Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 49

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: 0.86.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The machine reads it as

  1. PRTNOTPTA MATHEMAEICA.
  2. Sed punctis Q _c P cocuntibuS, aquatuE2 P C _ C V. Ergo echiSPEO. LruEN
  3. portionalia L. X Q R et Q E quad. ae quantur. Ducantur taec aequalia in Puruvs
  4. E
  5. 2g. XdTG
  6. R _ CEL XSP g. Xquale.
  7. e
  8. Ergo (per Corol L
  9. _C5 PrOD. VI.) vis centripeta reciproce est ut L. Z SP g. id est, reci-
  10. proce in rarione duplicata distancia SP. 9. F. I.
  11. Idem aliter.
  12. Cum vis ad centrum Ellipseos cendens, qua corpus F in F IlipsI
  13. illa revolri pocest, siE (per COrOl. I PFOD. Z) ut C F distantia cOr
  14. Doris. ab Ellipseos CentrO C: duCatUF CF. Parallela FMip(eOS tan-
  15. senti P R: _ vis qua corpus idem P, circum aliud quodris Ellip-
  16. seos punctum S revolri potest, (IC. F dC P SCOnCUTranE In F, Crit uE
  17. L Cub
  18. e∞ (Der COrOL. 3PFOD. VIT,) hoc eAt, Si punctum S sic umbili-
  19. cus Ellipseos, adeoque P F detUT, UE S P g rCcIpEOCC. Q. F. I.
  20. Eadem brevicace qua craduximus Problema quintum ad Parab0-
  21. lam, ex EIyperbolam, liceret idem hic Facere: verum ob dignita-
  22. tem Problematis ex ulum ejus in sequentibus, non pisebut caus cc-
  23. ceros demonstratione contirmare.
  24. PROPOSITIO XII. PROBLEMA. VII.
  25. Noveatur corpus in Eyperbola: requiritur L ex vis centripeta ten-
  26. dentis ad umbilicum ficurae.
  27. Sunto C A. CB Temi- aXes FIyperboIx; P G, K D diametri con-
  28. JugaCX; P F, Q Derpendicula ad diametros; ex 9u ordinarim
  29. applicata ad diametrum G P. ABatuE SF sccanS cum diametrum
  30. DK in P, cum ordinatim applicatam QV in a, de compleatur pa-
  31. rallelogrammum e R P ∞. PatCE P P aequalem esse semiaxi erans-
  32. verio AC, eo quod, acta ab altero IIy perbolae umbilico sI linca
  33. TTT ipA F C parallela, ob aequales CS, C FL, Xqueneur ES, L I;
  34. adeo uE F F semiditerentia sIC ipTarum F S, PF, id eR (Ob P2
  35. rallelas YFI, P R ex angulos aequales IP R, TYP Z) ipsarum F S
  36. PTI. quarum differentia aZCm tOtum 2 AC adae quat. Ad S F de-
  37. mittatur perpendicularis T. Et Hyperbolae lacere recto princi
  38. Dali (seu 2BC
  39. qC dicto L CrIE L X Q R ad L. Z P V uE Q R ad F V)
  40. idt CA, UE P L. seu AC ad PC: PF L. X X v ad C v P ue L 2d
  41. 2

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 49. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0083?run=74