几何原本

译者序 (1) 导读 (1)第 1 卷?几何基础 / 1定义 (2)公设 (4)公理 (4)命题I.1 (5)命题I.2 (7)命题I.3 (8)命题I.4 (9)命题I.5 (10)命题I.6 (12)命题I.7 (13)命题I.8 (14命题I.9 (15)命题I.10 (17)命题I.11 (18)命题I.12 (19)命题I.13 (19)命题I.14 (20)命题I.15 (21)命题I.16 (22)命题I.17 (24)命题I.18 (25)命题I.19 (26)命题I.20 (27)命题I.21 (28)命题I.22 (29)命题I.23 (30)命题I.24 (31)命题I.25 (32)命题I.26 (33)命题I.27 (35)命题I.28 (36)命题I.29 (37)命题I.30 (38)命题I.31 (39)命题I.32 (40)命题I.33 (41)命题I.34 (42)命题I.35 (43)命题I.36 (44)命题I.37 (45)命题I.38 (46)命题I.39 (47)命题I.40 (48)命题I.41 (49)命题I.42 (50)命题I.43 (51)命题I.44 (52)命题I.45 (53)命题I.46 (55)命题I.47 (56)命题I.48 (57)第2卷?几何与代数 / 59 命题II.1 (60)命题II.2 (61)命题II.3 (62)命题II.4 (63)命题II.5 (65)命题II.6 (66)命题II.7 (67)命题II.8 (68)命题II.9 (70)命题II.10 (71)命题II.11 (74)命题II.12 (75)命题II.13 (76)命题II.14 (77)第3卷?圆与角 / 79定义 (80)命题III.1 (80)命题III.2 (82)命题III.3 (83)命题III.4 (84)命题III.5 (85)命题III.6 (86)命题III.7 (86)命题III.8 (88)命题III.9 (90)命题III.10 (92)命题III.11 (93)命题III.12 (94)命题III.13 (95)命题III.14 (96)命题III.15 (98)命题III.16 (99)命题III.17 (101)命题III.18 (102)命题III.19 (103)命题III.20 (103)命题III.21 (104)命题III.22 (105)命题III.23 (106)命题III.24 (107)命题III.25 (108)命题III.26 (109)命题III.27 (110)命题III.28 (111)命题III.29 (112)命题III.30 (113)命题III.31 (114)命题III.32 (115)命题III.33 (116)命题III.34 (118)命题III.35 (119)命题III.36 (121)命题III.37 (123)第4卷?圆与正多边形 / 125定义 (126)命题IV.1 (126)命题IV.2 (127)命题IV.3 (128)命题IV.4 (129)海伦公式 (130)命题IV.5 (132)命题IV.6 (134)命题IV.7 (135)命题IV.8 (136)命题IV.9 (137)命题IV.10 (138)命题IV.11 (140)命题IV.12 (141)命题IV.13 (143)命题IV.14 (144)命题IV.15 (145)命题IV.16 (147)第5卷?比 例 / 149定义 (151)命题V.1 (152)命题V.2 (153)命题V.3 (154)命题V.4 (156)命题V.5 (157)命题V.6 (158)命题V.7 (160)命题V.8 (161)命题V.9 (162)命题V.10 (163)命题V.11 (165)命题V.12 (166)命题V.13 (167)命题V.14 (168)命题V.15 (169)命题V.16 (170)命题V.17 (171)命题V.18 (172)命题V.19 (173)命题V.20 (174)命题V.21 (175)命题V.22 (176)命题V.23 (177)命题V.24 (179)命题V.25 (180)第6卷?相 似 / 181定义? (182)命题VI.1 (182)命题VI.2 (184)命题VI.3 (185)命题VI.4 (187)命题VI.5 (188)命题VI.6 (189)命题VI.7 (191)命题VI.8 (192)命题VI.9 (193)命题VI.10 (194)命题VI.11 (195)命题VI.12 (196)命题VI.13 (197)命题VI.14 (197)命题VI.15 (199)命题VI.16 (200)命题VI.17 (201)命题VI.18 (202)命题VI.19 (204)命题VI.20 (205)命题VI.21 (208)命题VI.22 (208)命题VI.23 (210)命题VI.24 (211)命题VI.25 (213)命题VI.26 (214)命题VI.27 (215)命题VI.28 (216)命题VI.29 (218)命题VI.30 (220)命题VI.31 (221)命题VI.32 (222)命题VI.33 (223)第7卷?数 论（一） / 225定义 (226)命题VII.1 (227)命题VII.2 (228)命题VII.3 (230)命题VII.4 (232)命题VII.5 (233)命题VII.6 (234)命题VII.7 (235)命题VII.8 (236)命题VII.9 (237)命题VII.10 (238)命题VII.11 (239)命题VII.12 (240)命题VII.13 (240)命题VII.14 (241)命题VII.15 (242)命题VII.16 (243)命题VII.17 (243)命题VII.18 (244)命题VII.19 (245)命题VII.20 (246)命题VII.21 (247)命题VII.22 (248)命题VII.23 (249)命题VII.24 (249)命题VII.25 (250)命题VII.26 (251)命题VII.27 (252)命题VII.28 (253)命题VII.29 (254)命题VII.30 (255)命题VII.31 (256)命题VII.32 (257)命题VII.33 (257)命题VII.34 (259)命题VII.35 (260)命题VII.36 (261)命题VII.37 (262)命题VII.38 (263)命题VII.39 (264)第8卷?数 论（二） / 265命题VIII.1 (266)命题VIII.2 (267)命题VIII.3 (269)命题VIII.4 (270)命题VIII.5 (272)命题VIII.6 (273)命题VIII.7 (274)命题VIII.8 (274)命题VIII.9 (275)命题VIII.10 (277)命题VIII.11 (278)命题VIII.12 (279)命题VIII.13 (280)命题VIII.14 (281)命题VIII.15 (281)命题VIII.16 (283)命题VIII.17 (283)命题VIII.18 (284)命题VIII.19 (285)命题VIII.20 (287)命题VIII.21 (288)命题VIII.22 (290)命题VIII.23 (290)命题VIII.24? (291)命题VIII.25? (292)命题VIII.26? (292)命题VIII.27? (293)第9卷?数 论（三） / 295命题IX.1? (296)命题IX.2? (297)命题IX.3? (298)命题IX.4? (299)命题IX.5? (300)命题IX.6? (300)命题IX.7? (301)命题IX.8? (302)命题IX.9? (303)命题IX.10? (305)命题IX.11? (307)命题IX.12? (308)命题IX.13? (309)命题IX.14? (312)命题IX.15? (313)命题IX.16? (314)命题IX.17? (315)命题IX.18? (316)命题IX.19? (317)命题IX.20? (317)命题IX.21? (318)命题IX.22? (320)命题IX.23? (320)命题IX.24? (321)命题IX.25? (321)命题IX.26? (322)命题IX.27? (322)命题IX.28? (323)命题IX.29? (323)命题IX.30? (324)命题IX.31? (325)命题IX.32? (326)命题IX.33? (326)命题IX.34? (327)命题IX.35? (328)命题IX.36? (330)第10卷?无理量 / 333定义（一) (334)命题X.1? (336)命题X.2? (337)命题X.3? (338)命题X.4? (340)命题X.5? (341)命题X.6? (342)命题X.7? (344)命题X.8? (344)命题X.9? (345)命题X.10? (347)命题X.11? (348)命题X.12? (349)命题X.13? (350)命题X.14? (351)命题X.15? (352)命题X.16? (353)命题X.17? (355)命题X.18? (357)命题X.19? (359)命题X.20? (360)命题X.21? (361)命题X.22? (363)命题X.23? (365)命题X.24? (366)命题X.25? (367)命题X.26? (368)命题X.27? (370)命题X.28? (370)命题X.29? (373)命题X.30? (374)命题X.31? (375)命题X.32? 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(479)命题X.107? (479)命题X.108? (480)命题X.109? (481)命题X.110? (482)命题X.111? (484)命题X.112? (486)命题X.113? (488)命题X.114? (490)命题X.115? (491)第11卷?立体几何 / 493定义? (494)命题XI.1? (495)命题XI.2? (496)命题XI.3? (497)命题XI.4? (498)命题XI.5? (499)命题XI.6? (500)命题XI.7? (501)命题XI.8? (502)命题XI.9? (503)命题XI.10? (504)命题XI.11? (505)命题XI.12? (506)命题XI.13? (507)命题XI.14? (508)命题XI.15? (509)命题XI.16? (510)命题XI.17? (511)命题XI.18? (512)命题XI.19? (512)命题XI.20? (513)命题XI.21? (514)命题XI.22? (515)命题XI.23? (517)命题XI.24? (519)命题XI.25? (521)命题XI.26? (522)命题XI.27? (523)命题XI.28 (524)命题XI.29 (525)命题XI.30 (526)命题XI.31 (527)命题XI.32 (530)命题XI.33 (530)命题XI.34 (532)命题XI.35 (535)命题XI.36 (538)命题XI.37 (539)命题XI.38 (540)命题XI.39 (541)第12卷?立体的测量 / 543命题XII.1 (544)命题XII.2 (545)命题XII.3 (548)命题XII.4 (551)命题XII.5 (553)命题XII.6 (555)命题XII.7 (556)命题XII.8 (558)命题XII.9 (560)命题XII.10 (562)命题XII.11 (565)命题XII.12 (567)命题XII.13 (571)命题XII.14 (572)命题XII.15 (573)命题XII.16 (575)命题XII.17 (576)命题XII.18 (581)?第13卷?作正多面体 / 583命题XIII.1 (584)命题XIII.2 (585)命题XIII.3 (587)命题XIII.4 (588)命题XIII.5 (590)命题XIII.6 (591)命题XIII.7 (592)命题XIII.8 (593)命题XIII.9 (595)命题XIII.10 (596)命题XIII.11 (598)命题XIII.12 (601)命题XIII.13 (602)命题XIII.14 (604)命题XIII.15 (605)命题XIII.16 (607)命题XIII.17 (611)命题XIII.18 (615)附录：数学的历史年谱 / 620

《几何原本》的发行量仅次于《圣经》而位居世界第二。从两千多年前开始，就一直都是学习数学几何的主要教材。中的一题一图，并附有精美插画。经过了数次修订和改版，是最为读者首肯的最新版本。《几何原本》共有十三卷，其中第一卷讲三角形全等的条件，三角形边和角的大小关系，平行线理论，三角形和多角形面积相等的条件；第二卷讲如何把三角形变成面积相等的正方形；第三卷讲圆；第四卷讨论内接和外切多边形；第六卷讲相似多边形理论；第五、第七、第八、第九、第十卷讲述比例和算术的理论；最后讲述立体几何的内容。从这些内容可以看出，目前属于中学课程里的初等几何的主要内容已经完全包含在《几何原本》里了【作者简介】欧几里得（公元前325年—公元前265年），古希腊数学家，被称为“几何之父”。他活跃于托勒密一世时期的亚历山大里亚，他最著名的著作《几何原本》是欧洲数学的基础，总结了平面几何五大公设，被广泛的认为是历史上最成功的教科书。欧几里得也写了一些关于透视、圆锥曲线、球面几何学及数论的作品。译者简介：邹忌, 1977年生于上海,职业翻译人,毕业于中国邮电大学。致力于西方名著的翻译，尤以翻译科普读物成绩卓著。 译作有《笛卡尔哲学原理》、《自然哲学的数学原理》等。