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Leibniz-Handschriften zur Mathematik LH 35, 5, 4, fol. 30r

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: 0.77.

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. 31v); this page is its right half.

The machine reads it as

  1. pars XIV perediasmatis desenrebus et summis
  2. si in formula subifinem Tabule praecedentis ponas e, et b nihilo
  3. aequales fiet
  4. Fd a + gac
  5. S2Y + fβ y gatB
  6. +25 ga.. grar
  7. si jam mominatorem hujus formulae
  8. cum ista conferas: fV +2Mfy+ ma
  9. fiet: esta ef + 2ga p hma, sive M, f +2ga. Ergo quia E haff
  10. 2a
  11. fier: etst + ap ga a) ga f ( (9a) vel et f n0
  12. 4a
  13. quod cum sit contra porpositum, quia f posita Y0. in nominatore restabit tantum gar
  14. contra propositum, quia nto quaerimus quantitatem varianterio. At C poni no
  15. non licet quia differentia alioquni quae quaritur erit infinite parva seu nulla, quod
  16. non nisi in geometricisordinatarum seriebus locum habet. Hinc colligo seriem
  17. ipsarum x summatricem non posse habere terminorm sive ordinatam
  18. in nominator
  19. vatorem purum, in qua V, ultra non uscendat. Quare necesse esse ut ascendat
  20. aaltius, sed ut postea divisone AC. deprimatur differentia ad haberidas
  21. ve.
  22. videamus jam an quadrata erunitate minuta, per saltum assumtas quae
  23. ita exprimi potest:
  24. 1
  25. .ponendo ( esse per quam crescunt ipsae Y. quod
  26. aequale ipsi 4. erit series crculi quadratix; quam
  27. C
  28. fomulesenein, ut conflramus speriori, dividamus nominatore, supercoris per f, fier:
  29. V + s+B y. (+ gafB F et confernda: + BZ. explicando y
  30. 2+ 2f9a. aga
  31. + d2fa
  32. fBd
  33. +2f9ad
  34. +gat
  35. sive +4d + 3β
  36. sta
  37. F s
  38. EF fiet: _ Y ( Z + d. et fier.
  39. Jam si 2df + +B + 2ga + Berit 4d(+Df(+ aga (FB)
  40. ac pro inde 2df + fβ+ 4ga p v. et 95 -4d fβ
  41. 16 a2
  42. 25. Bda
  43. rea
  44. diviso nominatore per f, fiet nominater
  45. +aa
  46. 9325 485 das
  47. +N = β
  48. x 1Z1, suc d e)+ su + =β. quadhi ero
  49. C V + Cß
  50. fry arfgay +g4 Ut aute.
  51. +frB . +fβ9a
  52. 1a
  53. sive 16d - 3B 4d + 9B fI2βV + 9
  54. quod cum sit magni momenti repetem calculum.
  55. + da
  56. -2e
  57. 16 d - r2 3d X - 3 f
  58. nullus enor in calculo, videtur haberi exita
  59. Cy
  60. g
  61. (1AdFaD
  62. sive
  63. a
  64. ag ad 7 + 8fd B + f2V. et in serendo tos valoues,
  65. a
  66. ga
  67. + cf y (= fda V + fBda
  68. 45βC (49a3)
  69. +gac
  70. +cf. (+ fcBY) + gacB
  71. Ffda..) (4ga d)
  72. gac).
  73. V + 2f9ay - g 2
  74. +f3. 4 fega
  75. y (+ 29a Y pe qua. Unde facondo 2 ga + fB ( F Lβ, sive 49a + B F() fier: G⊓
  76. et g +F
  77. 4a
  78. 5C. 245B9a
  79. Jm NaY + fBG⊓ fei 31- fB. quod
  80. contradicit pristi, quare ut haberi possit exitus quemadmodum susea, ita hpaulo ante feci, explucanda
  81. 6a2
  82. 13
  83. ones
  84. atur
  85. verte.
  86. es di l purc
  87. +2
  88. +f
  89. 429a..
  90. Sga
  91. sive Hda+ gac B
  92. da 1)

Cite

Leibniz-Handschriften zur Mathematik LH 35, 5, 4, fol. 30r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068022:0059?run=73