Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 142r

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: 0.85.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

One image of two folio pages side by side, registered by the library under both labels (also fol. 143v); this page is its right half.

The machine reads it as

1. problema, sive uno sive altero im ajore assunt (66) (B
2. Batis AC a. (4
3. Atitudo BD. B
4. 3 Summa lateii FC. semper enim summa laterum
5. ALatisrus differentia est major basi
6. differentia laterum X. . () ) nter Basim &. summam cateru C = (7
7. 5Latus minus C +C = X F37 AB
8. bLatus majus (t E +X (5)
9. 7. B (5)
10. a +CFF + 2aC - 2aX - dCX F) AAB
11. 8 (7) - b = D AD F
12. 9. Rg (8) = AD. Fo
13. 10 DC = a = R9(8) Y (
14. ADC = a + (8) - 2aRg (8)
15. 2 B BC = (11) + b = FI (6) = 1 BC.
16. B. B6) = a + C +X + 2ac + 2ax + ZCX. = ( BC. (2
17. 1a Ergo per (12) (19). sequatio plese scripta
18. (7)- 36
19. tio cuum ab aus latere sunt munes incogniti, et, forma A d + _ + C + x + 2aC - 2aX - 2 cX-b
20. aA a
21. 15. Peliatur aequatio in L. abjiciendo a addilum ad Ealitura simplicis
22. abjiciendo multiplicatorem contra 2. divisorem si lituras.
23. abjiciendo in 1. -4b contra + 4b litura
24. Dividendo omnia per a.
25. il 1. (13)
26. 24 Targantur incogniti in vnua
27. quod rurae felicitatis) no potest deprimi aequa 16. Transponatur aquatio, ut TRq. sit ab uno latere sol.
28. Mathematica
29. Et videndum an non hoc semper eveniaa quolus Nata Basi altitudme et summa laterum inveire triangulum
30. Y - (13 = 4sq LL. Fo7
31. 17 quadretur utrumque aequationis latus fict:
32. 1I - (+ () 17 = 2 + (13)
33. 8. 17. Abjiciantur communia in L et (13) lilura quinlupliti
34. nempe + a + C + X + 2aC, et ad subtrahendo
35. utrobique, et 2aX - 2Cx addendo utrabique abjici.
36. antuo in L. et pro 2. scribatur 8 in 13.)
37. fiet:
38. (basiet
39. Patet ex hujus problematis
40. solutione:
41. Utile esse alia quoque theoremata adhibere
42. prater ea duo quibus solis se utiait Cartesius
43. Si scilicet in Triangulo rectangulo quadhacum
44. quadratis, item, in similibus Triangulis
45. omnia esse proportionalia:) nam
46. nisiexpertus sum, cum theorema illud:
47. summam laterum esse majorem basi
48. Aquod vide hic num 3.) nondum adhiberem
49. apparuisse. Imo idem hoblema ose
50. alterius cujusdam Theorematis, pod scilicet
51. +a- 4ax ∞+ Cx = _T. + Rq 1I. () secd anguli Ga peta. rectangulo ex dasferentia laterum et suma
52. 10 quadretur (17) fict:
53. ver
54. (seu quod EC= CF EC AAC. ita enims umenrtatrum
55. (0) 1b 1b 4. 32 1b 1b 36 2sb 64 b4 12 25b 2
56. gX+gC X + 18aCN I a + C + X + 2aC - 2aX - 2CX. 4b - a C esta Y tralra x. 2a x
57. A S
58. 9 arstiplicando ma per a, fat et dicidendo per 16.
59. a utrume latus
60. Gumuma talerum posila d. s
61. ilere minor
62. 1I = 16, aa iNC 2aX 2Ca X sas + ra erit ex dicto tcon GC d
63. AGerit a dX. Ego a Ad eriu
64. x a. dr. lius eo. unctum )Bd. b
65. e Apriatur at atre Aequationis (19) latere absinatur. 9a x.
66. Nam abjiciatur subtrahatur sum a TI. ubi reperituri, sum 9a X, dabit: a= 2a dx + d X + 44b = d- 2d +X
67. tum a WV, ubi eperitur 1ba x, restabit: Ta
68. in IV. notata hac mucatione, litura simplicis.
69. x+2aC-2
70. Multiplicando utiume
71. a et dvidinod
72. 16, fiet:
73. acareni da
74. ca + 2ac - 4ab = ex = raX
75. 256+ 512 = 516= 64 + 128
76. 2) Ergo dividendo omn
77. 2ac
78. 2 Et Radicem extrahendo:
79. +2ac-
80. per C 4+ 24c
81. atig a tC + N + 2C -2a2 2CL = (13)
82. hypotenusae aequami aterorum laterum
83. difficillimam problimatis hujus solutionem,
84. Iim a
85. ad + dX +4ab = d a - 2daX + aX
86. dx aX= a- 4a6 a
87. da- 46 a7. 1024-576-256: 19
88. d- u
89. 182 d 48

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 142r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068195:0283?run=74