \ud604\ub300\uc5b4\ub85c \uc62e\uae30\uba74 \u201c1\uc744 \ubc18\uc73c\ub85c \ub098\ub204\uace0, \uadf8 \uc808\ubc18\uc744 \uc81c\uacf1\ud558\uc5ec \\(\\frac14\\)\uc744 \uc5bb\uace0, \uc774\ub97c \\(\\frac34\\)\uc5d0 \ub354\ud574 1\uc744 \ub9cc\ub4e0 \ub2e4\uc74c, \uadf8 \uc81c\uacf1\uadfc 1\uc5d0\uc11c \\(\\frac12\\)\uc744 \ube80\ub2e4\u201d\uac00 \ub41c\ub2e4. \ub530\ub77c\uc11c \ub2f5\uc740 \\(\\frac12\\)\uc774\ub2e4. \uae30\ud638\ub85c \uc555\ucd95\ud558\uba74<br \/>\n\\[<br \/>\nx=\\sqrt{\\left(\\frac12\\right)^2+\\frac34}-\\frac12<br \/>\n\\]<br \/>\n\uac00 \ub41c\ub2e4. \uc774\uac83\uc740 \ud604\ub300\uc758 \uc644\uc804\uc81c\uacf1\uc2dd \ub9cc\ub4e4\uae30\uc640 \ub300\uc751\ud558\uc9c0\ub9cc, \uc60c\uc2a4 \ud68c\uc774\ub8e8\ud504(Jens H\u00f8yrup)\uc758 \ubb38\ud5cc\ud559\uc801 \ubd84\uc11d\uc5d0 \ub530\ub974\uba74 \uc6d0\ubb38\uc758 \u2018\ubd99\uc774\uae30\u2019, \u2018\ub5bc\uc5b4\ub0b4\uae30\u2019, \u2018\ubd99\ub4e4\uac8c \ud558\uae30\u2019 \uac19\uc740 \uc5b4\ud718\ub294 \uc218\ub9cc \uae30\uacc4\uc801\uc73c\ub85c \ub300\uc785\ud55c \uacf5\uc2dd\ubcf4\ub2e4 \ub113\uc774\uc758 \uc808\ub2e8\uacfc \uc7ac\ubc30\uce58\ub97c \uc774\uc6a9\ud55c \uae30\ud558\uc801 \uc808\ucc28\ub85c \uc77d\ub294 \ud3b8\uc774 \ub0ab\ub2e4<a class=\"math-abs-series-ref\" title=\"H\u00f8yrup, J. (2002). Lengths, Widths, Surfaces: A Portrait of Old Babylonian Algebra and Its Kin. Springer.\" href=\"#ref-Hoyrup2002\">[H\u00f8yrup2002, Chs. 3, 5]<\/a>.<\/p>\n<p>BM 13901\uc5d0\ub294 \uacc4\uc218\ub9cc \ubc14\uafbc \ubb38\uc81c\uac00 \uc815\ud655\ud788 20\uac1c\uac00 \uc544\ub2c8\ub77c \ubaa8\ub450 24\uac1c \uc218\ub85d\ub418\uc5b4 \uc788\uc73c\uba70, \ub09c\ub3c4\uac00 \ub192\uc544\uc9c0\ub294 \ubcc0\ud615\ub4e4\uc774 \ubc30\uc5f4\ub418\uc5b4 \uc788\ub2e4. \uba85\uc2dc\uc801\uc778 \uc77c\ubc18\uc2dd \\(x^2+bx=c\\)\ub294 \uc5c6\uc9c0\ub9cc, \ubb38\uc81c\uad70\uc758 \uccb4\uacc4\uc801\uc778 \ubcc0\uc8fc\uc640 \uacf5\ud1b5\ub41c \uc870\uc791 \uc5b4\ud718\ub294 \uac1c\ubcc4 \ub2f5\uc744 \ub118\uc5b4\uc120 \ubc29\ubc95\uc774 \uad50\uc721\ub418\uc5c8\uc74c\uc744 \ubcf4\uc5ec\uc900\ub2e4. \uc77c\ubc18\uc131\uc740 \ubb38\uc790 \uacf5\uc2dd \ud558\ub098\ub85c \uc120\uc5b8\ub418\uae30\ubcf4\ub2e4 \uc608\uc81c\uc758 \ubc30\uc5f4\uacfc \ubc18\ubcf5 \uac00\ub2a5\ud55c \uc808\ucc28\uc5d0 \ub2f4\uaca8 \uc788\uc5c8\ub2e4. <!-- \uc774 \ud615\uc2dd\uc740 \uc815\uc758\uc640 \uacf5\ub9ac\uc5d0\uc11c \uba85\uc81c\ub97c \uc5f0\uc5ed\ud558\ub294 \uadf8\ub9ac\uc2a4\uc758 \ubb38\ud5cc \ud615\uc2dd\uacfc \ub2e4\ub974\uc9c0\ub9cc, \ucc28\uc774\ub97c \uace7 \u2018\uc0ac\uace0 \ub300 \ubb34\uc0ac\uace0\u2019 \ub610\ub294 \u2018\uc99d\uba85 \ub300 \ub9f9\ubaa9\uc801 \uacc4\uc0b0\u2019\uc758 \ub300\ub9bd\uc73c\ub85c \ubc14\uafb8\uc5b4\uc11c\ub294 \uc548 \ub41c\ub2e4<a class=\"math-abs-series-ref\" title=\"H\u00f8yrup, J. (2002). Lengths, Widths, Surfaces: A Portrait of Old Babylonian Algebra and Its Kin. Springer.\" href=\"#ref-Hoyrup2002\">[H\u00f8yrup2002, pp. 110\u2013118]<\/a>. --><\/p>\n<h4>\uc99d\uba85\uc774 \uc694\uad6c\ud55c \ucd94\uc0c1\ud654<\/h4>\n<p>\uae30\uc6d0\uc804 5\u20134\uc138\uae30\uc758 \uadf8\ub9ac\uc2a4 \uc218\ud559\uc5d0\uc11c\ub294 \ubb38\uc790\ub85c \ub3c4\ud615\uc758 \ubd80\ubd84\uc744 \uc9c0\uc2dc\ud558\uace0, \uc815\ud615\ud654\ub41c \uc5b8\uc5b4\ub85c \uc77c\ubc18 \uba85\uc81c\ub97c \uc9c4\uc220\ud558\uba70, \uc120\ud589 \uacb0\uacfc\uc5d0\uc11c \uacb0\ub860\uc744 \uc5f0\uc5ed\ud558\ub294 \uad00\ud589\uc774 \ubc1c\ub2ec\ud588\ub2e4. \uadf8 \uacfc\uc815\uc758 \ucd08\uae30 \uc5ed\uc0ac\ub294 \ub2e8\ud3b8\uc801\uc778 \ud6c4\ub300 \uc790\ub8cc\uc5d0 \uc758\uc874\ud558\ubbc0\ub85c \uc5b4\ub290 \ud55c \uc0ac\ub78c\uc758 \u2018\ud601\uba85\u2019\uc73c\ub85c \ub2e8\uc21c\ud654\ud558\uae30 \uc5b4\ub835\ub2e4<a class=\"math-abs-series-ref\" title=\"Netz, R. (1999). The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History. Cambridge University Press.\" href=\"#ref-Netz1999\">[Netz1999, Chs. 1\u20132]<\/a>. \uae30\uc6d0\uc804 300\ub144 \ubb34\ub835 \ud3b8\ucc2c\ub41c \uac83\uc73c\ub85c \uc5ec\uaca8\uc9c0\ub294 \uc720\ud074\ub9ac\ub4dc\uc758 \u201c\uc6d0\ub860\u201d\uc740 \uc815\uc758, \uacf5\uc900, \uacf5\ud1b5 \uad00\ub150\uc744 \uc81c\uc2dc\ud558\uace0 \uba85\uc81c\uc640 \uc99d\uba85\uc744 \uc870\uc9c1\ud55c \uc774 \uc804\ud1b5\uc758 \uac00\uc7a5 \uc601\ud5a5\ub825 \uc788\ub294 \ud604\uc874 \uc0ac\ub840\ub2e4<a class=\"math-abs-series-ref\" title=\"Euclid. (2008). Euclid's Elements of Geometry (R. Fitzpatrick, Trans.).\" href=\"#ref-Euclid2008\">[Euclid2008, Book I]<\/a>.<\/p>\n<p>[\ud6c4\ub300 \uc804\uc2b9\uc740 \ub17c\uc99d\uc801 \uae30\ud558\ud559\uc758 \ucd08\uae30 \uc778\ubb3c\ub85c \ud0c8\ub808\uc2a4(Thales)\ub97c \uc9c0\ubaa9\ud55c\ub2e4. \uc6d0\uc758 \uc9c0\ub984\uc774 \uc6d0\uc744 \uc774\ub4f1\ubd84\ud55c\ub2e4\ub294 \uc0ac\uc2e4 \ub4f1\uc744 \uadf8\uac00 \uc99d\uba85\ud588\ub2e4\ub294 \uc774\uc57c\uae30\ub294 \uc8fc\ub85c \uae30\uc6d0\ud6c4 5\uc138\uae30\uc758 \uc8fc\uc11d\uac00 \ud504\ub85c\ud074\ub85c\uc2a4(Proclus)\uac00 \uc804\ud55c \ub354 \uc624\ub798\ub41c \uc790\ub8cc\uc5d0 \uc758\uc874\ud55c\ub2e4. \ud0c8\ub808\uc2a4 \uc790\uc2e0\uc758 \uc218\ud559 \uc800\uc220\uc774 \ub0a8\uc544 \uc788\uc9c0 \uc54a\uc73c\ubbc0\ub85c, \uc774 \uc804\uc2b9\uc744 \uc9c1\uc811 \uc0ac\ub8cc\uc640 \uac19\uc740 \ud655\uc2e4\uc131\uc73c\ub85c \ub2e4\ub8f0 \uc218\ub294 \uc5c6\ub2e4<a class=\"math-abs-series-ref\" title=\"Heath, T. L. (1921). A History of Greek Mathematics (Vol. I). Clarendon Press. Reissued by Cambridge University Press. Chapter on Thales.\" href=\"#ref-Heath1921\">[Heath1921, Vol. I, Ch. 4]<\/a>.]<\/p>\n<p>\ubcf4\ud3b8\uc801\uc778 \uba85\uc81c\ub97c \ud558\ub098\uc758 \ubb38\uc790 \ub3c4\ud615\uc73c\ub85c \uc99d\uba85\ud558\ub824\uba74, \uadf8\ub9bc\uc758 \uc5b4\ub5a4 \ud2b9\uc9d5\uc774 \ub17c\uc99d\uc5d0 \ud544\uc694\ud558\uace0 \uc5b4\ub5a4 \ud2b9\uc9d5\uc774 \uc6b0\uc5f0\ud55c\uc9c0\ub97c \ud1b5\uc81c\ud574\uc57c \ud55c\ub2e4. \uc608\ucee8\ub300 \uc784\uc758\uc758 \uc0bc\uac01\ud615\uc5d0 \uad00\ud55c \uc815\ub9ac\ub97c \uc99d\uba85\ud558\uba74\uc11c \ub208\uc55e\uc758 \uc0bc\uac01\ud615\uc774 \uc6b0\uc5f0\ud788 \uc608\uac01\uc0bc\uac01\ud615\uc774\ub77c\ub294 \uc0ac\uc2e4, \uad6c\uccb4\uc801\uc778 \ubcc0\uc758 \uae38\uc774, \uc885\uc774 \uc704 \ubc29\ud5a5\uc744 \uadfc\uac70\ub85c \uc0ac\uc6a9\ud560 \uc218\ub294 \uc5c6\ub2e4. \ub808\ube44\uc5d8 \ub124\uce20(Reviel Netz)\uc758 \ubd84\uc11d\uc5d0 \ub530\ub974\uba74 \ubb38\uc790 \ud45c\uc9c0, \uc815\ud615\ud654\ub41c \uc5b8\uc5b4, \ub3c4\ud574\ub294 \uadf8\ub9ac\uc2a4 \uc218\ud559\uc758 \uc77c\ubc18\uc801\uc778 \uc5f0\uc5ed\uc744 \ud568\uaed8 \uac00\ub2a5\ud558\uac8c \ud55c \uc778\uc9c0\uc801 \ub3c4\uad6c\uc600\ub2e4<a class=\"math-abs-series-ref\" title=\"Netz, R. (1999). The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History. Cambridge University Press.\" href=\"#ref-Netz1999\">[Netz1999, Chs. 1, 3]<\/a>. \uc774\ub7f0 \uc758\ubbf8\uc5d0\uc11c \uc99d\uba85\uc740 \ubb34\uc5c7\uc744 \ubcf4\uc874\ud558\uace0 \ubb34\uc5c7\uc744 \ubb34\uc2dc\ud560\uc9c0 \uc9c0\uc18d\uc801\uc73c\ub85c \uad00\ub9ac\ud558\ub294 \ucd94\uc0c1\ud654\uc758 \uc2e4\ucc9c\uc774\ub2e4. <!-- \ub2e4\ub9cc \uc99d\uba85\uc774 \uc5ed\uc0ac\uc801\uc73c\ub85c \ucd94\uc0c1\ud654\ub97c \u2018\ud544\uc5f0\uc801\uc73c\ub85c \ubc1c\uba85\ud588\ub2e4\u2019\ub294 \uc778\uacfc \uba85\uc81c\ub77c\uae30\ubcf4\ub2e4, \uc774 \uae00\uc774 \uc99d\uba85 \uad00\ud589\uc744 \ud574\uc11d\ud558\ub294 \ud558\ub098\uc758 \uad00\uc810\uc774\ub77c\uace0 \ud574\uc57c \uc815\ud655\ud558\ub2e4. --><\/p>\n<p>[\ud2b9\uc218\ud55c \uc131\uc9c8\uc744 \uc0ac\uc6a9\ud558\uc9c0 \uc54a\uace0 \uc784\uc758\ub85c \ud0dd\ud55c \ub300\uc0c1\uc5d0 \ub300\ud574 \ub17c\uc99d\ud55c \ub4a4 \uc77c\ubc18 \uacb0\ub860\uc744 \uc5bb\ub294 \ubaa8\uc2b5\uc744 \ud604\ub300 \ub17c\ub9ac\ud559\uc758 <span class=\"defined\">\ubcf4\ud3b8 \uc77c\ubc18\ud654<\/span>(universal generalization; \ubcf4\ud3b8\ud654 \uaddc\uce59)\uc640 \ube44\uad50\ud560 \uc218 \uc788\ub2e4. \uadf8\ub7ec\ub098 \uc720\ud074\ub9ac\ub4dc\uc758 \ub17c\uc99d\uc744 \ud604\ub300 \uc220\uc5b4\ub17c\ub9ac\uc758 \ud615\uc2dd \uaddc\uce59\uc744 \uadf8\ub300\ub85c \uc801\uc6a9\ud55c \uac83\uc73c\ub85c \ub3d9\uc77c\uc2dc\ud574\uc11c\ub294 \uc548 \ub41c\ub2e4. \uc774 \ub300\uad04\ud638 \uc548\uc758 \uc124\uba85\uc740 \ud604\ub300\uc801 \ub300\uc751 \uad00\uacc4\uc774\uc9c0 \uace0\ub300 \uc6a9\uc5b4\uc758 \ubc88\uc5ed\uc774 \uc544\ub2c8\ub2e4.]<\/p>\n<p>\u201c\uc6d0\ub860\u201d 1\uad8c\uc758 \uc815\uc758 1\uc740 \uc810\uc744 \u201c\ubd80\ubd84\uc774 \uc5c6\ub294 \uac83\u201d, \uc815\uc758 2\ub294 \uc120\uc744 \u201c\ud3ed \uc5c6\ub294 \uae38\uc774\u201d\ub77c\uace0 \ub9d0\ud55c\ub2e4<a class=\"math-abs-series-ref\" title=\"Euclid. (2008). Euclid's Elements of Geometry (R. Fitzpatrick, Trans.).\" href=\"#ref-Euclid2008\">[Euclid2008, Book I, Definitions 1\u20132]<\/a>. \uc774 \uc815\uc758\ub4e4\uc774 \ud6c4\uc18d \uc99d\uba85\uc5d0\uc11c \uba85\uc2dc\uc801 \uc804\uc81c\ub85c \uc790\uc8fc \uc778\uc6a9\ub418\uac70\ub098 \uc810\uacfc \uc120\uc758 \uc874\uc7ac\ub97c \ubcf4\uc7a5\ud558\ub294 \uc791\ub3c4 \uaddc\uce59\uc73c\ub85c \uc0ac\uc6a9\ub418\ub294 \uac83\uc740 \uc544\ub2c8\uc9c0\ub9cc, \uadf8\ub798\uc11c \uc544\ubb34 \uc5ed\ud560\ub3c4 \ud558\uc9c0 \uc54a\ub294\ub2e4\uace0 \ub2e8\uc815\ud560 \uc218\ub294 \uc5c6\ub2e4<a class=\"math-abs-series-ref\" title=\"Beeson, M., Narboux, J., &amp; Wiedijk, F. (2019). Proof-checking Euclid. Annals of Mathematics and Artificial Intelligence, 85(2\u20134), 213\u2013257.\" href=\"#ref-BeesonEtAl2019\">[Beeson, Narboux, &amp; Wiedijk 2019, pp. 213\u2013220]<\/a>. \uadf8\uac83\ub4e4\uc740 \ub17c\uc758 \ub300\uc0c1\uc758 \uacbd\uacc4\ub97c \uc138\uc6b0\uace0 \uae30\ud558\ud559\uc801 \ub2f4\ub860\uc758 \uc5b4\ud718\ub97c \uc81c\uacf5\ud55c\ub2e4. \uc774 \uae00\uc758 \ucd94\uc0c1\ud654 \uad00\uc810\uc5d0\uc11c\ub294 \uc774\ub97c \ud604\uc2e4\uc758 \uc810\uacfc \uc120\uc5d0\uc11c \uba74\uc801, \ud3ed \uac19\uc740 \ubb3c\uc9c8\uc801 \uc131\uc9c8\uc744 \uace0\ub824\ud558\uc9c0 \ub9d0\ub77c\ub294 \uc77c\uc885\uc758 \u2018\ucd94\uc0c1\ud654 \uc120\uc5b8\u2019\uc73c\ub85c \uc77d\uc744 \uc218 \uc788\ub2e4. <!-- \ub2e4\ub9cc \uc774\uac83\uc740 \uac00\ub2a5\ud55c \ucca0\ud559\uc801 \ub3c5\ud574\uc774\uc9c0, \uc720\ud074\ub9ac\ub4dc\uac00 \uc9c1\uc811 \ubc1d\ud78c \ud3b8\ucc2c \uc758\ub3c4\ub098 \ud559\uacc4\uc758 \uc720\uc77c\ud55c \ud574\uc11d\uc740 \uc544\ub2c8\ub2e4. --><\/p>\n<p>\uc815\uc758\uc640 \uacf5\uc900\uc758 \ubaa9\ub85d\uc740 \ub9e4\uc6b0 \uc601\ud5a5\ub825 \uc788\uc5c8\uc9c0\ub9cc, \uc624\ub298\ub0a0\uc758 \ud615\uc2dd \uacf5\ub9ac\uacc4\ucc98\ub7fc \ubaa8\ub4e0 \ud5c8\uc6a9 \ucd94\ub860\uc744 \ube60\uc9d0\uc5c6\uc774 \uba85\ubb38\ud654\ud55c \ubaa9\ub85d\uc740 \uc544\ub2c8\uc5c8\ub2e4. \uadf8 \uc0ac\uc2e4\uc740 \u201c\uc6d0\ub860\u201d 1\uad8c \uba85\uc81c 1\uc744 \ud604\ub300\uc801 \uae30\uc900\uc73c\ub85c \ubd84\uc11d\ud560 \ub54c \uace7\ubc14\ub85c \ub4dc\ub7ec\ub09c\ub2e4.<\/p>\n<h4>\u201c\uc6d0\ub860\u201d 1\uad8c \uba85\uc81c 1<\/h4>\n<p>\uba85\uc81c 1\uc758 \ub0b4\uc6a9\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\n<p style=\"text-align: center\">\u201c\uc8fc\uc5b4\uc9c4 \uc120\ubd84 \uc704\uc5d0 \uc815\uc0bc\uac01\ud615\uc744 \uc791\ub3c4\ud558\ub77c.\u201d<\/p>\n<p>\uc120\ubd84\uc758 \ub450 \ub05d\uc810\uc744 \\(A,\\) \\(B\\)\ub77c\uace0 \ud558\uc790. \uc720\ud074\ub9ac\ub4dc\ub294 \\(A\\)\ub97c \uc911\uc2ec\uc73c\ub85c \ubc18\uc9c0\ub984 \\(AB\\)\uc778 \uc6d0\uc744 \uadf8\ub9ac\uace0, \\(B\\)\ub97c \uc911\uc2ec\uc73c\ub85c \ubc18\uc9c0\ub984 \\(BA\\)\uc778 \uc6d0\uc744 \uadf8\ub9b0\ub2e4. \ub450 \uc6d0\uc758 \uad50\uc810\uc744 \\(C\\)\ub85c \uc7a1\uc544 \\(CA\\)\uc640 \\(CB\\)\ub97c \uc787\ub294\ub2e4. \\(AC=AB\\)\uc640 \\(BC=BA\\)\ub294 \uac01\uac01 \uac19\uc740 \uc6d0\uc758 \ubc18\uc9c0\ub984\uc774\ub77c\ub294 \uc0ac\uc2e4\uc5d0\uc11c \ub098\uc624\uba70, \uacf5\ud1b5 \uad00\ub150 1\uc744 \uc801\uc6a9\ud558\uba74 \uc138 \ubcc0\uc774 \ubaa8\ub450 \uac19\uc73c\ubbc0\ub85c \\(ABC\\)\ub294 \uc815\uc0bc\uac01\ud615\uc774\ub2e4<a class=\"math-abs-series-ref\" title=\"Euclid. (2008). Euclid's Elements of Geometry (R. Fitzpatrick, Trans.).\" href=\"#ref-Euclid2008\">[Euclid2008, Book I, Proposition 1]<\/a>.<\/p>\n<p>\ud604\ub300 \uacf5\ub9ac\ub860\uc758 \uad00\uc810\uc5d0\uc11c \ubb38\uc81c\ub294 \u201c\ub450 \uc6d0\uc758 \uad50\uc810\uc744 \\(C\\)\ub85c \uc7a1\ub294\ub2e4\u201d\ub294 \ub2e8\uacc4\ub2e4. \uacf5\uc900 3\uc740 \uc8fc\uc5b4\uc9c4 \uc911\uc2ec\uacfc \ubc18\uc9c0\ub984\uc73c\ub85c \uc6d0\uc744 \uadf8\ub9b4 \uc218 \uc788\uac8c \ud558\uc9c0\ub9cc, \uc81c\uc2dc\ub41c \uc870\uac74\uc758 \ub450 \uc6d0\uc774 \ubc18\ub4dc\uc2dc \ub9cc\ub09c\ub2e4\ub294 \ubcc4\ub3c4\uc758 \uc6d0\ub9ac\ub294 \u201c\uc6d0\ub860\u201d \uc11c\ub450\uc5d0 \uba85\uc2dc\ub418\uc5b4 \uc788\uc9c0 \uc54a\ub2e4. \uc624\ub298\ub0a0\uc5d0\ub294 \uc774\ub97c \uc6d0\u2013\uc6d0 \uad50\uc810 \uacf5\ub9ac \ub610\ub294 \uadf8\uac83\uc744 \ud568\ucd95\ud558\ub294 \ucda9\ubd84\ud55c \uc5f0\uc18d\uc131 \uc6d0\ub9ac\ub85c \ubcf4\uc644\ud560 \uc218 \uc788\ub2e4<a class=\"math-abs-series-ref\" title=\"De Risi, V. (2021). Gapless lines and gapless proofs: Intersections and continuity in Euclid's Elements. Apeiron, 54(2), 233\u2013259.\" href=\"#ref-DeRisi2021\">[DeRisi2021, pp. 233\u2013241]<\/a><a class=\"math-abs-series-ref\" title=\"Beeson, M., Narboux, J., &amp; Wiedijk, F. (2019). Proof-checking Euclid. Annals of Mathematics and Artificial Intelligence, 85(2\u20134), 213\u2013257.\" href=\"#ref-BeesonEtAl2019\">[Beeson, Narboux, &amp; Wiedijk 2019, pp. 214\u2013215]<\/a>.<\/p>\n<p>\uc65c \ucd94\uac00 \uc870\uac74\uc774 \ud544\uc694\ud55c\uc9c0 \uc88c\ud45c\ub97c \uc774\uc6a9\ud55c \ud604\ub300\uc801 \uc608\ub85c \ud655\uc778\ud574 \ubcf4\uc790. \uc88c\ud45c\uac00 \ubaa8\ub450 \uc720\ub9ac\uc218\uc778 \uc810\ub9cc \ud5c8\uc6a9\ud558\ub294 \\(\\mathbb Q\\times\\mathbb Q\\)\uc5d0\uc11c \\(A=(0,0)\\), \\(B=(1,0)\\)\uc744 \ud0dd\ud558\uba74 \ub450 \uc6d0\uc758 \ubc29\uc815\uc2dd\uc740<br \/>\n\\[<br \/>\nx^2+y^2=1,\\quad (x-1)^2+y^2=1<br \/>\n\\]<br \/>\n\uc774\ub2e4. \ub450 \uc2dd\uc744 \ube7c\uba74 \\(x=\\frac12\\)\uc774\uace0, \uc774\ub97c \ub300\uc785\ud558\uba74 \\(y=\\pm\\frac{\\sqrt3}{2}\\)\uc774\ub2e4. \uc774 \\(y\\)\uc88c\ud45c\ub294 \uc720\ub9ac\uc218\uac00 \uc544\ub2c8\ubbc0\ub85c \ud5c8\uc6a9\ub41c \uc810 \uc9d1\ud569 \uc548\uc5d0\ub294 \uad50\uc810\uc774 \uc5c6\ub2e4. \uc774 \uc608\ub294 \uc6d0\uc758 \ubc29\uc815\uc2dd\uacfc \ub450 \uc911\uc2ec, \ubc18\uc9c0\ub984 \uc815\ubcf4\ub9cc\uc73c\ub85c\ub294 \ud5c8\uc6a9\ub41c \uc810 \uc9d1\ud569 \uc548\uc758 \uad50\uc810 \uc874\uc7ac\uac00 \ubcf4\uc7a5\ub418\uc9c0 \uc54a\uc74c\uc744 \uc9c1\uad00\uc801\uc73c\ub85c \ubcf4\uc5ec\uc900\ub2e4.<\/p>\n<p>\uc774\ub97c \uc774 \uae00\uc758 \uc5b8\uc5b4\ub85c \ud45c\ud604\ud558\uba74, \uc720\ud074\ub9ac\ub4dc\uc758 \ub17c\uc99d\uc740 \uc120\ubd84\uc758 \uad6c\uccb4\uc801\uc778 \uae38\uc774, \uc704\uce58, \ubc29\ud5a5, \uc120\uc758 \uad75\uae30\uc5d0\ub294 \uc758\uc874\ud558\uc9c0 \uc54a\uc9c0\ub9cc, \uadf8\ub824\uc9c4 \ub450 \uc6d0\uc774 \ubcf4\uc774\ub294 \ub300\ub85c \ub9cc\ub09c\ub2e4\ub294 \uad00\uacc4\ub294 \uc0ac\uc6a9\ud55c\ub2e4. \ud604\ub300 \uc218\ud559\uc790\ub294 \uc774\ub97c \uad50\uc810 \uc874\uc7ac \ub610\ub294 \uc5f0\uc18d\uc131 \uacc4\uc5f4\uc758 \uac00\uc815\uc73c\ub85c \uba85\ubb38\ud654\ud55c\ub2e4. \uadf8\ub7ec\ub098 \ube48\uccb8\ucd08 \ub370 \ub9ac\uc2dc(Vincenzo De Risi)\ub294 \uace0\ub300 \uae30\ud558\ud559\uc790\uac00 \uc774 \ucd94\ub860\uc744 \ud604\ub300\uc801 \u2018\uacf5\uac04\uc758 \uc5f0\uc18d\uc131\u2019 \uac1c\ub150\uc73c\ub85c \uc815\ub2f9\ud654\ud588\ub2e4\uace0 \ubcf4\ub294 \uac83\uc740 \uc2dc\ub300\ucc29\uc624\uc801\uc774\ub77c\uace0 \uc9c0\uc801\ud55c\ub2e4. \uace0\ub300\uc758 \ub3c4\ud574 \uad00\ud589\uc5d0\uc11c\ub294 \uc120\ub4e4\uc774 \uadf8\ub9bc\uc5d0\uc11c \uad50\ucc28\ud558\ub294 \uac83\ucc98\ub7fc \uc81c\uc2dc\ub41c \uacbd\uc6b0 \uadf8 \uad50\uc810\uc744 \ucde8\ud558\ub294 \uac83\uc774 \ud5c8\uc6a9\ub41c \ucd94\ub860\uc774\uc5c8\ub2e4\ub294 \uac83\uc774\ub2e4<a class=\"math-abs-series-ref\" title=\"De Risi, V. (2021). Gapless lines and gapless proofs: Intersections and continuity in Euclid's Elements. Apeiron, 54(2), 233\u2013259.\" href=\"#ref-DeRisi2021\">[DeRisi2021, pp. 241\u2013259]<\/a>.<\/p>\n<p><a href=\"..\/math-abstraction-01-essence\/\">1\ubd80<\/a>\uc5d0\uc11c \uc218\ud559\uc801 \ucd94\uc0c1\ud654\uc758 \uc5c4\ubc00\uc131\uc740 \ubb34\uc5c7\uc744 \uace0\ub824\ud558\uace0 \ubb34\uc5c7\uc744 \uc81c\uc678\ud560\uc9c0\ub97c \uba85\uc2dc\ud558\ub294 \ub370\uc11c \ub098\uc628\ub2e4\uace0 \ub9d0\ud588\ub2e4. \uba85\uc81c 1\uc740 \uadf8 \ubaa9\ub85d\uc758 \uc5ed\uc0ac\uc801 \uae30\uc900\uc774 \uace0\uc815\ub418\uc5b4 \uc788\uc9c0 \uc54a\uc558\uc74c\uc744 \ubcf4\uc5ec\uc900\ub2e4. 19\uc138\uae30\uc5d0\ub294 \ud30c\uc288\uac00 \uc21c\uc11c\uc640 \uad50\ucc28\uc5d0 \uad00\ud55c \uc554\ubb35\uc801 \uac00\uc815\ub4e4\uc744 \uc804\uba74\uc801\uc73c\ub85c \ubd84\uc11d\ud588\uace0, \ud790\ubca0\ub974\ud2b8\ub294 \uacb0\ud569, \uc21c\uc11c, \ud569\ub3d9, \ud3c9\ud589, \uc5f0\uc18d\uc131 \uacf5\ub9ac\ub4e4\uc744 \uccb4\uacc4\uc801\uc73c\ub85c \uc7ac\uad6c\uc131\ud588\ub2e4<a class=\"math-abs-series-ref\" title=\"Pasch, M. (1882). Vorlesungen \u00fcber neuere Geometrie. B. G. Teubner. Internet Archive.\" href=\"#ref-Pasch1882\">[Pasch1882]<\/a><a class=\"math-abs-series-ref\" title=\"Hilbert, D. (1902). The Foundations of Geometry (E. J. Townsend, Trans.). Open Court. (Original work published 1899.) Digital edition.\" href=\"#ref-Hilbert1902\">[Hilbert1902]<\/a>. \uc624\ub298\ub0a0\uc5d0\ub294 \ud544\uc694\ud55c \uc6d0\u2013\uc6d0 \uad50\uc810 \uc870\uac74\uc744 \uc9c1\uc811 \uacf5\ub9ac\ub85c \ub458 \uc218\ub3c4 \uc788\uace0, \ub354 \uac15\ud55c \uc5f0\uc18d\uc131, \uc644\ube44\uc131 \uc870\uac74\uc5d0\uc11c \uc720\ub3c4\ud560 \uc218\ub3c4 \uc788\ub2e4.<\/p>\n<p>[1882\ub144 \ud30c\uc288(Moritz Pasch)\uc758 \u300e<i>Vorlesungen \u00fcber neuere Geometrie<\/i>\u300f\ub294 \uae30\ud558\ud559\uc758 \uc21c\uc11c, \uad50\ucc28 \ucd94\ub860\uc5d0 \uc228\uc5b4 \uc788\ub358 \uc804\uc81c\ub97c \uc5c4\ubc00\ud558\uac8c \ubd84\uc11d\ud55c \uc804\ud658\uc810\uc774\uba70, 1899\ub144 \ud790\ubca0\ub974\ud2b8(David Hilbert)\uc758 \u300e<i>Grundlagen der Geometrie<\/i>\u300f\ub294 \uc720\ud074\ub9ac\ub4dc \uae30\ud558\ud559\uc758 \uacf5\ub9ac\uc801 \uc7ac\uad6c\uc131\uc744 \ud06c\uac8c \uc9c4\uc804\uc2dc\ucf30\ub2e4. \ub2e4\ub9cc \ud30c\uc288\uac00 \ubc14\ub85c \uba85\uc81c 1\uc758 \uc6d0\u2013\uc6d0 \uad50\uc810 \ubb38\uc81c\ub97c \u2018\ucd5c\ucd08\ub85c\u2019 \uc9c0\uc801\ud588\uace0 \ud790\ubca0\ub974\ud2b8\uc758 \ucd08\ud310\uc774 \uc624\ub298\ub0a0 \uac00\ub2a5\ud55c \uc720\uc77c\ud55c \u2018\uc644\ube44\u2019 \uccb4\uacc4\ub97c \uc644\uc131\ud588\ub2e4\uace0 \uc555\ucd95\ud558\uba74 \uacfc\ub3c4\ud558\ub2e4. \uad50\uc810 \ubb38\uc81c\uc758 \ub354 \uae34 \uc5ed\uc0ac\uc640 \uc5ec\ub7ec \ud604\ub300\uc801 \ubcf4\uc644 \ubc29\uc2dd\uc740 \ub370 \ub9ac\uc2dc\uc758 \uc5f0\uad6c\ub97c \ucc38\uc870\ud560 \uc218 \uc788\ub2e4<a class=\"math-abs-series-ref\" title=\"De Risi, V. (2021). Gapless lines and gapless proofs: Intersections and continuity in Euclid's Elements. Apeiron, 54(2), 233\u2013259.\" href=\"#ref-DeRisi2021\">[DeRisi2021]<\/a>.]<\/p>\n<p><!-- \uc774 \ubd84\uc11d\uc740 \uc720\ud074\ub9ac\ub4dc\uc758 \ubd80\uc8fc\uc758\ub97c \uc870\ub871\ud558\uae30 \uc704\ud55c \uac83\uc774 \uc544\ub2c8\ub2e4. -->\uace0\ub300 \uadf8\ub9ac\uc2a4\uc758 \uc99d\uba85\uc5d0\uc11c \ub3c4\ud574\ub294 \ub2e8\uc21c\ud55c \uc7a5\uc2dd\uc774 \uc544\ub2c8\ub77c \ud1b5\uc81c\ub41c \uc815\ubcf4\uc6d0\uc774\uc5c8\ub2e4. \ucf00\ub124\uc2a4 \ub9e8\ub354\uc2a4(Kenneth Manders)\ub294 \uae38\uc774\uc758 \uc815\ud655\ud55c \uac19\uc74c\uc774\ub098 \ube44\ub840 \uac19\uc740 <i>exact<\/i> \uc815\ubcf4\ub294 \uba85\uc2dc\ub41c \ub17c\uc99d\uc5d0\uc11c \uc5bb\ub294 \ubc18\uba74, \uad50\ucc28, \ud3ec\ud568, \uc778\uc811 \uac19\uc740 \uadf8\ub9bc\uc758 \uc791\uc740 \ubcc0\ud615\uc5d0\ub3c4 \uc548\uc815\uc801\uc778 <i>co-exact<\/i> \uc815\ubcf4\ub294 \ub3c4\ud574\uc5d0\uc11c \uc77d\uc5b4\ub0bc \uc218 \uc788\uc5c8\ub2e4\uace0 \ubd84\uc11d\ud55c\ub2e4<a class=\"math-abs-series-ref\" title=\"Manders, K. (2008). The Euclidean diagram. In P. Mancosu (Ed.), The Philosophy of Mathematical Practice (pp. 80\u2013133). Oxford University Press.\" href=\"#ref-Manders2008\">[Manders2008, pp. 80\u2013133]<\/a>.<\/p>\n<p>[\uacfc\ud559\uc0ac\uc640 \uc218\ud559\ucca0\ud559 \uc5f0\uad6c\uc5d0 \ub530\ub974\uba74 \uace0\ub300 \uadf8\ub9ac\uc2a4 \uae30\ud558\ud559\uc5d0\uc11c \uadf8\ub9bc\uc740 \ub17c\uc99d\uc758 \uc815\ub2f9\ud55c \uc77c\ubd80\uc600\ub2e4. \ud2b9\ud788 \uad50\ucc28\ub098 \uc601\uc5ed\uc758 \ud3ec\ud568 \uad00\uacc4\ucc98\ub7fc \uadf8\ub9bc\uc744 \uc870\uae08 \ubcc0\ud615\ud574\ub3c4 \uc720\uc9c0\ub418\ub294 \uad00\uacc4\ub294 \ub3c4\ud574\ub85c\ubd80\ud130 \uc77d\ub418, \uc815\ud655\ud55c \uae38\uc774\uc758 \uac19\uc74c\uc774\ub098 \uac01\uc758 \ud06c\uae30\ub294 \uadf8\ub9bc\uc758 \uc678\uad00\ub9cc\uc73c\ub85c \ucd94\ub860\ud558\uc9c0 \uc54a\ub294 \uaddc\uc728\uc774 \uc791\ub3d9\ud588\ub2e4<a class=\"math-abs-series-ref\" title=\"Manders, K. (2008). The Euclidean diagram. In P. Mancosu (Ed.), The Philosophy of Mathematical Practice (pp. 80\u2013133). Oxford University Press.\" href=\"#ref-Manders2008\">[Manders2008]<\/a>.]<\/p>\n<p>\uadf8\ub7ec\ubbc0\ub85c \uba85\uc81c 1\uc758 \u2018\ud2c8\u2019\uc740 \uace0\ub300\uc758 \uc99d\uba85\uc774 \ubb34\ub17c\ub9ac\uc801\uc774\uc5c8\ub2e4\ub294 \uc99d\uac70\uac00 \uc544\ub2c8\ub2e4. \uc624\ud788\ub824 \ud5c8\uc6a9\ub418\ub294 \ub3c4\ud574 \ucd94\ub860\uacfc \uba85\uc2dc\uc801 \uacf5\ub9ac \uc0ac\uc774\uc758 \uacbd\uacc4\ub97c \ud6c4\ub300\uac00 \ub2e4\ub974\uac8c \uadf8\ub9ac\uac8c \ub418\uc5c8\uc74c\uc744 \ubcf4\uc5ec\uc900\ub2e4. \ucd94\uc0c1\ud654\uc758 \uae30\uc900, \uadf8\ub9ac\uace0 \uc5c4\ubc00\uc131\uc758 \uae30\uc900 \uc790\uccb4\ub3c4 \uc5ed\uc0ac \uc18d\uc5d0\uc11c \uba85\uc2dc\ud654\ub418\uace0 \uc7ac\uad6c\uc131\ub41c \uac83\uc774\ub2e4.<\/p>\n<h4>\ucd94\uc0c1\ud654\uc5d0 \ub300\ud55c \uace0\ub300\uc758 \uc774\ub860<\/h4>\n<p>\uace0\ub300 \uadf8\ub9ac\uc2a4 \ucca0\ud559\uc790\ub4e4\uc740 \u201c\uc218\ud559\uc774 \ubb34\uc5c7\uc744 \ub300\uc0c1\uc73c\ub85c \uc0bc\ub294\uac00?\u201d\ub77c\ub294 \uc9c8\ubb38\uc744 \uba85\uc2dc\uc801\uc73c\ub85c \ub17c\uc758\ud588\ub2e4. \ud50c\ub77c\ud1a4\uacfc \uc544\ub9ac\uc2a4\ud1a0\ud154\ub808\uc2a4\ub294 \uc774 \ubb38\uc81c\uc5d0 \uc11c\ub85c \ub2e4\ub978 \uac15\uc870\uc810\uc744 \uc81c\uc2dc\ud588\uc73c\uba70, \ud6c4\ub300\uc758 \ud50c\ub77c\ud1a4\uc8fc\uc758\uc640 \uc544\ub9ac\uc2a4\ud1a0\ud154\ub808\uc2a4\uc8fc\uc758\ub294 \uc218\ud559\uc801 \ub300\uc0c1\uc758 \ub3c5\ub9bd\uc131\uacfc \uac10\uac01\uc801 \uc0ac\ubb3c\uacfc\uc758 \uad00\uacc4\ub97c \ub450\uace0 \uc624\ub798 \ub17c\uc7c1\ud588\ub2e4. <!-- \ub2e4\ub9cc \ub450 \uc0ac\ub78c\uc758 \uacac\ud574\ub97c \uc624\ub298\ub0a0\uc758 \u2018\ubc1c\uacac \ub300 \ubc1c\uba85\u2019\uc774\ub77c\ub294 \ud55c \uc30d\uc758 \ud45c\uc5b4\ub85c \uc644\uc804\ud788 \ud658\uc6d0\ud574\uc11c\ub294 \uc548 \ub41c\ub2e4. --><\/p>\n<p>\ud50c\ub77c\ud1a4\uc758 \u201c\uad6d\uac00\u201d 6\uad8c\uc5d0\uc11c \uc18c\ud06c\ub77c\ud14c\uc2a4\ub294 \uae30\ud558\ud559\uc790\ub4e4\uc774 \ub208\uc5d0 \ubcf4\uc774\ub294 \ub3c4\ud615\uc744 \uc0ac\uc6a9\ud558\uc9c0\ub9cc, \ub17c\uc99d\uc740 \uadf8\ub824\uc9c4 \uc0ac\uac01\ud615\uacfc \ub300\uac01\uc120\uc774 \uc544\ub2c8\ub77c \u2018\uc0ac\uac01\ud615 \uc790\uccb4\u2019\uc640 \u2018\ub300\uac01\uc120 \uc790\uccb4\u2019\ub97c \ud5a5\ud55c\ub2e4\uace0 \uc124\uba85\ud55c\ub2e4<a class=\"math-abs-series-ref\" title=\"Plato. Republic, 510d\u2013511a. D. Horan (Trans.). Plato's Republic online translation.\" href=\"#ref-PlatoRepublic\">[Plato, <i>Republic<\/i> 510d\u2013511a]<\/a>. \uc774 \uad6c\uc808\uc740 \uac10\uac01\uc801 \uadf8\ub9bc\uacfc \uc0ac\uace0\uc758 \ub300\uc0c1\uc744 \ubd84\uba85\ud788 \uad6c\ubcc4\ud55c\ub2e4. \uadf8\ub7ec\ub098 \ud50c\ub77c\ud1a4\uc758 \uc218\ud559\uc801 \ub300\uc0c1\uc774 \uc774\ub370\uc544\uc640 \uc815\ud655\ud788 \uac19\uc740\uc9c0, \uc774\ub370\uc544\uc640 \uac10\uac01\ubb3c \uc0ac\uc774\uc758 \ubcc4\ub3c4 \u2018\uc911\uac04\uc790\u2019\uc778\uc9c0\uc5d0 \uad00\ud574\uc11c\ub294 \uace0\ub300\uc758 \uc99d\uc5b8\uacfc \ud604\ub300 \ud574\uc11d\uc774 \uc77c\uce58\ud558\uc9c0 \uc54a\ub294\ub2e4<a class=\"math-abs-series-ref\" title=\"Silverman, A. (2022). Plato's middle period metaphysics and epistemology. In E. N. Zalta &amp; U. Nodelman (Eds.), The Stanford Encyclopedia of Philosophy (Fall 2022 ed.).\" href=\"#ref-Silverman2022\">[Silverman2022, \u00a7\u00a712\u201313]<\/a>. <!-- \ub530\ub77c\uc11c \u201c\uc218\ud559\uc801 \ub300\uc0c1\uc774 \ub3c5\ub9bd\ub41c \uc774\ub370\uc544\uacc4\uc5d0 \ub193\uc5ec \uc788\ub2e4\u201d\ub294 \ubb38\uc7a5\uc740 \ub113\uc740 \ud50c\ub77c\ud1a4\uc8fc\uc758\uc801 \ub3c5\ud574\ub85c\ub294 \uc774\ud574\ud560 \uc218 \uc788\uc9c0\ub9cc, \ud50c\ub77c\ud1a4\uc758 \ud655\uc815\ub41c \ub2e8\uc77c \uad50\uc124\ucc98\ub7fc \uc81c\uc2dc\ud558\uba74 \uc9c0\ub098\uce58\uac8c \ub2e8\uc21c\ud558\ub2e4. --><\/p>\n<p>\ub300\ud654\ud3b8 \u201c\uba54\ub17c\u201d\uc5d0\uc11c \uc18c\ud06c\ub77c\ud14c\uc2a4\ub294 \uc218\ud559\uc744 \ubc30\uc6b0\uc9c0 \uc54a\uc558\ub2e4\ub294 \ud55c \uc18c\ub144\uc5d0\uac8c \uc815\uc0ac\uac01\ud615\uc758 \ub113\uc774\ub97c \ub450 \ubc30\ub85c \ub9cc\ub4dc\ub294 \ubb38\uc81c\ub97c \ubb3b\uace0, \uadf8\ub9bc\uacfc \uc5f0\uc18d\ub41c \uc9c8\ubb38\uc744 \ud1b5\ud574 \uc6d0\ub798 \uc815\uc0ac\uac01\ud615\uc758 \ub300\uac01\uc120\uc744 \uc0c8 \uc815\uc0ac\uac01\ud615\uc758 \ubcc0\uc73c\ub85c \uc0bc\ub294 \ub2f5\uc5d0 \uc774\ub974\uac8c \ud55c\ub2e4<a class=\"math-abs-series-ref\" title=\"Plato. Meno (B. Jowett, Trans.), 81a\u201386c. MIT Classics Archive.\" href=\"#ref-PlatoMeno\">[Plato, <i>Meno<\/i> 81a\u201386c]<\/a>. \uc774 \uc7a5\uba74\uc740 \ub300\ud654 \uc18d\uc5d0\uc11c <span class=\"defined\">\uc0c1\uae30<\/span>(anamnesis)\uc124\uc744 \ub4b7\ubc1b\uce68\ud558\ub294 \uadf9\uc801 \uc608\ub85c \uae30\ub2a5\ud55c\ub2e4. <!-- \uadf8\ub7ec\ub098 \uc18c\ud06c\ub77c\ud14c\uc2a4\uac00 \ub3c4\ud615\uc744 \uadf8\ub9ac\uace0 \uc120\ud0dd\uc9c0\ub97c \uc81c\uc2dc\ud558\ub294 \uc720\ub3c4 \uc9c8\ubb38\uc744 \uacc4\uc18d \uc0ac\uc6a9\ud558\ubbc0\ub85c, \uc774\uac83\uc774 \uc601\ud63c\uc758 \uc120\uc7ac\ub098 \u2018\ubaa8\ub4e0 \uc218\ud559\uc740 \ubc1c\uacac\ub41c\ub2e4\u2019\ub294 \uba85\uc81c\ub97c \ub3c5\ub9bd\uc801\uc73c\ub85c \uc99d\uba85\ud55c\ub2e4\uace0 \ub9d0\ud560 \uc218\ub294 \uc5c6\ub2e4. \uc815\ud655\ud788 \ub9d0\ud558\uba74 \ud50c\ub77c\ud1a4\uc740 \uc774 \uc7a5\uba74\uc744 \ud0d0\uad6c\uac00 \uac00\ub2a5\ud558\uace0 \uc18c\ub144 \uc548\uc758 \ucc38\ub41c \uc758\uacac\uc774 \uc77c\uae68\uc6cc\uc9c8 \uc218 \uc788\ub2e4\ub294 \ub17c\uc99d\uc5d0 \uc0ac\uc6a9\ud55c\ub2e4. --> \ud50c\ub77c\ud1a4\uc740 \uc18c\ud06c\ub77c\ud14c\uc2a4\uc758 \uc9c8\ubb38\uc5d0 \uc2a4\uc2a4\ub85c \ub2f5\uc744 \ucc3e\uc544\uac00\ub294 \uc18c\ub144\uc758 \ubaa8\uc2b5\uc744 \ud1b5\ud574, \ud0d0\uad6c\uac00 \uac00\ub2a5\ud558\uba70 \uc6b0\ub9ac \uc548\uc758 \ucc38\ub41c \uc54e\uc774 \ub300\ud654\ub85c \uc77c\uae68\uc6cc\uc9c8 \uc218 \uc788\uc74c\uc744 \ubc1d\ud78c\ub2e4.<\/p>\n<p>\uc544\ub9ac\uc2a4\ud1a0\ud154\ub808\uc2a4\ub294 \uc218\ud559\uc801 \ub300\uc0c1\uc774 \uac10\uac01\ubb3c\uacfc \ubd84\ub9ac\ub41c \ubcc4\ub3c4\uc758 \uc2e4\uccb4\ub85c \uc874\uc7ac\ud574\uc57c \ud55c\ub2e4\ub294 \uacac\ud574\ub97c \ube44\ud310\ud55c\ub2e4. \u201c\ud615\uc774\uc0c1\ud559\u201d M\uad8c\uc5d0\uc11c \uadf8\ub294 \uae30\ud558\ud559\uc790\uac00 \uac10\uac01\uc801 \ub300\uc0c1\uc744 \uae38\uc774, \uba74, \ubd80\ud53c\ub77c\ub294 \uce21\uba74\uc5d0\uc11c, \uc989 \uadf8\uac83\uc774 \uc591\uc744 \uc9c0\ub2c8\ub294 \ud55c\uc5d0\uc11c \uc5f0\uad6c\ud560 \uc218 \uc788\ub2e4\uace0 \uc124\uba85\ud55c\ub2e4<a class=\"math-abs-series-ref\" title=\"Aristotle. (1998). The Metaphysics (H. Lawson-Tancred, Trans.). Penguin Classics. Google Books.\" href=\"#ref-Aristotle1998\">[Aristotle1998, <i>Metaphysics<\/i> XIII.3, 1077b17\u20131078a31]<\/a>. \u201c\uc790\uc5f0\ud559\u201d 2\uad8c\uc5d0\uc11c\ub3c4 \uc218\ud559\uc790\ub294 \uc790\uc5f0\ubb3c\uc758 \uc18d\uc131 \uac00\uc6b4\ub370 \ud615\uc0c1\uacfc \uc591\uc744 \uc0ac\uace0 \uc18d\uc5d0\uc11c \ubd84\ub9ac\ud574 \uace0\ucc30\ud558\uc9c0\ub9cc, \uadf8\uac83\uc744 \ubb3c\ub9ac\uc801 \uc0ac\ubb3c\uacfc \ubcc4\uac1c\uc758 \uc2e4\uccb4\ub85c \ub9cc\ub4e4 \ud544\uc694\ub294 \uc5c6\ub2e4\uace0 \ub9d0\ud55c\ub2e4<a class=\"math-abs-series-ref\" title=\"Aristotle. (2018). Physics (C. D. C. Reeve, Trans.). Hackett Publishing. Publisher page.\" href=\"#ref-Aristotle2018\">[Aristotle2018, <i>Physics<\/i> II.2, 193b22\u2013194a12]<\/a>.<\/p>\n<p>\uc774 \ub17c\uc758\uc640 \uad00\ub828\ud574 \uc544\ub9ac\uc2a4\ud1a0\ud154\ub808\uc2a4\ub294 <span class=\"defined\">\uc544\ud30c\uc774\ub808\uc2dc\uc2a4<\/span>(aphairesis, \uc81c\uac70, \ub5bc\uc5b4\ub0c4) \uacc4\uc5f4\uc758 \ud45c\ud604\uacfc \u201c\ubd84\ub9ac\ub41c \uac83\uc73c\ub85c\uc11c\u201d \uace0\ucc30\ud55c\ub2e4\ub294 \ud45c\ud604, \uadf8\ub9ac\uace0 \uc5b4\ub5a4 \uac83\uc744 \u2018\ubb34\uc5c7\uc778 \ud55c\uc5d0\uc11c(<i>qua<\/i>)\u2019 \uc5f0\uad6c\ud55c\ub2e4\ub294 \ud45c\ud604\uc744 \uc0ac\uc6a9\ud55c\ub2e4. \ud604\ub300 \uc5f0\uad6c\ub294 \uc774 \uc14b\uc744 \ub2e8\uc21c\ud788 \ud558\ub098\uc758 \uc2ec\ub9ac\uc801 \u2018\ube84\uc148\u2019 \uc774\ub860\uc73c\ub85c \ud569\uce58\uc9c0 \uc54a\uace0 \ubb38\ub9e5\ubcc4 \uc5ed\ud560\uc744 \uad6c\ubd84\ud55c\ub2e4<a class=\"math-abs-series-ref\" title=\"Mendell, H. (2016). Aristotle and mathematics. In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Fall 2016 ed.).\" href=\"#ref-Mendell2016\">[Mendell2016, \u00a7\u00a77.1\u20137.4]<\/a><a class=\"math-abs-series-ref\" title=\"Cleary, J. J. (1985). On the terminology of \u201cabstraction\u201d in Aristotle. Phronesis, 30(1), 13\u201345.\" href=\"#ref-Cleary1985\">[Cleary1985]<\/a>.<\/p>\n<p>[\uc774 \ub17c\uc758\uc758 \ud575\uc2ec \uc790\ub8cc\ub294 \uc544\ub9ac\uc2a4\ud1a0\ud154\ub808\uc2a4\uc758 \u201c\ud615\uc774\uc0c1\ud559\u201d M\uad8c, \ud2b9\ud788 XIII.3(1077b17\u20131078a31), \uadf8\ub9ac\uace0 \u201c\uc790\uc5f0\ud559\u201d II.2\uc774\ub2e4. \uadf8\ub294 \u2018\uc81c\uac70\uc5d0\uc11c \ub098\uc628 \uac83\ub4e4\u2019(<i>ta ex aphairese\u014ds<\/i>)\uc774\ub77c\ub294 \ud45c\ud604\uc744 \uc0ac\uc6a9\ud558\uc9c0\ub9cc, \uadf8\uc758 \uc218\ud559\ucca0\ud559 \uc804\uccb4\ub97c \ud604\ub300\uc5b4 \u2018abstraction\u2019 \ud558\ub098\ub85c \ubc88\uc5ed\ud560 \ub54c\uc5d0\ub294 \uc81c\uac70, \uc0ac\uace0\uc0c1\uc758 \ubd84\ub9ac, \u2018~\uc778 \ud55c\uc5d0\uc11c\u2019\uc758 \uace0\ucc30\uc744 \uad6c\ubd84\ud560 \ud544\uc694\uac00 \uc788\ub2e4<a class=\"math-abs-series-ref\" title=\"Mendell, H. (2016). Aristotle and mathematics. In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Fall 2016 ed.).\" href=\"#ref-Mendell2016\">[Mendell2016]<\/a>.]<\/p>\n<p><i>Aphairesis<\/i>\uac00 \uc0b0\uc220\uc5d0\uc11c \ube84\uc148\uc744 \ub73b\ud558\uae30\ub3c4 \ud55c\ub2e4\ub294 \uc810\uc740 \u2018\uc18d\uc131\uc744 \ucc28\uac10\ud55c\ub2e4\u2019\ub294 \ube44\uc720\ub97c \ub9e4\ub825\uc801\uc73c\ub85c \ub9cc\ub4e0\ub2e4. \uadf8\ub7ec\ub098 \uc218\ud559\uc801 \ub300\uc0c1\uc774 \ubb38\uc790 \uadf8\ub300\ub85c \uc2ec\ub9ac\uc801 \ube84\uc148\uc758 \uc0b0\ubb3c\uc774\ub77c\ub294 \ub73b\uc73c\ub85c \uc77d\uc73c\uba74 \uc544\ub9ac\uc2a4\ud1a0\ud154\ub808\uc2a4\uc758 \ubcf5\ud569\uc801\uc778 \uc124\uba85\uc744 \ub193\uce5c\ub2e4. \ub77c\ud2f4\uc5b4 <i>abstractio<\/i>\ub97c \uac70\uccd0 \uadfc\ub300\uc758 \u2018abstraction\u2019 \ub2f4\ub860\uc774 \ud615\uc131\ub41c \uae34 \ubc88\uc5ed\uc0ac\uc640, <a href=\"..\/math-abstraction-01-essence\/\">1\ubd80<\/a>\uc5d0\uc11c \uc0b4\ud3b4\ubcf8 \uadfc\ub300 \ub3d9\uc544\uc2dc\uc544\uc758 \u2018\ucd94\uc0c1(\u62bd\u8c61)\u2019, \u2018\uc0ac\uc0c1(\u6368\u8c61)\u2019\uc774\ub77c\ub294 \ubc88\uc5ed\uc5b4\uc758 \uc5ed\uc0ac\ub294 \uc11c\ub85c \uad00\ub828\ub418\uc9c0\ub9cc, \ud55c\uc790\uc5b4\uac00 \uace0\ub300 \uadf8\ub9ac\uc2a4\uc5b4\uc5d0\uc11c \uc9c1\uc811 \uc720\ub798\ud588\ub2e4\uace0 \ub9d0\ud560 \uc218\ub294 \uc5c6\ub2e4.<\/p>\n<p>\ud50c\ub77c\ud1a4\uacfc \uc544\ub9ac\uc2a4\ud1a0\ud154\ub808\uc2a4\uc758 \ub17c\uc758\uac00 \ubcf4\uc5ec\uc8fc\ub294 \uacb0\ub860\uc740 \uace0\ub300\uc5d0 \ucd94\uc0c1\ud654\uc758 \uc790\uac01\uc774 \uc804\ud600 \uc5c6\uc5c8\ub2e4\ub294 \uac83\uc774 \uc544\ub2c8\ub77c, \uc218\ud559\uc801 \uc2e4\ucc9c\uc5d0 \ub300\ud55c \ucca0\ud559\uc801 \uc124\uba85\uc774 \uc774\ubbf8 \uc874\uc7ac\ud588\ub2e4\ub294 \uac83\uc774\ub2e4. \ub2e4\ub9cc \uadf8 \uc124\uba85\uc774 \uc720\ud074\ub9ac\ub4dc\uc758 \ubaa8\ub4e0 \ub3c4\ud574 \ucd94\ub860\uc744 \ud615\uc2dd \uaddc\uce59\uc73c\ub85c \ubc14\uafb8\uac70\ub098, \ud6c4\ub300 \uc9d1\ud569\ub860\ucc98\ub7fc \uc0c8\ub85c\uc6b4 \ub300\uc0c1\uc744 \uad6c\uc131\ud558\ub294 \uc77c\ubc18 \uc808\ucc28\ub97c \uc81c\uacf5\ud55c \uac83\uc740 \uc544\ub2c8\ub2e4. \uc774 \uae00\uc774 \u2018\uc554\ubb35\uc801\u2019\uc774\ub77c\uace0 \ubd80\ub974\ub294 \uac83\uc740 \uc774 \uc2e4\ubb34\uc801, \ud615\uc2dd\uc801 \uce35\uc704\ub2e4. \ub610\ud55c \uc544\ub9ac\uc2a4\ud1a0\ud154\ub808\uc2a4\uc758 \ucca0\ud559\uc774 \ub4a4\uc774\uc740 0\uacfc \uc74c\uc218\uc758 \uc218\uc6a9\uc744 \uc9c1\uc811 \uac00\ub85c\ub9c9\uc558\ub2e4\uace0 \uc785\uc99d\ud560 \uc790\ub8cc\ub3c4 \uc5c6\uc73c\ubbc0\ub85c, \uc774\uc81c\ubd80\ud130\uc758 \uc0ac\ub840\ub294 \ud558\ub098\uc758 \ucca0\ud559\uc774 \ub9cc\ub4e0 \ub2e8\uc120\uc801 \uacb0\uacfc\uac00 \uc544\ub2c8\ub77c \ubb38\ud654\uad8c\uacfc \uacc4\uc0b0 \uad00\ud589\uc5d0 \ub530\ub77c \ub2ec\ub77c\uc9c4 \uc5ed\uc0ac\ub85c \ubcf4\uc544\uc57c \ud55c\ub2e4.<\/p>\n<h4>0\uacfc \uc74c\uc218<\/h4>\n<p>0\uacfc \uc74c\uc218\ub294 \uc218 \uac1c\ub150\uc774 \uad6c\uccb4\uc801 \ud06c\uae30\uc640 \uc5b4\ub5bb\uac8c \ubd84\ub9ac\ub418\ub294\uc9c0\ub97c \uc798 \ubcf4\uc5ec\uc8fc\uc9c0\ub9cc, \uadf8 \uc5ed\uc0ac\ub97c \u2018\ubb3c\ub9ac\uc801 \uc6d0\ucc9c\uc774 \uc5c6\uc5b4\uc11c \ubaa8\ub450\uac00 \uac70\ubd80\ud588\ub2e4\u2019\ub294 \ud558\ub098\uc758 \uc6d0\uc778\uc73c\ub85c \uc124\uba85\ud560 \uc218\ub294 \uc5c6\ub2e4. \uc790\ub9ac\uac12 \ud45c\uae30\uc758 \ud544\uc694, \ucc9c\ubb38 \uacc4\uc0b0, \ubd80\ucc44\uc640 \uc7ac\uc0b0\uc758 \uacc4\uc0b0, \ubc29\uc815\uc2dd\uc758 \ud574\uc5d0 \ub300\ud55c \uc870\uac74, \uae30\ud558\ud559\uc801 \ud06c\uae30\uc758 \ud574\uc11d\uc774 \ubb38\ud654\uc640 \uc2dc\ub300\ub9c8\ub2e4 \ub2e4\ub974\uac8c \uc791\uc6a9\ud588\ub2e4. \ud2b9\ud788 \uae30\ud638\ub97c \uc0ac\uc6a9\ud558\ub294 \uac83, \uc5f0\uc0b0 \uaddc\uce59\uc744 \uc544\ub294 \uac83, \ubc29\uc815\uc2dd\uc758 \ub2f5\uc73c\ub85c \uc778\uc815\ud558\ub294 \uac83, \ub3c5\ub9bd\ub41c \uc218\ud559\uc801 \ub300\uc0c1\uc73c\ub85c \ud574\uc11d\ud558\ub294 \uac83\uc740 \uc11c\ub85c \ub2e4\ub978 \ub2e8\uacc4\ub2e4.<\/p>\n<p>\ud6c4\uae30 \ubc14\ube4c\ub85c\ub2c8\uc544\uc758 60\uc9c4 \uc790\ub9ac\uac12 \ud45c\uae30\uc5d0\ub294 \ube44\uc5b4 \uc788\ub294 \uc911\uac04 \uc790\ub9ac\ub97c \ub098\ud0c0\ub0b4\ub294 \uc804\uc6a9 \uc410\uae30 \uae30\ud638\uac00 \ub098\ud0c0\ub09c\ub2e4. \uc774\uac83\uc740 \ubaa8\ud638\uc131\uc744 \uc904\uc774\ub294 \uc790\ub9ac\ud45c\uc2dc\uc790\uc600\uc9c0\ub9cc \ud604\ub300\uc758 \uc22b\uc790 0\uacfc \uc0ac\uc6a9 \ubc94\uc704\uac00 \uac19\uc9c0 \uc54a\uc558\uace0, \ubaa8\ub4e0 \uc704\uce58\uc5d0\uc11c \uc77c\uad00\ub418\uac8c \uc4f0\uc774\uc9c0\ub3c4 \uc54a\uc558\ub2e4. \ud55c\ud3b8 \uc81c1\ucc9c\ub144\uae30 \uc218\ub9ac\ucc9c\ubb38\ud559\uc5d0\uc11c\ub294 \u2018\uc544\ubb34\uac83\ub3c4 \uc5c6\uc74c\u2019\uc5d0 \ud574\ub2f9\ud558\ub294 \uac12\uc774 \uacc4\uc0b0 \uc18d\uc5d0\uc11c \ub354 \uc801\uadf9\uc801\uc778 \uc5ed\ud560\uc744 \ud558\uae30\ub3c4 \ud588\ub2e4. \ub530\ub77c\uc11c \ubc14\ube4c\ub85c\ub2c8\uc544\uc758 \uc0ac\ub840\ub97c \ub2e8\uc21c\ud788 \u2018\ub744\uc5b4\uc4f0\uae30\uc77c \ubfd0\uc778 \uac00\uc9dc 0\u2019\uc73c\ub85c \ud3c4\ud558\ud558\uae30\ubcf4\ub2e4, \uc790\ub9ac\ud45c\uc2dc\uc640 \uc218\ub85c\uc11c\uc758 0 \uc0ac\uc774\uc5d0 \uc5ec\ub7ec \uae30\ub2a5\uc801 \ub2e8\uacc4\uac00 \uc788\uc5c8\uc74c\uc744 \uc778\uc815\ud574\uc57c \ud55c\ub2e4<a class=\"math-abs-series-ref\" title=\"Ritter, J. (2024). Babylonian zeros. In P. Gobets &amp; R. L. Kuhn (Eds.), The Origin and Significance of Zero: An Interdisciplinary Perspective (pp. 35\u201363). Brill.\" href=\"#ref-Ritter2024\">[Ritter2024, pp. 35\u201363]<\/a>.<\/p>\n<p>\uc778\ub3c4 \uc218\ud559\uc790 \ube0c\ub77c\ub9c8\uad7d\ud0c0(Brahmagupta)\ub294 628\ub144\uc5d0 \uc644\uc131\ud55c \u201c\ube0c\ub77c\ub9c8\uc2a4\ud478\ud0c0\uc2ef\ub2e8\ud0c0\u201d 18\uc7a5\uc5d0\uc11c \uc591\uc218, \uc74c\uc218, 0\uc758 \uacc4\uc0b0 \uaddc\uce59\uc744 \ud604\uc874 \uc790\ub8cc \uac00\uc6b4\ub370 \uc774\ub978 \uc2dc\uae30\uc5d0 \uccb4\uacc4\uc801\uc73c\ub85c \uc11c\uc220\ud588\ub2e4. \uadf8\ub294 \uc591\uc218\ub97c \u2018\uc7ac\uc0b0\u2019, \uc74c\uc218\ub97c \u2018\ube5a\u2019\uc5d0 \ube44\uc720\ud558\uc5ec \ub367\uc148\uacfc \ube84\uc148\uc744 \uc124\uba85\ud558\uace0, \uc11c\ub85c \ub2e4\ub978 \ubd80\ud638\uc758 \uacf1\uacfc \uac19\uc740 \ubd80\ud638\uc758 \uacf1, 0\uc744 \uacf1\ud55c \uacb0\uacfc\ub97c \uaddc\uc815\ud588\ub2e4<a class=\"math-abs-series-ref\" title=\"Brahmagupta &amp; Bh\u0101skara. (1817). Algebra, with Arithmetic and Mensuration, from the Sanscrit of Brahmegupta and Bh\u00e1scara (H. T. Colebrooke, Trans.). John Murray. Internet Archive.\" href=\"#ref-Colebrooke1817\">[Colebrooke1817, Ch. 18, vv. 30\u201335]<\/a>.<\/p>\n<ul>\n<li>\uc591\uc218\uc640 \uc74c\uc218\uc758 \ud569\uc740 \ub450 \uc808\ub313\uac12\uc758 \ucc28\uc5d0 \ub530\ub77c \ubd80\ud638\uac00 \uc815\ud574\uc9c4\ub2e4.<\/li>\n<li>\uc591\uc218\uc5d0\uc11c \uc74c\uc218\ub97c \ube7c\uac70\ub098 \uc74c\uc218\uc5d0\uc11c \uc591\uc218\ub97c \ube7c\ub294 \uaddc\uce59\uc744 \uc7ac\uc0b0\uacfc \ube5a\uc758 \uc5b8\uc5b4\ub85c \ud45c\ud604\ud55c\ub2e4.<\/li>\n<li>\uc11c\ub85c \ub2e4\ub978 \ubd80\ud638\uc758 \uacf1\uc740 \uc74c\uc218\uc774\uace0, \uac19\uc740 \ubd80\ud638\uc758 \uacf1\uc740 \uc591\uc218\uc774\uba70, 0\uacfc\uc758 \uacf1\uc740 0\uc774\ub2e4.<\/li>\n<\/ul>\n<p>[\ube0c\ub77c\ub9c8\uad7d\ud0c0\ub3c4 0\uc73c\ub85c \ub098\ub204\uae30\ub97c \ud604\ub300\uc801\uc73c\ub85c \ucc98\ub9ac\ud558\uc9c0\ub294 \ubabb\ud588\ub2e4. \uadf8\ub294 \\(0\/0=0\\)\uc774\ub77c\uace0 \uc37c\uace0, \uc591\uc218\ub098 \uc74c\uc218\ub97c 0\uc73c\ub85c \ub098\ub208 \uacbd\uc6b0\uc5d0\ub294 0\uc744 \uc81c\uc218\ub85c \ub454 \ubd84\uc218 \ud615\ud0dc\ub97c \ub9d0\ud560 \ubfd0 \uc624\ub298\ub0a0\ucc98\ub7fc \u2018\uc815\uc758\ub418\uc9c0 \uc54a\ub294\ub2e4\u2019\uace0 \uaddc\uc815\ud558\uc9c0 \uc54a\uc558\ub2e4<a class=\"math-abs-series-ref\" title=\"Brahmagupta &amp; Bh\u0101skara. (1817). Algebra, with Arithmetic and Mensuration, from the Sanscrit of Brahmegupta and Bh\u00e1scara (H. T. Colebrooke, Trans.). John Murray. Internet Archive.\" href=\"#ref-Colebrooke1817\">[Colebrooke1817, Ch. 18, vv. 34\u201335]<\/a>.]<\/p>\n<p>\uc774 \uc0ac\ub840\uc758 \ud575\uc2ec\uc740 0\uc774 \ub2e8 \ud55c\uc21c\uac04\uc5d0 \u2018\ubc1c\uba85\u2019\ub418\uc5c8\ub2e4\ub294 \uc601\uc6c5 \uc11c\uc0ac\uac00 \uc544\ub2c8\ub2e4. \ud45c\uae30\uc0c1\uc758 \ube48\uc790\ub9ac, \uc591\uc774 \uc5c6\uc74c\uc744 \ub098\ud0c0\ub0b4\ub294 \uac12, \ub2e4\ub978 \uc218\uc640 \uc5f0\uc0b0\ud558\ub294 \uc218\ub77c\ub294 \uae30\ub2a5\uc744 \uad6c\ubd84\ud560 \ub54c, \ube0c\ub77c\ub9c8\uad7d\ud0c0\uc758 \ud14d\uc2a4\ud2b8\uac00 \ud2b9\ubcc4\ud55c \uae4c\ub2ed\uc740 0\uacfc \ubd80\ud638 \uc788\ub294 \uc591\uc744 \uc5f0\uc0b0 \uaddc\uce59\uc758 \ub3d9\uc77c\ud55c \uccb4\uacc4 \uc548\uc5d0 \uba85\uc2dc\uc801\uc73c\ub85c \ub123\uc5c8\ub2e4\ub294 \ub370 \uc788\ub2e4. <!-- \uc5ec\uae30\uc11c \u201c\uaddc\uce59\uc774 \ub300\uc0c1\uc744 \uc131\ub9bd\uc2dc\ud0a8\ub2e4\u201d\ub294 \uacb0\ub860\uc740 \uc774 \uae00\uc758 \ucca0\ud559\uc801 \ud574\uc11d\uc774\uba70, \ube0c\ub77c\ub9c8\uad7d\ud0c0 \uc790\uc2e0\uc758 \uc874\uc7ac\ub860\uc801 \uc120\uc5b8\uc73c\ub85c \uc778\uc6a9\ud574\uc11c\ub294 \uc548 \ub41c\ub2e4. --> \ubb3c\ub860 \uc774\ub294 \ube0c\ub77c\ub9c8\uad7d\ud0c0\uc758 \uba85\uc2dc\uc801 \uc131\uba85\uc774\ub77c\uae30\ubcf4\ub2e4, \uadf8\uc758 \uacc4\uc0b0 \uaddc\uce59\uc744 \ud604\ub300 \uc218\ud559\uc758 \uad00\uc810\uc5d0\uc11c \ubc14\ub77c\ubcf8 \ud574\uc11d\uc774\ub2e4.<\/p>\n<p>\uc911\uad6d\uc758 \u201c\uad6c\uc7a5\uc0b0\uc220(\u4e5d\u7ae0\u7b97\u8853)\u201d\uc740 \uc5ec\ub7ec \uc138\ub300\uc5d0 \uac78\uccd0 \ud615\uc131\ub418\uc5b4 \ud55c\ub300\uc5d0 \ud604\uc7ac\uc640 \uac00\uae4c\uc6b4 \ud615\ud0dc\ub97c \uac16\ucd98 \ubb38\uc81c\uc640 \uc808\ucc28\uc758 \ubaa8\uc74c\uc774\uba70, \uc720\ud718(\u5289\u5fbd)\ub294 263\ub144\uc5d0 \uc0c1\uc138\ud55c \uc8fc\uc11d\uc744 \ub0a8\uacbc\ub2e4. \uc81c8\uc7a5 \u300c\ubc29\uc815(\u65b9\u7a0b)\u300d\uc740 \uc0b0\uac00\uc9c0\ub97c \uacc4\uc0b0\ud310\uc5d0 \ubc30\uc5f4\ud558\uc5ec \uc5f0\ub9bd\uc77c\ucc28\ubb38\uc81c\ub97c \uc18c\uac70\ud558\ub294 \uc808\ucc28\ub97c \uc81c\uc2dc\ud55c\ub2e4. \uc774\uac83\uc740 \ud604\ub300\uc758 \uac00\uc6b0\uc2a4 \uc18c\uac70\ubc95\uacfc \uad6c\uc870\uc801\uc73c\ub85c \ube44\uad50\ud560 \uc218 \uc788\uc9c0\ub9cc, \ud604\ub300 \ud589\ub82c \uae30\ud638\ub97c \uadf8\ub300\ub85c \uc0ac\uc6a9\ud55c \uac83\uc740 \uc544\ub2c8\ub2e4<a class=\"math-abs-series-ref\" title=\"Shen, K., Crossley, J. N., &amp; Lun, A. W.-C. (1999). The Nine Chapters on the Mathematical Art: Companion and Commentary. Oxford University Press. Google Books.\" href=\"#ref-Shen1999\">[Shen, Crossley, &amp; Lun 1999, Ch. 8]<\/a>.<\/p>\n<p>\uc591\uc218\uc640 \uc74c\uc218\uc758 \ub367\uc148\uacfc \ube84\uc148 \uaddc\uce59\uc778 <span class=\"defined\">\uc815\ubd80\uc220<\/span>(\u6b63\u8ca0\u8853)\uc740 \ubcc4\ub3c4\uc758 \uc7a5\uc774 \uc544\ub2c8\ub77c \uc774 \u300c\ubc29\uc815\u300d \uc7a5 \uc548\uc5d0 \ub4e4\uc5b4 \uc788\ub2e4. \ub610\ud55c \uc591\uc218\uc5d0\ub294 \ubd89\uc740 \uc0b0\uac00\uc9c0, \uc74c\uc218\uc5d0\ub294 \uac80\uc740 \uc0b0\uac00\uc9c0\ub97c \uc4f0\ub77c\ub294 \uc124\uba85\uc740 \ud604\uc804\ud558\ub294 \ubcf8\ubb38 \uc790\uccb4\ubcf4\ub2e4 \uc720\ud718\uc758 \uc8fc\uc11d\uc5d0\uc11c \ud655\uc778\ub41c\ub2e4. \uc0c9\uc744 \uc4f8 \uc218 \uc5c6\uc744 \ub54c\uc5d0\ub294 \uc0b0\uac00\uc9c0\uc758 \ubc30\uce58\ub098 \ud45c\uc2dc\ub97c \ub2ec\ub9ac\ud558\ub294 \ubc29\ubc95\ub3c4 \uc788\uc5c8\ub2e4<a class=\"math-abs-series-ref\" title=\"Shen, K., Crossley, J. N., &amp; Lun, A. W.-C. (1999). The Nine Chapters on the Mathematical Art: Companion and Commentary. Oxford University Press. Google Books.\" href=\"#ref-Shen1999\">[Shen, Crossley, &amp; Lun 1999, pp. 358\u2013360]<\/a>. \uc74c\uc218\ub294 \uc18c\uac70 \uacfc\uc815\uc5d0\uc11c \uc0dd\uae30\ub294 \uacc4\uc0b0\uac12\uc744 \ud45c\ud604\ud558\uace0 \uacc4\uc18d \uc870\uc791\ud558\uae30 \uc704\ud55c \uc2e4\uc6a9\uc801\uc778 \uc5ed\ud560\uc744 \ud588\ub2e4.<\/p>\n<p>\uc11c\uc720\ub77c\uc2dc\uc544\uc758 \uc5ed\uc0ac\ub3c4 \ub2e8\uc21c\ud55c \u2018\uac70\ubd80\uc758 \uc5f0\uc18d\u2019\uc740 \uc544\ub2c8\ub2e4. \ub514\uc624\ud310\ud1a0\uc2a4\uc758 \u201c\uc0b0\uc220\u201d\uc740 \ubcf4\ud1b5 \uc591\uc758 \uc720\ub9ac\uc218 \ud574\ub97c \uc694\uad6c\ud588\uace0, \ud604\ub300\uc2dd\uc73c\ub85c \uc74c\uc218 \ud574\ub9cc \ub098\uc624\ub294 \ud55c \ubb38\uc81c\ub97c \ubd80\uc801\uc808\ud558\uac70\ub098 \ubd88\uac00\ub2a5\ud55c \uac83\uc73c\ub85c \ucc98\ub9ac\ud588\ub2e4<a class=\"math-abs-series-ref\" title=\"Hettle, C. (2015). The symbolic and mathematical influence of Diophantus's Arithmetica. Journal of Humanistic Mathematics, 5(1), 139\u2013166.\" href=\"#ref-Hettle2015\">[Hettle2015, pp. 146\u2013149]<\/a>. \ub974\ub124\uc0c1\uc2a4\uc758 \uce74\ub974\ub2e4\ub178\ub294 \uc591\uc758 \uadfc\uc744 \u2018\ucc38\u2019, \uc74c\uc758 \uadfc\uc744 \u2018\ud5c8\uad6c\u2019\ub77c\uace0 \ubd80\ub974\ub294 \uc5b8\uc5b4\ub97c \uc0ac\uc6a9\ud588\uc9c0\ub9cc \uc2e4\uc81c \uacc4\uc0b0\uc5d0\uc11c\ub294 \uc74c\uc758 \uac12\uc744 \ub2e4\ub8e8\uc5c8\ub2e4. \ub370\uce74\ub974\ud2b8\ub3c4 \uc591\uc758 \uadfc\uc744 \u2018\ucc38\u2019, \uc74c\uc758 \uadfc\uc744 \u2018\uac70\uc9d3\u2019\uc774\ub77c\uace0 \ubd88\ub800\uc73c\ub098, \uc74c\uc758 \uadfc\uc744 \uc138\uace0 \ubd80\ud638 \ubcc0\ud658\uc73c\ub85c \uc591\uc758 \uadfc\uc73c\ub85c \ubc14\uafb8\ub294 \ubc29\ubc95\uc744 \uc124\uba85\ud588\ub2e4. \uadf8\ub7ec\ubbc0\ub85c \u2018\ud5c8\uad6c\u2019\uc640 \u2018\uac70\uc9d3\u2019\uc774\ub77c\ub294 \uba85\uce6d\uc744 \uace7 \uc0ac\uc6a9 \uac70\ubd80\uc640 \ub3d9\uc77c\uc2dc\ud560 \uc218 \uc5c6\ub2e4<a class=\"math-abs-series-ref\" title=\"Rabouin, D. (2024). Negatives as fictions in 16th and 17th century mathematics. Historia Mathematica, 69, 41\u201361.\" href=\"#ref-Rabouin2024\">[Rabouin2024, pp. 41\u201361]<\/a>.<\/p>\n<p>\ud30c\uc2a4\uce7c\uc758 \u201c\ud321\uc138\u201d\uc5d0\ub294 \u201c\ubb34(0)\uc5d0\uc11c 4\ub97c \ube7c\ub3c4 \ubb34\uac00 \ub0a8\ub294\ub2e4\ub294 \uac83\uc744 \uc774\ud574\ud558\uc9c0 \ubabb\ud558\ub294 \uc0ac\ub78c\ub4e4\uc774 \uc788\ub2e4\u201d\ub294 \ucde8\uc9c0\uc758 \ubb38\uc7a5\uc774 \uc788\ub2e4. \uc6d0\ubb38\uc5d0\uc11c \ud30c\uc2a4\uce7c\uc740 \\(0-4=-4\\)\ub97c \uc639\ud638\ud558\uba70 \ud0c0\uc778\uc744 \uafb8\uc9d6\ub294 \uac83\uc774 \uc544\ub2c8\ub77c, \uc624\ud788\ub824 \u2018\ubb34\u2019\uc5d0\uc11c \ubb34\uc5c7\uc744 \ube7c\ub3c4 \u2018\ubb34\u2019\ub77c\ub294 \uad00\ub150\uc744 \uc608\ub85c \ub4e0\ub2e4<a class=\"math-abs-series-ref\" title=\"Pascal, B. (1670). Pens\u00e9es, Lafuma 199 \/ Sellier 230, \u201cTransition\u201d, fragment 4. Critical text; commentary.\" href=\"#ref-Pascal1670\">[Pascal1670, \u201cTransition\u201d, fr. 4]<\/a>. \ub530\ub77c\uc11c \uc6d0\ubb38\uacfc \ubc18\ub300 \uc758\ubbf8\uc758 \uc74c\uc218 \uc639\ud638 \ubc1c\uc5b8\uc73c\ub85c \uc778\uc6a9\ud574\uc11c\ub294 \uc548 \ub41c\ub2e4.<\/p>\n<p>[\uc774 \ub300\ubaa9\uc740 \uc74c\uc218 \uac1c\ub150\uc5d0 \ub300\ud55c \uc778\uc2dd\ub860\uc801 \uc800\ud56d\uc758 \uc0ac\ub840\ub85c \uc790\uc8fc \uc778\uc6a9\ub418\uc9c0\ub9cc, \ud310\ubcf8\ub9c8\ub2e4 \ub2e8\ud3b8 \ubc88\ud638\uc640 \ubc88\uc5ed\uc774 \ub2e4\ub974\uace0 \ubb38\uc7a5 \uc790\uccb4\uac00 \uc9e7\uc740 \ube44\uc720\uc801 \uc0bd\uc785\uc774\ubbc0\ub85c \ud30c\uc2a4\uce7c\uc758 \uc644\uc131\ub41c \uc74c\uc218 \uc774\ub860\ucc98\ub7fc \uacfc\ub300\ud574\uc11d\ud558\uc9c0 \uc54a\ub294 \ud3b8\uc774 \uc548\uc804\ud558\ub2e4<a class=\"math-abs-series-ref\" title=\"Pascal, B. (1670). Pens\u00e9es, Lafuma 199 \/ Sellier 230, \u201cTransition\u201d, fragment 4. Critical text; commentary.\" href=\"#ref-Pascal1670\">[Pascal1670]<\/a>.]<\/p>\n<p>18\uc138\uae30 \ub9d0 \uc601\uad6d\uc758 \uc70c\ub9ac\uc5c4 \ud504\ub80c\ub4dc(William Frend)\ub294 \u201c\ub300\uc218\ud559\uc758 \uc6d0\ub9ac\u201d\uc5d0\uc11c \u2018\uc544\ubb34\uac83\ub3c4 \uc5c6\ub294 \uac83\ubcf4\ub2e4 \uc791\uc740 \uc218\u2019\ub97c \ubc30\uaca9\ud558\uace0, \ube84\uc148\uc5d0\uc11c \ube7c\ub294 \uc218\uac00 \ube7c\uc784\uc744 \ub2f9\ud558\ub294 \uc218\ubcf4\ub2e4 \ud070 \uacbd\uc6b0\ub97c \uc218 \uc790\uccb4\uc758 \uacb0\uacfc\ub85c \uc778\uc815\ud558\uc9c0 \uc54a\uc73c\ub824 \ud588\ub2e4<a class=\"math-abs-series-ref\" title=\"Frend, W. (1796). The Principles of Algebra. J. Davis for G. G. and J. Robinson. Internet Archive.\" href=\"#ref-Frend1796\">[Frend1796, pp. x\u2013xi]<\/a>. \uc774 \uc0ac\ub840\ub294 \uc74c\uc218\uac00 \uc774\ubbf8 \ub110\ub9ac \uacc4\uc0b0\uc5d0 \uc4f0\uc774\ub358 \uc2dc\uae30\uc5d0\ub3c4 \uadf8 \uc758\ubbf8\uc640 \uae30\ucd08\ub97c \ub458\ub7ec\uc2fc \ubc18\ub300\uac00 \ub0a8\uc544 \uc788\uc5c8\uc74c\uc744 \ubcf4\uc5ec\uc900\ub2e4. <!-- \uadf8\ub7ec\ub098 \ud55c \uc800\uc790\uc758 \ubc18\ub300\uac00 \ub2f9\uc2dc \u2018\uc11c\uad6c \uc218\ud559\uacc4 \uc804\uccb4\u2019\uc758 \ud569\uc758\ub97c \ub300\ud45c\ud55c\ub2e4\uace0 \ub9d0\ud574\uc11c\ub294 \uc548 \ub41c\ub2e4. --><\/p>\n<p><!--\n[\ud504\ub80c\ub4dc\uc758 \ucc45\uc758 \uc815\uc2dd \uc11c\uba85\uc740 <i>The Principles of Algebra<\/i>(1796)\uc774\ub2e4. \ud6d7\ub0a0 \uc218\ud559\uc790\uc774\uc790 \ub17c\ub9ac\ud559\uc790\uc778 \uc624\uac70\uc2a4\ud130\uc2a4 \ub4dc\ubaa8\ub974\uac04(Augustus De Morgan)\uc740 \ud504\ub80c\ub4dc\uc758 \ub9cf\ub538 \uc18c\ud53c\uc544 \uc5d8\ub9ac\uc790\ubca0\uc2a4 \ud504\ub80c\ub4dc\uc640 1837\ub144\uc5d0 \uacb0\ud63c\ud588\uc73c\ubbc0\ub85c, \ud504\ub80c\ub4dc\uc758 \uc0ac\uc704\uac00 \ub418\uc5c8\ub2e4<a class=\"math-abs-series-ref\" title=\"Frend, W. (1796). The Principles of Algebra. J. Davis for G. G. and J. Robinson. Internet Archive.\" href=\"#ref-Frend1796\">[Frend1796]<\/a><a class=\"math-abs-series-ref\" title=\"Richards, J. L. (2024). De Morgan's family: Sophia and the children. In Augustus De Morgan, Polymath. Open Book Publishers.\" href=\"#ref-Richards2024\">[Richards2024, Ch. 9]<\/a>. \uc774 \uac00\uc871 \uad00\uacc4\ub294 \ud765\ubbf8\ub85c\uc6b4 \ud6c4\uc77c\ub2f4\uc774\uc9c0\ub9cc \uc74c\uc218\uc758 \uc5ed\uc0ac\uc5d0 \ub300\ud55c \ub17c\uac70 \uc790\uccb4\ub294 \uc544\ub2c8\ub2e4.]<\/p>\n\n\n--><\/p>\n<p>\uc774 \uae34 \uc5ed\uc0ac\uc758 \uad50\ud6c8\uc740 \uc74c\uc218\uac00 \uc5b4\ub290 \ub0a0 \ucca0\ud559\uc801 \ubc18\ub300\ub97c \uc774\uae30\uace0 \uac11\uc790\uae30 \u2018\uc9c4\uc9dc \uc218\u2019\uac00 \ub418\uc5c8\ub2e4\ub294 \ub370 \uc788\uc9c0 \uc54a\ub2e4. \ubd80\ucc44\uc640 \ubc18\ub300 \ubc29\ud5a5 \uac19\uc740 \ud574\uc11d, \uacc4\uc0b0 \uaddc\uce59\uc758 \uc548\uc815\ud654, \ubc29\uc815\uc2dd \uc774\ub860, \uc218\uc9c1\uc120\uacfc \uae30\ud558\uc801 \ud45c\ud604, \ub300\uc218 \ubc95\uce59\uc758 \uc77c\ubc18\ud654\uac00 \uc11c\ub85c \ub2e4\ub978 \uc2dc\uae30\uc640 \uc7a5\uc18c\uc5d0\uc11c \ucd95\uc801\ub418\uc5c8\ub2e4. \u2018\uc218\uc758 \uc0ac\uc6a9\u2019, \u2018\ud574\uc758 \ud5c8\uc6a9\u2019, \u2018\uc874\uc7ac\ub860\uc801 \uc9c0\uc704\u2019\uac00 \uc5b4\uae0b\ub0a0 \uc218 \uc788\uc5c8\uae30 \ub54c\ubb38\uc5d0 \uce74\ub974\ub2e4\ub178\uc640 \ub370\uce74\ub974\ud2b8\ub294 \ubd80\uc815\uc801\uc778 \uba85\uce6d\uc744 \uc4f0\uba74\uc11c\ub3c4 \uc74c\uc218\ub97c \uacc4\uc0b0\ud560 \uc218 \uc788\uc5c8\ub2e4<a class=\"math-abs-series-ref\" title=\"Rabouin, D. (2024). Negatives as fictions in 16th and 17th century mathematics. Historia Mathematica, 69, 41\u201361.\" href=\"#ref-Rabouin2024\">[Rabouin2024]<\/a>. <a href=\"..\/math-abstraction-03-algebraic-symbols\/\">3\ubd80<\/a>\uc5d0\uc11c \ub2e4\ub8f0 \uae30\ud638\ub300\uc218\uc758 \uc804\uac1c\ub294 \uc774 \ubcc0\ud654\uc758 \uc911\uc694\ud55c \uc77c\ubd80\uc774\uc9c0\ub9cc \uc720\uc77c\ud55c \uc6d0\uc778\uc740 \uc544\ub2c8\ub2e4.<\/p>\n<h4>\ubb34\uc5c7\uc744 \ubc84\ub838\uace0, \ubb34\uc5c7\uc774 \ub0a8\uc558\ub294\uac00<\/h4>\n<p><!-- \uc774 \uae00\uc5d0\uc11c\ub294 \uace0\ub300 \uc218\ud559\uc744 \u2018\ucd94\uc0c1\ud654\ub97c \ubaa8\ub974\ub358 \uc2dc\ub300\u2019\ub77c\uace0 \ub2e8\uc815\ud558\ub294 \ub300\uc2e0, \ucd94\uc0c1\uc801 \uc2e4\ucc9c, \ucca0\ud559\uc801 \uc124\uba85, \ud615\uc2dd\uc801 \ubc29\ubc95\ub860\uc744 \uad6c\ubd84\ud588\ub2e4. -->\uba54\uc18c\ud3ec\ud0c0\ubbf8\uc544\uc758 \ud1a0\ud070\uacfc \uc6d0\uc2dc \uc124\ud615\ubb38\uc790\ub294 \ubb3c\ud488 \uad00\ub9ac \uc18d\uc5d0\uc11c \uc218\ub7c9 \uc815\ubcf4\ub97c \ubb3c\uc9c8\uc801\uc73c\ub85c \ud45c\ud604\ud558\uace0 \uc7ac\uc870\ud569\ud55c \uacfc\uc815\uc744 \ubcf4\uc5ec\uc8fc\uc9c0\ub9cc, \u2018\uad6c\uccb4\uc801 \uc148\uc5d0\uc11c \uc21c\uc218\ud55c \uc218\uac00 \ud55c \ubc88\uc5d0 \ud0c4\uc0dd\ud588\ub2e4\u2019\ub294 \ub2e8\uc120\uc801 \uc11c\uc0ac\ub294 \ub17c\uc7c1\uc801\uc774\ub2e4. \uc774\uc9d1\ud2b8\uc640 \ubc14\ube4c\ub85c\ub2c8\uc544\uc758 \ubb38\uc81c \ubb38\ud5cc\uc740 \uc77c\ubc18\uc2dd\uc744 \uba85\uc2dc\ud558\uc9c0 \uc54a\uc73c\uba74\uc11c\ub3c4 \uc608\uc81c\uc758 \ubc30\uc5f4, \ubc18\ubcf5 \uac00\ub2a5\ud55c \uc808\ucc28, \uac80\uc0b0\uacfc \uae30\ud558\uc801 \uc870\uc791\uc744 \ud1b5\ud574 \ubc29\ubc95\uc744 \uc804\ub2ec\ud588\ub2e4.<\/p>\n<p>\uadf8\ub9ac\uc2a4\uc758 \uc5f0\uc5ed\uc801 \uc218\ud559\uc740 \ubb38\uc790 \ub3c4\ud615\uc5d0\uc11c \uc6b0\uc5f0\ud55c \ud2b9\uc9d5\uacfc \ub17c\uc99d\uc5d0 \ud5c8\uc6a9\ub418\ub294 \ud2b9\uc9d5\uc744 \uad6c\ubd84\ud558\ub294 \uac15\ub825\ud55c \uad00\ud589\uc744 \ubc1c\uc804\uc2dc\ucf30\ub2e4. \uc720\ud074\ub9ac\ub4dc \uba85\uc81c 1\uc758 \uad50\uc810 \ub2e8\uacc4\ub294 \ud604\ub300\uc801 \uacf5\ub9ac \uae30\uc900\uc5d0\uc11c\ub294 \ubcf4\uc644\uc774 \ud544\uc694\ud558\uc9c0\ub9cc, \uace0\ub300\uc758 \ud1b5\uc81c\ub41c \ub3c4\ud574 \ucd94\ub860 \uc548\uc5d0\uc11c\ub294 \uc815\ub2f9\ud55c \ub2e8\uacc4\uc600\ub2e4. \ud50c\ub77c\ud1a4\uacfc \uc544\ub9ac\uc2a4\ud1a0\ud154\ub808\uc2a4\ub294 \uac10\uac01\uc801 \uadf8\ub9bc, \uc0ac\ubb3c\uacfc \uc218\ud559\uc801 \uc0ac\uace0 \ub300\uc0c1\uc758 \uad00\uacc4\ub97c \uba85\uc2dc\uc801\uc73c\ub85c \uc774\ub860\ud654\ud588\ub2e4. <!-- \uadf8\ub7ec\ubbc0\ub85c \uace0\ub300\uc5d0 \ucd94\uc0c1\ud654\uc758 \ucca0\ud559\uc801 \uc790\uac01\uc774 \uc804\ud600 \uc5c6\uc5c8\ub2e4\uace0 \ub9d0\ud560 \uc218\ub294 \uc5c6\uc73c\uba70, \ub2e4\ub9cc \uadf8 \uc790\uac01\uc774 \uc624\ub298\ub0a0\uc758 \ud615\uc2dd\uc801 \uad6c\uc131 \uaddc\uce59\uacfc \ub3d9\uc77c\ud558\uc9c0 \uc54a\uc558\ub2e4\uace0 \ud574\uc57c \ud55c\ub2e4. --> \uace0\ub300 \uc5ed\uc2dc \ucd94\uc0c1\ud654\uc5d0 \ub300\ud558\uc5ec \ucca0\ud559\uc801\uc73c\ub85c \uc790\uac01\ud558\uace0 \uc788\uc5c8\uc73c\ub098, \uadf8 \ubc29\uc2dd\uc774 \uc624\ub298\ub0a0\uc758 \ud615\uc2dd\uc801 \uaddc\uce59\uacfc \ub2ec\ub790\ub2e4.<\/p>\n<p>0\uacfc \uc74c\uc218\uc758 \uc0ac\ub840\ub3c4 \ud558\ub098\uc758 \ubb38\ud654\uac00 \uba3c\uc800 \u2018\ud569\ub9ac\uc801\u2019\uc774\uc5c8\uace0 \ub2e4\ub978 \ubb38\ud654\uac00 \ucca0\ud559 \ub54c\ubb38\uc5d0 \ucc9c \ub144 \ub3d9\uc548 \uba48\ucdc4\ub2e4\ub294 \ub3c4\uc2dd\ubcf4\ub2e4 \ubcf5\uc7a1\ud558\ub2e4. \uc790\ub9ac\ud45c\uc2dc\uc790, \uacc4\uc0b0 \uc911\uc758 \ubd80\ud638 \uc788\ub294 \uc591, \ubc29\uc815\uc2dd\uc758 \ud5c8\uc6a9\ub418\ub294 \ud574, \ub3c5\ub9bd\ub41c \uc218\ub77c\ub294 \uc9c0\uc704\ub294 \uc11c\ub85c \ub2e4\ub978 \ubb38\uc81c\uc600\ub2e4. \uc5ec\ub7ec \uc804\ud1b5\uc5d0\uc11c \uacc4\uc0b0 \uaddc\uce59\uacfc \ud45c\ud604\ubc95\uc774 \uba3c\uc800 \uc548\uc815\ub418\uace0, \uadf8 \uc758\ubbf8\uc640 \uae30\ucd08\uc5d0 \ub300\ud55c \uc124\uba85\uc740 \ub4a4\ub530\ub974\uac70\ub098 \uacbd\uc7c1\ud588\ub2e4. \uc774 \uac04\uadf9\uc740 \ucd94\uc0c1\uc801 \ub300\uc0c1\uc774 \ud604\uc2e4\uc758 \ubb34\uc5c7\uc744 \ub2ee\uc558\ub294\uac00\ubfd0 \uc544\ub2c8\ub77c, \uc5b4\ub5a4 \uaddc\uce59 \uc548\uc5d0\uc11c \uc5b4\ub5a4 \uc5ed\ud560\uc744 \uc77c\uad00\ub418\uac8c \uc218\ud589\ud558\ub294\uac00\ub97c \ubb3b\uac8c \ub9cc\ub4e0\ub2e4.<\/p>\n<p><a href=\"..\/math-abstraction-03-algebraic-symbols\/\">3\ubd80<\/a>\uc5d0\uc11c\ub294 \ube44\uc5d0\ud2b8(Fran\u00e7ois Vi\u00e8te), \ud53c\ucf55(George Peacock), \ud574\ubc00\ud134(William Rowan Hamilton)\uc774 \uc11c\ub85c \ub2e4\ub978 \ubb38\uc81c\uc640 \uc815\ub2f9\ud654 \ubc29\uc2dd \uc18d\uc5d0\uc11c \uae30\ud638\ub300\uc218\ub97c \ubcc0\ud654\uc2dc\ud0a8 \uacfc\uc815\uc744 \uc0b4\ud3b4\ubcf8\ub2e4. \ubbf8\uc9c0\uc218\uc640 \uacc4\uc218\ub97c \ubb38\uc790\ub85c \ud45c\ud604\ud558\ub294 \uc77c, \uae30\ud638 \uc5f0\uc0b0\uc758 \ud5c8\uc6a9 \ubc94\uc704\ub97c \uc124\uba85\ud558\ub294 \uc77c, \uc0c8\ub85c\uc6b4 \uc218 \uccb4\uacc4\ub97c \uad6c\uc131\ud558\ub294 \uc77c\uc740 \ud55c \ubc88\uc758 \uc120\uc5b8\uc73c\ub85c \uc644\uc131\ub41c \ub3d9\uc77c\ud55c \uc0ac\uac74\uc774 \uc544\ub2c8\uc5c8\ub2e4. \ub2e4\uc74c \uae00\uc5d0\uc11c\ub294 \uc774 \ucc28\uc774\ub97c \uad6c\ubd84\ud558\uba70 \ucd94\uc0c1\ud654\uac00 \uc810\ucc28 \uba85\uc2dc\uc801\uc778 \uc218\ud559\uc801 \ubc29\ubc95\uc73c\ub85c \uc790\ub9ac \uc7a1\ub294 \uacfc\uc815\uc744 \ub2e4\ub8ec\ub2e4.<\/p>\n<h4>\ucc38\uace0\ubb38\ud5cc<\/h4>\n<ul>\n<li id=\"ref-Aristotle1998\">[Aristotle1998] Aristotle. (1998). <i>The Metaphysics<\/i> (H. Lawson-Tancred, Trans.). Penguin Classics. <a href=\"https:\/\/books.google.com\/books?id=AdoSOFVYSO0C\">Google Books<\/a>.<\/li>\n<li id=\"ref-Aristotle2018\">[Aristotle2018] Aristotle. (2018). <i>Physics<\/i> (C. D. C. Reeve, Trans.). Hackett Publishing. <a href=\"https:\/\/hackettpublishing.com\/physics\">Publisher page<\/a>.<\/li>\n<li id=\"ref-BeesonEtAl2019\">[BeesonEtAl2019] Beeson, M., Narboux, J., &amp; Wiedijk, F. (2019). Proof-checking Euclid. <i>Annals of Mathematics and Artificial Intelligence<\/i>, 85(2\u20134), 213\u2013257. <a href=\"https:\/\/doi.org\/10.1007\/s10472-018-9606-x\">https:\/\/doi.org\/10.1007\/s10472-018-9606-x<\/a>.<\/li>\n<li id=\"ref-BennisonChapman2019\">[BennisonChapman2019] Bennison-Chapman, L. E. (2019). Reconsidering \u201ctokens\u201d: The Neolithic origins of accounting or multifunctional, utilitarian tools? <i>Cambridge Archaeological Journal<\/i>, 29(2), 233\u2013259. <a href=\"https:\/\/doi.org\/10.1017\/S0959774318000513\">https:\/\/doi.org\/10.1017\/S0959774318000513<\/a>.<\/li>\n<li id=\"ref-Chace1927\">[Chace1927] Chace, A. B., Bull, L., Manning, H. P., &amp; Archibald, R. C. (1927). <i>The Rhind Mathematical Papyrus: British Museum 10057 and 10058<\/i> (Vol. I). Mathematical Association of America. <a href=\"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/7\/7b\/The_Rhind_Mathematical_Papyrus%2C_Volume_I.pdf\">Public-domain PDF<\/a>.<\/li>\n<li id=\"ref-Cleary1985\">[Cleary1985] Cleary, J. J. (1985). On the terminology of \u201cabstraction\u201d in Aristotle. <i>Phronesis<\/i>, 30(1), 13\u201345. <a href=\"https:\/\/doi.org\/10.1163\/156852885X00165\">https:\/\/doi.org\/10.1163\/156852885X00165<\/a>.<\/li>\n<li id=\"ref-Colebrooke1817\">[Colebrooke1817] Brahmagupta &amp; Bh\u0101skara. (1817). <i>Algebra, with Arithmetic and Mensuration, from the Sanscrit of Brahmegupta and Bh\u00e1scara<\/i> (H. T. Colebrooke, Trans.). John Murray. <a href=\"https:\/\/archive.org\/details\/algebrawitharith00brahuoft\">Internet Archive<\/a>.<\/li>\n<li id=\"ref-DeRisi2021\">[DeRisi2021] De Risi, V. (2021). Gapless lines and gapless proofs: Intersections and continuity in Euclid\u2019s <i>Elements<\/i>. <i>Apeiron<\/i>, 54(2), 233\u2013259. <a href=\"https:\/\/doi.org\/10.1515\/apeiron-2019-0012\">https:\/\/doi.org\/10.1515\/apeiron-2019-0012<\/a>.<\/li>\n<li id=\"ref-Euclid2008\">[Euclid2008] Euclid. (2008). <i>Euclid\u2019s Elements of Geometry<\/i> (R. Fitzpatrick, Trans.). <a href=\"https:\/\/farside.ph.utexas.edu\/Books\/Euclid\/Elements.pdf\">https:\/\/farside.ph.utexas.edu\/Books\/Euclid\/Elements.pdf<\/a>.<\/li>\n<li id=\"ref-Frend1796\">[Frend1796] Frend, W. (1796). <i>The Principles of Algebra<\/i>. J. Davis for G. G. and J. Robinson. <a href=\"https:\/\/archive.org\/details\/principlesalgeb00frengoog\">Internet Archive<\/a>.<\/li>\n<li id=\"ref-Heath1921\">[Heath1921] Heath, T. L. (1921). <i>A History of Greek Mathematics<\/i> (Vol. I). Clarendon Press. Reissued by Cambridge University Press. <a href=\"https:\/\/doi.org\/10.1017\/CBO9781139600576.006\">Chapter on Thales<\/a>.<\/li>\n<li id=\"ref-Hettle2015\">[Hettle2015] Hettle, C. (2015). The symbolic and mathematical influence of Diophantus\u2019s <i>Arithmetica<\/i>. <i>Journal of Humanistic Mathematics<\/i>, 5(1), 139\u2013166. <a href=\"https:\/\/doi.org\/10.5642\/jhummath.201501.08\">https:\/\/doi.org\/10.5642\/jhummath.201501.08<\/a>.<\/li>\n<li id=\"ref-Hilbert1902\">[Hilbert1902] Hilbert, D. (1902). <i>The Foundations of Geometry<\/i> (E. J. Townsend, Trans.). Open Court. (Original work published 1899.) <a href=\"https:\/\/math.berkeley.edu\/~wodzicki\/160\/Hilbert.pdf\">Digital edition<\/a>.<\/li>\n<li id=\"ref-Hoyrup2002\">[H\u00f8yrup2002] H\u00f8yrup, J. (2002). <i>Lengths, Widths, Surfaces: A Portrait of Old Babylonian Algebra and Its Kin<\/i>. Springer. <a href=\"https:\/\/doi.org\/10.1007\/978-1-4757-3685-4\">https:\/\/doi.org\/10.1007\/978-1-4757-3685-4<\/a>.<\/li>\n<li id=\"ref-Imhausen2016\">[Imhausen2016] Imhausen, A. (2016). <i>Mathematics in Ancient Egypt: A Contextual History<\/i>. Princeton University Press. <a href=\"https:\/\/doi.org\/10.2307\/j.ctt1q1xs5f\">https:\/\/doi.org\/10.2307\/j.ctt1q1xs5f<\/a>.<\/li>\n<li id=\"ref-Mancosu2016\">[Mancosu2016] Mancosu, P. (2016). <i>Abstraction and Infinity<\/i>. Oxford University Press. <a href=\"https:\/\/global.oup.com\/academic\/product\/abstraction-and-infinity-9780198746829\">Publisher page<\/a>.<\/li>\n<li id=\"ref-Manders2008\">[Manders2008] Manders, K. (2008). The Euclidean diagram. In P. Mancosu (Ed.), <i>The Philosophy of Mathematical Practice<\/i> (pp. 80\u2013133). Oxford University Press. <a href=\"https:\/\/doi.org\/10.1093\/acprof:oso\/9780199296453.003.0005\">https:\/\/doi.org\/10.1093\/acprof:oso\/9780199296453.003.0005<\/a>.<\/li>\n<li id=\"ref-Mendell2016\">[Mendell2016] Mendell, H. (2016). Aristotle and mathematics. In E. N. Zalta (Ed.), <i>The Stanford Encyclopedia of Philosophy<\/i> (Fall 2016 ed.). <a href=\"https:\/\/plato.stanford.edu\/archives\/fall2016\/entries\/aristotle-mathematics\/\">https:\/\/plato.stanford.edu\/archives\/fall2016\/entries\/aristotle-mathematics\/<\/a>.<\/li>\n<li id=\"ref-Netz1999\">[Netz1999] Netz, R. (1999). <i>The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History<\/i>. Cambridge University Press. <a href=\"https:\/\/doi.org\/10.1017\/CBO9780511543296\">https:\/\/doi.org\/10.1017\/CBO9780511543296<\/a>.<\/li>\n<li id=\"ref-Nissen1993\">[Nissen1993] Nissen, H. J., Damerow, P., &amp; Englund, R. K. (1993). <i>Archaic Bookkeeping: Early Writing and Techniques of Economic Administration in the Ancient Near East<\/i> (P. Larsen, Trans.). University of Chicago Press. <a href=\"https:\/\/books.google.com\/books?id=YBAzXV4YtQ8C\">Google Books<\/a>.<\/li>\n<li id=\"ref-Overmann2018\">[Overmann2018] Overmann, K. A. (2018). Updating the \u201cabstract\u2013concrete\u201d distinction in ancient Near Eastern numbers. <i>Cuneiform Digital Library Journal<\/i>, 2018(1), 1\u201322. <a href=\"https:\/\/cdli.earth\/articles\/cdlj\/2018-1\">https:\/\/cdli.earth\/articles\/cdlj\/2018-1<\/a>.<\/li>\n<li id=\"ref-Pasch1882\">[Pasch1882] Pasch, M. (1882). <i>Vorlesungen \u00fcber neuere Geometrie<\/i>. B. G. Teubner. <a href=\"https:\/\/archive.org\/details\/in.ernet.dli.2015.153742\">Internet Archive<\/a>.<\/li>\n<li id=\"ref-Pascal1670\">[Pascal1670] Pascal, B. (1670). <i>Pens\u00e9es<\/i>, Lafuma 199 \/ Sellier 230, \u201cTransition\u201d, fragment 4. <a href=\"https:\/\/www.penseesdepascal.fr\/Transition\/P-R-Transition4.php\">Critical text<\/a>; <a href=\"https:\/\/www.penseesdepascal.fr\/Transition\/Transition4-appro355.php\">commentary<\/a>.<\/li>\n<li id=\"ref-PlatoMeno\">[PlatoMeno] Plato. <i>Meno<\/i> (B. Jowett, Trans.), 81a\u201386c. <a href=\"https:\/\/classics.mit.edu\/Plato\/meno.html\">MIT Classics Archive<\/a>.<\/li>\n<li id=\"ref-PlatoRepublic\">[PlatoRepublic] Plato. <i>Republic<\/i>, 510d\u2013511a. D. Horan (Trans.). <a href=\"https:\/\/www.platonicfoundation.org\/translation\/republic\/\">Plato\u2019s Republic online translation<\/a>.<\/li>\n<li id=\"ref-Rabouin2024\">[Rabouin2024] Rabouin, D. (2024). Negatives as fictions in 16th and 17th century mathematics. <i>Historia Mathematica<\/i>, 69, 41\u201361. <a href=\"https:\/\/doi.org\/10.1016\/j.hm.2024.09.004\">https:\/\/doi.org\/10.1016\/j.hm.2024.09.004<\/a>.<\/li>\n<li id=\"ref-Richards2024\">[Richards2024] Richards, J. L. (2024). De Morgan\u2019s family: Sophia and the children. In <i>Augustus De Morgan, Polymath<\/i>. Open Book Publishers. <a href=\"https:\/\/doi.org\/10.11647\/obp.0408.09\">https:\/\/doi.org\/10.11647\/obp.0408.09<\/a>.<\/li>\n<li id=\"ref-Ritter2024\">[Ritter2024] Ritter, J. (2024). Babylonian zeros. In P. Gobets &amp; R. L. Kuhn (Eds.), <i>The Origin and Significance of Zero: An Interdisciplinary Perspective<\/i> (pp. 35\u201363). Brill. <a href=\"https:\/\/doi.org\/10.1163\/9789004691568_006\">https:\/\/doi.org\/10.1163\/9789004691568_006<\/a>.<\/li>\n<li id=\"ref-SchmandtBesserat1984\">[SchmandtBesserat1984] Schmandt-Besserat, D. (1984). Before numerals. <i>Visible Language<\/i>, 18(1), 48\u201360. <a href=\"https:\/\/journals.uc.edu\/index.php\/vl\/article\/view\/5376\">https:\/\/journals.uc.edu\/index.php\/vl\/article\/view\/5376<\/a>.<\/li>\n<li id=\"ref-SchmandtBesserat1992\">[SchmandtBesserat1992] Schmandt-Besserat, D. (1992). <i>Before Writing<\/i> (2 vols.). University of Texas Press. <a href=\"https:\/\/books.google.com\/books?id=_G74dDQO8gUC\">Google Books<\/a>.<\/li>\n<li id=\"ref-Shen1999\">[Shen1999] Shen, K., Crossley, J. N., &amp; Lun, A. W.-C. (1999). <i>The Nine Chapters on the Mathematical Art: Companion and Commentary<\/i>. Oxford University Press. <a href=\"https:\/\/books.google.com\/books?id=eiTJHRGTG6YC\">Google Books<\/a>.<\/li>\n<li id=\"ref-Silverman2022\">[Silverman2022] Silverman, A. (2022). Plato\u2019s middle period metaphysics and epistemology. In E. N. Zalta &amp; U. Nodelman (Eds.), <i>The Stanford Encyclopedia of Philosophy<\/i> (Fall 2022 ed.). <a href=\"https:\/\/plato.stanford.edu\/archives\/fall2022\/entries\/plato-metaphysics\/\">https:\/\/plato.stanford.edu\/archives\/fall2022\/entries\/plato-metaphysics\/<\/a>.<\/li>\n<li id=\"ref-Woods2010\">[Woods2010] Woods, C. (Ed.). (2010). <i>Visible Language: Inventions of Writing in the Ancient Middle East and Beyond<\/i>. Oriental Institute of the University of Chicago. <a href=\"https:\/\/isac.uchicago.edu\/sites\/default\/files\/uploads\/shared\/docs\/oimp32.pdf\">Official PDF<\/a>.<\/li>\n<\/ul>\n<h4>\uc800\uc791\uad8c<\/h4>\n<p>\uc774\uc2ac\ube44, 2026. designeralice\uff20daum.net.<\/p>\n<div class=\"math-abs-series-contents\">\n<p class=\"math-abs-series-menu-title\"><a href=\"..\/\">\uc218\ud559\uc801 \ucd94\uc0c1\ud654<\/a><\/p>\n<ol class=\"math-abs-series-menu-list\">\n        <!-- \ud604\uc7ac \ud398\uc774\uc9c0\uc5d0 \ud574\ub2f9\ud558\ub294 li \ud0dc\uadf8\uc5d0 class=\"math-abs-series-current-page\" \uc18d\uc131 \ucd94\uac00 --><\/p>\n<li><a href=\"..\/math-abstraction-01-essence\/\">\uc218\ud559\uc801 \ucd94\uc0c1\ud654\uc758 \uae30\ubcf8 \uac1c\ub150<\/a><\/li>\n<li class=\"math-abs-series-current-page\"><a href=\"..\/math-abstraction-02-implicit-era\/\">\ucd08\uae30 \uc218\ud559\uc5d0\uc11c\uc758 \uc554\ubb35\uc801 \ucd94\uc0c1\ud654<\/a><\/li>\n<li><a href=\"..\/math-abstraction-03-algebraic-symbols\/\">\ub300\uc218\uc801 \uae30\ud638\uc640 \uc5f0\uc0b0 \ubc95\uce59<\/a><\/li>\n<li><a href=\"..\/math-abstraction-04-axiomatic-method\/\">\uacf5\ub9ac\uc801 \ubc29\ubc95\uc5d0 \uc758\ud55c \ucd94\uc0c1\ud654<\/a><\/li>\n<li><a href=\"..\/math-abstraction-05-mathematical-structures\/\">\uc218\ud559\uc801 \uad6c\uc870\uc640 \ubc94\uc8fc\ub860<\/a><\/li>\n<li><a href=\"..\/math-abstraction-06-vector-spaces\/\">\ubca1\ud130\uacf5\uac04\uacfc \uc120\ud615 \uad6c\uc870<\/a><\/li>\n<li><a href=\"..\/math-abstraction-07-topological-spaces\/\">\uac70\ub9ac\uacf5\uac04\uacfc \uc704\uc0c1\uacf5\uac04<\/a><\/li>\n<li><a href=\"..\/math-abstraction-08-measure-spaces\/\">\uce21\ub3c4\uacf5\uac04\uacfc \ud655\ub960\uacf5\uac04<\/a><\/li>\n<li><a href=\"..\/math-abstraction-09-cognitive-process\/\">\uc218\ud559\uc801 \ucd94\uc0c1\ud654\uc758 \uc778\uc9c0\uc640 \ud559\uc2b5<\/a><\/li>\n<li><a href=\"..\/math-abstraction-10-optimal-generality\/\">\ud604\ub300 \uc218\ud559 \uc5f0\uad6c\uc5d0\uc11c\uc758 \ucd94\uc0c1\ud654<\/a><\/li>\n<li><a href=\"..\/math-abstraction-11-topography\/\">\uc218\ud559\uc801 \ucd94\uc0c1\ud654\uc758 \ubc29\ubc95\uacfc \ucca0\ud559<\/a><\/li>\n<\/ol>\n<\/div>\n<\/div>\n<p><!-- class=\"math-abs-series\" --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\uc591 \ub2e4\uc12f \ub9c8\ub9ac\uc640 \uc0ac\uacfc \ub2e4\uc12f \uac1c\uc5d0\uc11c \ub3d9\uc77c\ud55c \u2018\ub2e4\uc12f\u2019\uc744 \uc54c\uc544\ubcf4\ub294 \uc77c\uc740 \uc624\ub298\ub0a0 \ub108\ubb34\ub098 \ub2f9\uc5f0\ud574 \ubcf4\uc778\ub2e4. 1\ubd80\uc5d0\uc11c \uc81c\uc2dc\ud55c \uad00\uc810\uc73c\ub85c \ub9d0\ud558\uba74, \uc774\ub54c \uc6b0\ub9ac\ub294 \ub300\uc0c1\uc758 \uc885\ub958\ub97c \uace0\ub824\uc5d0\uc11c \uc81c\uc678\ud558\uace0 \uc218\ub7c9\ub9cc\uc744 \ubcf4\uc874\ud55c\ub2e4. 1\ubd80\uc5d0\uc11c\ub294 \ucd94\uc0c1\ud654\ub97c \u2018\ub300\uc0c1\uc5d0\uc11c \ud2b9\uc815\ud55c \uc131\uc9c8\uc5d0 \uc8fc\ubaa9\ud558\uace0 \ub098\uba38\uc9c0\ub97c \uace0\ub824\uc5d0\uc11c \uc81c\uc678\ud558\uc5ec \uc0c8\ub85c\uc6b4 \uac1c\ub150\uc774\ub098 \ub300\uc0c1\uc744 \uaddc\uc815\ud558\ub294 \uc870\uc791\u2019\uc73c\ub85c \uc124\uba85\ud588\ub2e4. \ub3d9\uce58\ub958\ub97c \uc774\uc6a9\ud55c \ud604\ub300\uc801 \uad6c\uc131\uacfc \u2018\ucd94\uc0c1\uc5d0 \uc758\ud55c \uc815\uc758\u2019\uc5d0 \ub300\ud55c \ub17c\ub9ac\uc801 \ubd84\uc11d\uc740 \uc8fc\ub85c 19\uc138\uae30 \uc774\ud6c4\uc5d0 \uc815\uad50\ud574\uc84c\uc9c0\ub9cc, \uc11c\ub85c \ub2e4\ub978 \ub300\uc0c1\uc744 \uac19\uc740 \uc218\ub85c \uc138\uac70\ub098 \uac1c\ubcc4 \ub3c4\ud615\uc744 \ud1b5\ud574&hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":9726,"menu_order":200,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"class_list":["post-9737","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/9737","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/comments?post=9737"}],"version-history":[{"count":28,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/9737\/revisions"}],"predecessor-version":[{"id":10007,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/9737\/revisions\/10007"}],"up":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/9726"}],"wp:attachment":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/media?parent=9737"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}