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Leibniz-Handschriften zur Mathematik LH 35, 2, 1, fol. 282v

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: 0.87.

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. 283r); this page is its left half.

The machine reads it as

  1. sesse
  2. l
  3. Quod si ergo proposita figura Analytica imenori potest
  4. alia etiam Analyticas cmjus crementa sint ordinatis datae proportionalia
  5. quadratura omnium partionum figurae propostae generali constructione
  6. Jam alibi a me demonstrutum est rectas crementis proportonales
  7. haberi potest.
  8. esse ad quales sunt ipsae BE, CF figmae ladiuita
  9. quandam constantem quam vocabimus ut ipsa DT pro ductam
  10. adi por quada ipsius HL, seu portio inter ordinatum
  11. DL, et tangentem L7, in exe DT intercepta
  12. in qua ratio DL ad DF, sit perpetuo ut
  13. Orposita ergo qualibet
  14. alia figura
  15. dinat
  16. ommunens
  17. Hoc problema per Analysin (so vere mndum satis esst in nostra potestati
  18. DG ad + a.
  19. advocanda est ergo synthesis, et datis figuris seu DL, inquirendae
  20. sunt DT. quod ordine faciendo et de gradibus ad gradus figurarum
  21. procedendo, condi poterit velut Tabula quam constantem
  22. quandam propessionem mox detentum in pm certo habendum
  23. est, quam facile sit antnuare in infinitum, etiam sine culculo
  24. singulis repetito; quo facto facile detegi poterit an ablata
  25. figura qualibet an sit ex numero quadrabilum per Quadratiaem
  26. Calculus autem investigandarum DS, ex datis DL. non est difficilis
  27. Analyticam.
  28. post publicatam a Slusio methodum tangentium
  29. Ut ergi ordine procedamus, s per omnes aequatiole duat incignitus
  30. aequa d incognitorum contnent, gradus assurgemus ac primum:
  31. X + b Y + c B 0. unde H b ponendo AD+ X, CD, V,
  32. vel contra; DF +. unde opo regulae stusianae, fiet:
  33. si ANX fer t H V D sin CDB e fier: t g a x
  34. jam pust aequatio multiplicetur per X ponendo AD X, CD y, vel
  35. E1) X
  36. 10X
  37. contra ADH V, CDHX. DT +.
  38. ex aequationibus sequentibus ita habebitur infor
  39. ipsis +, et huju ope valor ipsis =a , 2DG
  40. 2) a + Cy + BX B0. Ergo poncudo CDrS, D 2
  41. p =dx. et po X subsitendo= CG abcit te ly t ab
  42. Ergo Z H
  43. -cv- ab a5a∞ + Cy + ab pu - ac
  44. emendo vero CD X. Dt p y. fier: t) - cY, et pro y substituendo
  45. ajus valorem, - d X - ba fier: t p, 102 fba, ad eaq 25 e et
  46. erit Z - dx = ab a, dx + ba d F
  47. 21) ab 4 acy + at X + e y + fyX + gX , o.
  48. ad
  49. ponendo CDB V, DL B X. fier: ac + + 2cyt + f xt - ad X. fyX. 1g1.
  50. adeoque + = ad X - fV X - 29 X pro 2g X ponatur ejus valor,
  51. ac + 2Cy + fX + 2 ab + rac y +2 adX p Cy + 2f VX.
  52. unde + + adX + fY X + a a cV + 2CY, sie aed F~
  53. +20y-
  54. sive act arert +rac V + reV = s+. X N0. sue gX ract rey ra rerst
  55. -ft + ad +fy
  56. adeoque a b + ac ) + adX + e) + S. VX n actqe Xx + rcoto X -racvg X 2e) p
  57. At + ad + f

Cite

Leibniz-Handschriften zur Mathematik LH 35, 2, 1, fol. 282v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00067993:0566?run=73