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Leibniz-Handschriften zur Mathematik LH 35, 8, 10, fol. 1v

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: 0.90.

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. 2r); this page is its left half.

The machine reads it as

  1. Generaliter Datu figura BDB quaeritur curva cC
  2. talis ut sitit arcus iC 2C, 2C3C, ut spatia 1D1B2B. D.d,
  3. 2D2B3B3D2D posito puncta 1D. B. 1C, et 2D2B2C, ex
  4. esse in eadem recta, et has rectas semper esse parallelas,
  5. et si placet dxi BB normales.
  6. Quaeritur ergo relatio inter AB absissas, et BC ordinatas hujus
  7. curvae. i obscissae AB siat Z. A Ordinatae BC sint .
  8. V ax 1C2C
  9. a aut z(3C
  10. Axem cpAB constituta sit figura
  11. plata constitutum sit quadcilineum DBBd
  12. ns
  13. ut arcu DD, ordinatis IB duabus,
  14. et parte axis B
  15. comprehensum, Graeritur curva haic figurae
  16. proportioralis, ita, ut si ordinata DBsiopus
  17. producta alteri cur occurrat in E
  18. et ex E edacta noraralis se ipsi DE, seu parallela
  19. ipsi axi AB, curvae quaesitae CC occurrat in C
  20. sint arcus 1erE, 2C3E proportionalis spatiis
  21. quadrilineis, DIB2B2d1d 2D1B36302d
  22. per punctum fixum A educta recta axi AB
  23. normalis secet ipsas CE (si opus productas in F.
  24. et ex punctis C educanturl ordinatae
  25. m AB.
  26. sam AB vel FE sit X. 1B. B (sire 263B)el
  27. 1Et (sive 2E2t) sit e
  28. FX. sit AB vel FE
  29. dx 1B2B vel. EiL
  30. ut 2B3B vel 2E2l
  31. BD
  32. BE vel AF vel GC
  33. dzul BAx. 11.E vel 1F2 F vel . C.M
  34. auF2HSvel ZFBF vel 2C2M
  35. posito a esse
  36. constantem
  37. D AG vel FC C 1C2C
  38. d9 4 1G2G vel H2C
  39. a
  40. a
  41. aequo
  42. 2) K ax
  43. Posito jam puncta 1D2D. 3D. etc. distaentiam habere infintre indefinite parvam
  44. es: a
  45. eodemque modo et caetera, tunc quad rilinea D.B2B2D1B aequipollebiit rectangulis
  46. ut 1D. B2B. et recta arcur, C2C equi polle b rectis, et quia haec prquadrilinea
  47. deb vel haec rectangula, nempe 1D. B2B, 2D2B3B, proportionalia sunt arcubus
  48. sive rectis. C2Cp2F3C, et eadem rectangula proportionalia sunt ordinatis
  49. 1D1B, 2D2B, ob communem altitudinem, seu ob 1B2B, 2B3B aequales, igitur
  50. rectae 1CrC, 2C3C, proportio nalia esse debent ordinatis 1B1D, 2B2D. sive
  51. recta indefinite parva (vel etementum curvae CC) nempe 1C2C erit ad constam
  52. tem indefinite parvam 1B2B(vel BB, quae sune aequales) nempe dx, , ut
  53. hatulimus aegu. I arie hadebimus aequationem 33 dx aequ.
  54. aa
  55. t paa
  56. nempece aequ. deue + a
  57. aa
  58. aequatione divisa per dx fiet 3y aequ. v0 +coco. Haec aequatio
  59. aa
  60. Sed eadem 1C+C habetur per 1C,M et 1M2 C. equia quadratum il C aequale aequatinibus 12. 3.
  61. est m quadr, C.M + quadr. 1M2 C quorum cum salores paulo ante posuerimus
  62. vo
  63. ordinata, Bid est ad constantem rectam a. eritque. 1C, C ext 2C3 C aequ 3 dx aequ. c.
  64. x aequid
  65. 4)

Cite

Leibniz-Handschriften zur Mathematik LH 35, 8, 10, fol. 1v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068105:0002?run=73