Euclid and His Modern Rivals/Appendix IV.

by Charles L. Dodgson

 

 

APPENDIX IV.

 

List of Propositions of Euc. I, II, with references to their occurrence in the manuals of his Modern Rivals.

 

§ 1. References to Legendre, Cuthbertson, and Henrici.

 

Euclid	Legendre		Cuthbertson		Henrici
I	I	Page	I	Page		Page
Ax 10 Ax 11 Ax 12	Ax4 Th1 23	6 6„ 26	Ax Th 8 Cor	2 17	Ax4 Th Th„	22 58 72
1Pr 2Pr„ 3Pr„			PrA (p) (q)	11 74 75
4Th 5Th„ 5Cor 6Th 6Cor 7Th 8Th„	Th6 12 Cor Th13 Th11 Sch	10 14 14„ 15 14	Th1 2 4 (r) 5	4 5 7 76 8	Th Th	129 129
9Pr 10Pr„ 11Pr„ 12Pr„	Pr5 1 2 3	51 49 50 50„	PrB C 7 11	12 13 16 20

 

§ 1. References to Wilson, Pierce, and Willock.

 

Euclid	Wilson		Pierce		Willock
I	I	Page		Page		Page
Ax 10 Ax 11 Ax 12	Ax2 Th	3 7	§16Th	6	Th	10
1Pr 2Pr„ 3Pr„					§1 2 3	33 34 36
4Th 5Th„ 5Cor 6Th 6Cor 7Th 8Th„	Th16 8 Cor 10 Cor 18	26 21 „ 22 „ 28	§51, 52 55 56 58 59 60 61	15 16 17 „ „ 18 „	9 1 6 (1) 8	46 40 43 45
9Pr 10Pr„ 11Pr„ 12Pr„	Pr1 3 2 4	40 42 41 42	138 132 134 133	39 38 „ „	5 6 7 8	35 36 „ „
13Th 14Th„ 15Th„ 16 (a)Th„ (b)Th„ 17Th„ 18Th„ 19Th„ 20Th„ 21Th„	Th2 4 5 14 14„ 8 9	7 9 „ 15 „ 11 12	Th9 10 6 13 „ „ 14 15 16 17	18 19 14 22 „ 23 24 25 26 27	Th Th Th„ Th„	62 108 „ 109
	II
22Th 23Th„	Pr4	51	PrD E	30 31
	I
24Th 25Th„ 26 (a)Th„ (b)Th„	Th10 Sch 7	12 13 11	Th18 19 3 25 Cor	28 29 6 43	Th Th„ Th„	133 „ 129
27Th 28 (a)Th„ (b)Th„ 29 (a)Th„ (b)Th„ (c)Th„ 30Th	Th24 Sch Sch„ 22 24 Cor 2 Sch 24 25	28 „ 25 28 „ „ 29	Th20 20„ 20„ 21 21„ 21„ 22	36 37 „ 38 „ 39 40	Th Th„ Th„ Th„ Th„ Th„ Th„	71 „ „ „ „ „ 72
	II
31Pr	Pr6	52	Lemma	34
13Th 14Th„ 15Th„ 16 (a)Th„ (b)Th„ 17Th„ 18Th„ 19Th„ 20Th„ 21Th„	Th1 „ „ Th7 Cor 4 Cor„ 9 11 13 Th	8 „ 9 20 „ 21 22 24 35	§24 23 62 „ 40	8 7 18 „ 12	Th4 2 12 „ 6 6 (2) 7	11 10 13 „ 43 „ 44
22Th 23Th„	Pr5 5 Cor 1	43 44	143 136	40 39	1 9	54 37
24Th 25Th„ 26 (a)Th„ (b)Th„	Th17 19 16	27 29 26	63 54	19 16	12 12„ 10 11	47 „ 46 „
27Th 28 (a)Th„ (b)Th„ 29 (a)Th„ (b)Th„ (c)Th„ 30Th„
31Pr
	I
32 (a) Th (b)Th„ Cor 1 2 33Th 34 (a) Th„ (b)Th„	Th19 Cor 6 19 20 30 28 28„	23 20 23 32 30 31	Th24 24„ 30 Cor 30 23 26 26„	42 „ 49 48 41 44 „	Th Th„ Th„ Th„ Th„ Th„ Th„	81 „ 83 „ 121 120 „
35Th 36Th„ 37Th„ 38Th„ 39Th„ 40Th„ 41Th„			Th31 Cor Th32 Cor Cor„ 33 Cor 32	52 53 54 „ 55 „ 54
42Pr			PrL	59
43Th			Th34	56
44Pr 45Pr„ Cor 46Pr			PrM Cor N Cor Pr K	60 61 51
46Cor 47Th 48Th„	III Th11	71	Th27 35 36	45 57 58
32 (a) Th (b)Th„ Cor 1 2 33Th 34 (a) Th„ (b)Th„	Th7 „ 6Cor 6	20 „ 16 „	§71 65 72	21 20 21	Th14 Cor 1 14	15 14
35Th 36Th„ 37Th„ 38Th„ 39Th„ 40Th„ 41Th„
42Pr
43Th
44Pr 45Pr„ Cor 46Pr
46Cor 47Th 48Th„	29	63	256	74	14 18	84 88
II	III		II
1Th 2Th„ 3Th„ 4Th„ Cor 5Th Cor 6Th 7Th„ 8Th„ 9Th„ 10Th„	Th8 10 9	69 70 „	Th1 Cor 1 Cor 2 Th2 2 „ I Th(m) Cor	82 83 „ 84 84 85 72 „
			II
11Pr			PrB	89
12Th 13Th„	Th13 12	74 73	Th3 4	86 87
14Pr			PrB	88

|- style="text-align:center;" | style="border-right:4px double black;width:6em;;" | II | style="border-right:1px solid black;width:7em;;" | | style="border-right:4px double black;width:3em;;" | | style="border-right:1px solid black;width:7em;;" | | style="border-right:4px double black;width:3em;;" | | style="border-right:1px solid black;width:7em;;" | | style="width:3em;;" | |- style="vertical-align:top;" | style="border-right:4px double black;" | 1Th
2Th„
3Th„
4Th„
Cor
5Th
Cor
6Th
7Th
8Th„

9Th„
10Th„ | style="border-right:1px solid black;text-align:left;" |


Th25

27 Cor
27

26


28 | style="border-right:4px double black;" |


60

62
61

60


63 | style="border-right:1px solid black;text-align:left;" | | style="border-right:4px double black;" | | style="border-right:1px solid black;text-align:left;" |


Cor 3

10
6
11
5
9

12
13 |


74

82
76
83
75
78

83
84 |- style="vertical-align:top;" | style="border-top:1px solid black;border-right:4px double black;" | 11Pr | style="border-top:1px solid black;border-right:1px solid black;text-align:left;" | Ex3 | style="border-top:1px solid black;border-right:4px double black;" | 67 | style="border-top:1px solid black;border-right:1px solid black;text-align:left;" | | style="border-top:1px solid black;border-right:4px double black;" | | style="border-top:1px solid black;border-right:1px solid black;text-align:left;" | 14 | style="border-top:1px solid black;" | 104 |- style="vertical-align:top;" | style="border-right:4px double black;border-top:1px solid black;" | 12Th
13Th„ | style="border-right:1px solid black;border-top:1px solid black;text-align:left;" | Th31
30 | style="border-right:4px double black;border-top:1px solid black;" | 66
65 | style="border-right:1px solid black;border-top:1px solid black;text-align:left;" | | style="border-right:4px double black;border-top:1px solid black;" | | style="border-right:1px solid black;border-top:1px solid black;text-align:left;" | 16
17 | style="border-top:1px solid black;" | 87
88 |- style="vertical-align:top;" | style="border-right:4px double black;border-top:1px solid black;border-bottom:1px solid black;" | 14Pr | style="border-right:1px solid black;border-top:1px solid black;border-bottom:1px solid black;text-align:left;" | (4) | style="border-right:4px double black;border-top:1px solid black;border-bottom:1px solid black;" | 71 | style="border-right:1px solid black;border-top:1px solid black;border-bottom:1px solid black;text-align:left;" | §289 | style="border-right:4px double black;border-top:1px solid black;border-bottom:1px solid black;" | 84 | style="border-right:1px solid black;border-top:1px solid black;border-bottom:1px solid black;text-align:left;" | 3 | style="border-top:1px solid black;border-bottom:1px solid black;" | 96 |}

 

§ 2. References to the other Modern Rivals.

 

Euclid

Chauvenet

Loomis

'Syllabus'-
Manual

I

I

Page

I

Page

I

Page

Ax 10
Ax 11
Ax 12

Ax
 1Cor
14Cor 3

12
14
26

Ax11
 1Cor
23Cor 3

17
18
34

Def5
Th1

7
12

1Pr
2Pr„
3Pr„

4Th
5Th„
5Cor
6Th
6Cor
7Th
8Th„

20Th
25Th„
Cor
27Cor„
Cor

22Cor„

30
33
34
„
„

31

 6Th
10Th„
Cor 2
11Th„
Cor

15Cor„

22
24
25
„
„

27

Th5
6
Cor
8
Cor

15

18
20
„
22
„

28

9Pr
10Pr„
11Pr„
12Pr„

II
28Pr
25Pr„
26Pr„
27Pr„

78
76
77
„

V
5Pr
1Pr„
2Pr„
3Pr„

95
93
94
„

Pr1
4
2
3

61
63
62
„

13Th
14Th„
15Th„
16 (a)Th„
(b)Th„
17Th„
18Th„
19Th„
20Th„
21 (a)Th„
(b)Th„

I
2Th
3Th„
4Th„



26Th„
28Th„
17Th„

19Th„

15
17
„



34
35
29

30

I
2Th
3Th„
5Th„



12Th„
12„Th„
8Th„
9Th„

19
20
„



25
„
23
24

Th2
3
4
9
„
18
10
11
12
13

13
14
„
22
„
32
23
24
25
26

 

Euclid	Morell		Reynolds		Wright
I	I	Page	I	Page	I	Page
Ax 10 Ax 11 Ax 12	Ax Th1 Cor Th„25 Cor	1 5 26	Ax	2	Ax Th Th„16 Sch	1 6 35
1Pr 2Pr„ 3Pr„
4Th 5Th„ 5Cor 6Th 6Cor 7Th 8Th„	Th5 Th„10 Cor 1 Th„11 Cor Th„9	9 13 „ 14 15 12	Th14 Th„11 Cor 2 Th„12 Cor Th„13	15 12 „ 13 14	Th8(2) Th„9(3) Cor Th„9(1) Cor Th„8(3)	16 19 20 18 20 16
9Pr 10Pr„ 11Pr„ 12Pr„	Pr9 Pr„7	66 64	Pr2 Pr„1 Pr„3 Pr„„	30 29 31 „	II Pr9 Pr„8 Pr„11 Pr„11„	87 86 88 „
13Th 14Th„ 15Th„ 16 (a)Th„ (b)Th„ 17Th„ 18Th„ 19Th„ 20Th„ 21 (a)Th„ (b)Th„	Th2 Th„3 Th„4 Th„12 Th„12„ Th„8	6 7 8 15 „ 12	Th1 Th„„ Th„2 Th„10 Cor 2 Cor 2„ Th„12 Th„12„ Th„3 Th„4	3 „ 4 12 „ 13 „ 5 „	Th2 Th„3 Th„5 Th„9(4) Th„9(2) Th„ Th„6	8 „ 11 19 18 13 14
	II		V
22Pr 23Pr„	34Pr 29„	81 79	4Pr	95	Pr5 6	64 65
24Th 25Th„ 26 (a)Th„ (b)Th„	I 24Th Cor 21„	33 „ 31	I 13Th 14„  7„	26 27 23	Th14 16 7 17	27 29 21 30
27Th„ 28 (a)Th„ (b)Th„ 29 (a)Th„ (b)Th„ (c)Th„ 30Th„	14„ Cor 1 Cor„ 2 13„ Cor 2 Cor„ 3 12„	25 „ 26 24 25 „ 24	22„ 22„„ 21„ 23„ 24„	33 „ 32 33 34	Th21 22 23 Cor „ 24	43 44 46 „ „
31Pr	II 30Pr	79	V  6Pr	96	Pr7	66
32 (a) Th (b)Th„ Cor 1 Cor„2 33Th 34Th„	I 18Cor 1 18„Th 29„ Cor 2 32Cor 2„ 30„	29 „ 37 38 40 39	I 27Th 27„„ 28„ 29„ 32„ 30„	36 „ 37 „ „ 38	Th25 „ 26 Cor 30 27, 28 28	47 „ 48 49 53 50 „
35Th„ 36Th„ 37Th„ 38Th„ 39Th„ 40Th„ 41Th„					II Th1 Th2 Cor 3 „	82 84 „
					II
22Pr 23Pr„	Pr6 Pr„1	64 61	Pr7 Pr„4	32 32	Pr6 Pr„1	83 79
24Th 25Th„ 26 (a)Th„ (b)Th„	Th7 Th„6	10 10	Th15	16	Th7 Th„8(1)	15 16
27Th„ 28 (a)Th„ (b)Th„ 29 (a)Th„ (b)Th„ (c)Th„ 30Th„	Th„25 Th„„ Th„„ Th„24 Th„23 Th„24 Th„22	25 „ „ 24 22 24 22	Th„7 Cor 2 Th„7 Cor 3 Th„8 Cor 2 Th„8 Cor 3 Th„9	9 „ „ 10 „ „ 11	Th„16 Th„„ Th„„ Th„„ Th„„ Th„„ Th„14 Sch	33 „ „ „ „ „ 60
31Pr	Pr8	65			II Pr7	85
32 (a) Th (b)Th„ Cor 1 Cor„2 33Th 34Th„	Th28 Cor 1 Th„28 Th„29 Th„30 Th„33 Th„31	28 27 29 30 33 31	Th10 Th„„ Th„18 Th„„ Th„17 Th„16 and III 1	11 „ 20 „ 20 19 60	Th19 Cor Th„19 Th„20 Cor Th„22 Th„21	41 „ 42 43 48 47
35Th„ 36Th„ 37Th„ 38Th„ 39Th„ 40Th„ 41Th„			III Th2 Cor Th„4 Cor 1 Cor 2 Cor 2„ Th„3	61 „ 62 „ 63 „ 62	IV Th1 Cor Sch	185 186 187
42Pr				Pr1	99
43Th					Th4	86
44Pr 45Pr„ Cor 46Pr					Pr2	100 „
46Cor 47Th 48Th„	IV 10Th	133	IV 11Th	73	Th9	91
II 1Th 2Th„ 3Th„ 4Th„ Cor 5Th Cor 6Th 7Th„ 8Th„ 9Th„ 10Th„			8Th 10„  9„	71 73 72	II Th5 Cor 2 Cor 1 Th6 8 Cor 8 8 Cor 7 13 „	87 88 „ „ 91 90 91 89 96 „
11Pr					Pr6	103
12Th 13Th„	16Th 15Th„	113 112	13Th 12Th„	76 75	Th10 11	94 95
14Pr	12Pr	136	22Pr	103	Pr4	101

42Pr

Pr1

76

Pr2

198

43Th

Th1 Cor

60

44Pr
45Pr„
Cor
46Pr

46Cor
47Th
48Th„

V

Th8

149

Th12

69

IV

Th2

187

II
1Th
2Th„
3Th„
4Th„
Cor
5Th
Cor
6Th
7Th„
8Th„
9Th„
10Th„

Th9


Th„11

Th„10

151


152

152

Th9


Th„11

Th„10

67


68

67

IV



Th4

5
6 Cor
Th„6
5 Sch

190

191
193
192
191

11Pr

Pr3

198

12Th
13Th„

III
Th22
Th„21

101
100

IV
Th17
Th„16

97
„

Th7
8

193
194

14Pr

Pr2 Sch

198