Euclid and His Modern Rivals/Appendix IV.

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

Page

I

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

II

1⁠Th
2⁠Th„
3⁠Th„
4⁠Th„
⁠Cor
5⁠Th
⁠Cor
6⁠Th
7⁠Th
8⁠Th„

9⁠Th„
10⁠Th„

Th⁠25

⁠27 Cor
⁠27

⁠26

⁠28

60

62
61

60

63

⁠Cor 3

⁠10
⁠6
⁠11
⁠5
⁠9

⁠12
⁠13

74

82
76
83
75
78

83
84

11⁠Pr

Ex⁠3

67

⁠14

104

12⁠Th
13⁠Th„

Th⁠31
⁠30

66
65

⁠16
⁠17

87
88

14⁠Pr

⁠(4)

71

§⁠289

84

⁠3

96

§ 2. References to the other Modern Rivals.

Euclid

Chauvenet

Loomis

'Syllabus'-
Manual

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

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