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Leibniz-Handschriften zur Mathematik LH 35, 5, 17, fol. 3v

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: 0.78.

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. 4r); this page is its left half.

The machine reads it as

  1. b7
  2. Edtod
  3. etb7
  4. Nimirum annes formae, in quibus yX, redibunt ad:
  5. y4.
  6. 213
  7. ben 7.
  8. esi
  9. X3 oTt
  10. seu TA T. constans
  11. X+ 3
  12. V,H 3E
  13. seu a t
  14. 2
  15. X13X73~T+ Y ∞ 2723
  16. 13H=
  17. 15c 1
  18. 27E
  19. Sit aequatio y p X, constat esse +B YX. Nam. X Y
  20. eu et si 4 +n 3∞, fici te 3y.
  21. Sit jem aequatio Y HX. sumatur alia curva y + b p X unde uno in alterius locum
  22. substituto, fiet, X - y - b p0 iujus aequationis tantum maxima opus est quaedudum
  23. nota.
  24. sit X alia X_ sumatur y p X + c. fiet: X ++C. Ubi
  25. cum C possit pro assu sumi pro artitio, utique sic sumi potest, ut dividi possit per XX
  26. et hac methodo facile perveniri potest ad tangentes singulari via,
  27. Tentemus et hoc: Ad curram datae naturae et verticis, earum quas simplices voco
  28. ducenda ex puncto in axe dato F. maxinia TC quaeritur ipsa AB, vel BC.
  29. sit ABAX. BCHV et NAB. TB⊓ TAp, B. AB X
  30. TB1 X+ b.
  31. BCp y. TCB X + 2BX + B ( + y TC12
  32. erit Z omnium possibitium maxiima
  33. ehniteo
  34. Si SC tangit curvamus idem est ac si secet ilauerat ipsa C(C) s EB (B) mor quan ttate
  35. qualibet assignabili. Nam Hinc facili demonstratur tangere: nam si sec ponatuo in duibus
  36. punctis assignabilis intervulli, ostenderem statum intervallam horum duorum punctorum revera
  37. assiguato esse majus. Adeoque hypothesis foret absurda, adeoque non secaret, sed langeret
  38. Hoc ite a non tanget, secabit in duobus punctis assignabilis intervalli contra hypothesin
  39. unde Metrodum Fermatii de Magimis et Minimis, possumus habere pro
  40. demonstrata, quanquam et ab aliis dudum veterum more rigrrose demonstrata sit, unde non
  41. est cur actum agam, praesertim cum nihil hac propositione dicturu simi quod nnon inter Geometrus
  42. constet.
  43. V X7S
  44. a +42b +6 ab + b3 ( + 6 p 8+ 3Cd + 3cdh, d3
  45. a27 3.
  46. Ergo a ch
  47. 4abH3Cd
  48. 3cd ergo a p +Cb, e a Y
  49. 46
  50. 1d
  51. quem valorem inserendo vulori ipsius a fiet:
  52. a + 2ab +B c +d.
  53. a pC.
  54. 64 313
  55. 81 d3 B
  56. ap81 d
  57. 64b+
  58. 2abrj.
  59. 1+
  60. 30d
  61. 4b
  62. an L. _ C ap . ergo (ap 2b). ap. 20. 8.
  63. a +3ab + 3ab +B∞ 1+d aC. 3ab p d: erit a
  64. ergo (a p 3bC) et aep 9bc
  65. d. erit (C7 d.
  66. d H 3b
  67. 2763.)
  68. sed si quaramus si aBC. et 4ab p d. + erit (ap Hbc
  69. et ita porro ergo generoliter, a f 2) bc. et c
  70. posito a2
  71. c
  72. jam altius: 257
  73. jam ex 1. erit 1 2.. (4)
  74. (8)
  75. a
  76. a
  77. oZ. a2; b, d
  78. et
  79. (27
  80. 1
  81. C. seu 92
  82. t
  83. et erit lP 256b
  84. CoH . nisus ex 2, eris a (6) od Za ()
  85. et quia praeterea: a2 +Z, a b + 22 a2
  86. V a
  87. co-
  88. 13 d2
  89. d. Unde () co co
  90. c-1
  91. lons B Z ergo fier.
  92. 45co CAZb
  93. ergo CB Zba, et ccol) Zba co unde juncta 1. fiet: Zb c a2
  94. cod
  95. exprimendum in characteribus esse Z majorem quam co
  96. cod
  97. 1,2, 3
  98. ABHX.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 5, 17, fol. 3v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068035:0006?run=73