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Leibniz-Handschriften zur Mathematik LH 35, 4, 19, fol. 36r

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: 0.79.

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. 35v); this page is its right half.

The machine reads it as

  1. millena
  2. Problemata primum secundum tertium
  3. quartum una constructione complecti licet
  4. Datis leteribus summit
  5. p
  6. sint Z y. latera circa verticem
  7. aegmanta baseos a perpendiculo in ipsademip
  8. differentia seqmentorum v- XFa.
  9. e
  10. bZ +c n BZ + Vy + 9: d2 +8y + t:: b: c
  11. (2) 4b
  12. et Z. v seu CBZ+ 6p9+ Cq 7 d Z+ bdy + bt. seu yp- bn
  13. et Z: v:: d: e. seu CZ7 dv. seu 2p 2b. _
  14. Ex natura trianguli Z. y n X. seu (ob aequ.
  15. 5se
  16. fiet et Z. y ax ax. aqu2 erit yp
  17. (6)
  18. ob aequ 2 erit 3 77y1 + r AZ- p. Unde
  19. est
  20. run et- p
  21. A
  22. 2 + r12Y py (5)
  23. E rax
  24. et in aqu8 proy ponendo et pro yr. et Z. ponendo
  25. in aequ. 5. vatores ex aequ. 2. et 3. fiet.
  26. 6
  27. pr non render-p reavtrear
  28. ubi si posset fieri conticusat esse nr. problema
  29. solo ductu redtarum sobo solvetur. sed quia
  30. nos generalem solutionem volumus compendii causa ponatur
  31. vocetur Y d+ na (7), 4
  32. 1S
  33. tsit: v renden, ext r’eavtreax
  34. (10)
  35. cOmpendii causa v7 O set lvF l0
  36. (9
  37. jam
  38. aequatio 1. exaltata fat multiplicata per hvthx
  39. dabit hV = hX Y ha+ ho. Quam addendo subtrahendo ab
  40. 11)
  41. aequatione 10. fiet + tB quam addendo aequationi 10.
  42. fiet +lr = hx (12) MeI O +haB+ haX Quae aequatio
  43. (14)
  44. ut fiat ad circulum; faciamus +l + h - t. fiet lp - 2h.
  45. h.
  46. (16
  47. et ponendo nF- 1. erit l+ +2 et ex aequ. 12.
  48. fiet sequens _ +v + X (2O - ab - aX. sive ex aequ. 8. 9.
  49. fiet vex
  50. 2ld
  51. 617
  52. +rend p V +re a X + C p
  53. + rea
  54. sa a
  55. -
  56. (19
  57. - 5a a.
  58. v. x a
  59. vel per compendium v +X +v + 1X + g. quae est ad ciiculumus
  60. sui si conjungatur aequatio v- x ri a quae est ad
  61. lineam rectam habebitur pmoblematis solutio
  62. si novissimam aequationem quaeramus et pro X
  63. substituamus v- a. et pro x ponamus v2+ a- 2Da turce ex aequ. 19
  64. fiet 2V + a - 2av7 tv + Y v- Y a + g2. et
  65. 20
  66. ordinando fiet habetur aequatio plana:
  67. v- alv +a 10. Unde constrnctionem
  68. - 1- t - va
  69. reperire facillimum est
  70. Eadem constucte idem calculus eadem constrictio mutatis signis
  71. serviet etiam si perpendicularis ed ex triangulo
  72. in basiu demissa cadat extra triangulum AB(C)
  73. quo casu V etx non erunt segmenta seu partes baseos
  74. sed basis erit una ex A(C) erit pars major
  75. et minor X eunt segme sive (cId. erunt partes vel segmenta
  76. najoris V. sive AD
  77. et alia ad huc rem numero
  78. infinita
  79. LC
  80. vel per com
  81. -bt vel percmpendium
  82. b c
  83. y(2+
  84. nt1
  85. nernao
  86. arculus genecalis
  87. no on
  88. v ez vuille
  89. 2. 3 av+ ax
  90. n aer
  91. i2
  92. ts
  93. 2. 7 12ac20 a
  94. 2
  95. 2ez- a
  96. yA.
  97. 2v- vta
  98. +Y
  99. ex-ap

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 19, fol. 36r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068016:0071?run=73