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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 73v

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: 0.73.

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. 74r); this page is its left half.

The machine reads it as

  1. eundem calculum aliter perveniemus: si ex eodem puncto ducta perpendrentari
  2. ad sectionem Conicam, ordinata non ad latus rectanguli nscrpti sed in axem condeae
  3. sectionis demittatur qua ordinata appellata y, et ascista , ent aequatio:
  4. rax + X _= H0 Et ob Tringulaum similia ert de 1y de Cay in y
  5. Fa atqu
  6. Esti cum sa X. Uender da = pY + dax F C x7 1S) qutm aiu ad
  7. Unde ge AG D X p(t B y + de X + da
  8. F)
  9. sive per borachplogiand n g yX + Hy 4 daX H ad
  10. Ex puncto quaesito . H. ducntur ad Tangentem verticis AB ducata recta Z. sive A
  11. ita udt angulus HNL sit obliquus, i rectu HL est perpendicularis in Recta erquZ vel supra
  12. vel infra L. ocadere potest. Ponatur HL ad AZ ub seu X ne 20 Erit ) ∞
  13. et AZ V ciet A eni o t Z() ZL suive (4) 2. Est autems
  14. Erit ergo g v(+Si- Euso es s (4) si DX mdsirtana
  15. sus valores aequationibus insoentu fiit tee
  16. 3p aZY + a x. . Z v
  17. Et ex Aeq. 2. fiet Ay (1).
  18. Drioris aequa tonis sepis militis
  19. eam ita scribemus:
  20. e a emad rimuturs
  21. e. 10l 26 1
  22. (+)psu Z QSi Lnor
  23. (1 (V
  24. De. 9
  25. Ende fiet Aequalio ad circulum:
  26. ei
  27. u
  28. ZV 2a093d. + V (+)2 Sn 2
  29. Cao) a 1..
  30. x ervit
  31. edr
  32. squs
  33. 118.. + y P da
  34. i. le
  35. ar a io ii mua et i nn suans alai siner
  36. conferno cum facntia ad Cremlum:t
  37. 11+ Gr . nDZ = gr =ba Bo. et
  38. Et cnfeoie brmat YZ, e Habelinius Aequationes collatitias sequentes, quarum ope ante
  39. invenietur e seu obliquivas anguli, per collationem terminorum vy, Unde.
  40. 21. ri. (4 2 rut l 8 - im. 8. Unde jam patet putium signum (+) debere explicari
  41. per +, alioquin 21. 3 destiuetur iutobique et e fieret infiniti loaga, unde caeteraabsurda
  42. sequentur quae supra. Quare fiet: 2 r in = 2S + 19 - m ive si mavis
  43. eim- 20 . V. Ego m. A . al ma Est autem l p a. sive linitati. etm 1 +D a a.
  44. G Ergo 4 4es.: Va 4e sud e L m. sed = YB S
  45. Unde ae t am, es. Ergo 4d L im l- no. Jam um e + ) a3-a
  46. et la l n et a +Va3-a. Ergo 4a + 3 a sinc Ae Va
  47. Ergo 4C sin da s B l = m. Ergo 4a + 4a e l = m, sive B a - m. Nam
  48. a et lte aequivalet hoc loco a seu unitati. Mt-m r a Va - a. Ergo l- m ppl. V a- p
  49. : Ergo- 4a Pa4 + a, sive e ,V a + 4a2
  50. Inventa ergo est e. sambego conflrendo termines Z. Erit -ge P + aF- ut sive:
  51. et
  52. -2a + Y s. + dat, (a- n,) V s sue tag e 2a +e 4+ da,
  53. 1- a H 1 - =. Eno
  54. +4 - 4. Erpo HI a Quoniam autem P est quantit inexplieabus,
  55. bilis hocid tolendum est signum radicale fiet: et primum ordinetur sic: _gcd +8a V + d CV ea Y P
  56. Uende gre du9 e tbaerSed G + 9a e . In Ellipsi, uli + enter et a pa ibi
  57. in opus est Ha quad ratione
  58. landes t19 ones. p quo etta sidt a
  59. raen. prium G an A H
  60. l4ga. t hit cGr fac
  61. 9 ae
  62. 9 + 204
  63. nate na die ead
  64. Eet nen 1 sicet a) egeu 20 pdeet Poronus iam
  65. sive eged 8a) + ea S V. T enda irrulid nalitus, es emimi tali radx inexpica
  66. c +4148..... 5.
  67. gag L. ⊓ +
  68. Si Z. inderet ultra A. fiere AL , ZL A7.
  69. 1Z. constrnter erit
  70. t it
  71. 2. 18∞ seu +12Z. F 1~L
  72. 25p2S. -2. AS AZ- dZ)
  73. sia ss vtu Ego 5+ V(VZ (Cteq. (5.)
  74. 1Z51 Jam explicems aequalure
  75. 2. sclict eud upoplea
  76. ribit imutili celictis sigus Aeq. (4)
  77. ( 9ra
  78. et concilieturcu
  79. t r
  80. potes poni epe
  81. Schemat sequentidia
  82. a 505 Ada sid
  83. sui lssto ea
  84. An.
  85. erite 416, et Woti 6+ 2
  86. ponams Opo erit d et e
  87. 64 dn fiet X ∞ n. D
  88. da - v Omittatur D
  89. fiei a rn da p + mo.-
  90. 40 + 2O2 Erg
  91. B X -da - YC+
  92. vel da AYO -O2
  93. - Va + b B X.
  94. Ergo 7 N X 4 2bX +
  95. Ecce exitum hinc duci pes
  96. ubi problema alioqui
  97. planum reddi potest
  98. solidum hac sola rave
  99. quod asiogon eubo
  100. ersa en li

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 73v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0146?run=74