Leibniz-Handschriften zur Mathematik LH 35, 4, 12, fol. 12v

Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German. Mean line confidence on this page: 0.82.

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One image of two folio pages side by side, registered by the library under both labels (also fol. 11r); this page is its left half.

The machine reads it as

1. (10) Sil y a et a - b, il y aura = a =- b
2. Care il y aura (par 1) a a
3. Car a = a = b - b doni (par
4. VF) s’il y a a a = b, IkG aura a = b
5. cae Car (par ap. y). a - a = b - b.
6. donc (par 10) a = Donc (par ax. 1) a- a =
7. (1R) S il y a a - b = 0 il y aura a = b
8. aejlulos de purtcete’e Car ( pas A) il y aura
9. a - b + b = 0 + b donc (par ax 3 et 4) a = b
10. (3) S’il y a - a = - b il y aura a = b
11. car a - a = b - b donc (par ax. 11) a - a = b -a
12. donc (par ax. 10) a= b (par 11) a = b
13. (14) s’il y a c - a = c - b il y aura a = b
14. a= Car ( par 10) il y a - a = - b (donc par 13)
15. il y aura a =b Autrement.
16. s s’il y a c - a = c - b, il y aura c ta =
17. C- b + a c a t a = C - c -
18. adjontons de part et d’autre - c + a, il (par 4)
19. donc il y aura +C - C = a + a = c - c + b = a
20. et (par ax. 3) il y aura 0 = b -a, ( donc
21. par 12) il y aura l =b
22. (15) S’il y a, ac = bc, il y aura a = b
23. Car aC = bC (par 3) et a
24. et bc = b jam c
25. 2E
26. (5) aC = a. Car a C = a E (par 10) = a (par 9) L. E. d.
27. 16) s’il y a ac = bc, il y aura a =b.
28. dire
29. Car (par 8) il y aura ac = bc ; st 15) a = b
30. s’il y a a = b il y aura a = b, car
31. Car (par 7) il y aura ac = bc dons (par 5) a = b
32. (18) F’it y a = G, il y aura a = b
33. Car (par 8) il y aura ac
34. 18) s’ily a a = , il y aura a = b
35. Car (par 7) il y aura ab = ab donc (par 15) il y aura b = a
36. 19) 5’il y a a = es, il y aura a - b.
37. Car (par 8) il y aura = f donc (par 15)
38. il y aura à = C ou bien (par ax. 7)
39. =
40. aC
41. Car (par ax. 7) il y aura C = 1. C et (par 8)
42. Il y aura tC = e donc il y aura à =
43. ac
44. et par consequent a =b
45. (2) 5 - 12 +t = - 1
46. =a, b = - ab Nam -a = -1, a. Ergo - a 1b = - 1, a, b = -1, ab = - ab
47. a ee a. 1 - a
48. c a _ =a 1 = a . Nam = a 2,1- 1 = 0
49. a -a, 1+ = 0 = ta
50. on (pur 3) e be. 6 = b Gou (par 3) c: b.
51. a - 1 = a Nam = - a, 1 - 1 = - a1 + (- a -1) = - a + (- a - 1) = 0 = - a + a
52. ae a
53. t, + 1
54. -a Nam a = - a - c. Ego a: -, - - a, -1: - 1 = = a
55. Ergo (per .. ..) - a -1 = a
56. b= na ib. Nam aba a1, b. Egua: b- 4:, - l, b sed a: -1- a Eugo a b. = na ib
57. ene a, - b = ab. N
58. a: 1 = a
59. car a it a. = 1. a. 1 = a
60. 42C = a, 675
61. a
62. aCb.C) A +. 1. C C car t. C
63. ae CkC = a : (b. c) = ac. b
64. Car 1. (1:C) =1C: c(r. C) 1C = C (per ..)
65. d b
66. = a. t
67. : lb: c)
68. c = ac car
69. = a.
70. 4. c = a. c. = ac. + =
71. al
72. _ = à
73. ia
74. 4)
75. lb. a= 20) ab (par ap. 11) - 1
76. Et L a = a (par ex 12.) = 1. don 1 par prop 6. crol . 7) a
77. sod B FC, b
78. Car 4.
79. Car foit 4 = d, il y aura = d (par 15)
80. a. -
81. ac
82. (ur et
83. et
84. de
85. ac
86. ab
87. :c =
88. soit soit L c 4= e
89. l
90. 4: c = d: c. =-
91. 6
92. Modusb inveniendi demonstrationem, sa
93. eb demonstratio hujus veritato
94. _ :b = ab scribe : b =
95. et beb = b mais b. b =
96. donc a :b = ab
97. ons spar
98. donc a = b a ab P abc. b = acb
99. a. (V.C) = ac b a: (b. C) = ac :b
100. car a: (b: c) = a c: c lb: c) C (b. C) = b ednc
101. aC: c (b: C) = ac: b
102. = ad
103. bc
104. e car 4 :c = abd. c60 = ab. bc
105. bc
106. et CEt. C) = 1 donc 1: Cl:C) = C 1 = C
107. Alter a . c - a,
108. coroll. ac - 4.
109. a
110. a

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 12, fol. 12v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068009:0024?run=73