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[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 61

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.

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The machine reads it as

  1. PRIHOTPTA MATTIEMATICA
  2. PROPOSITIO ZZ. PROBLEMA XII.
  3. Circa datum umbilicum Trajectoriam quamvis specie datam de scribe-
  4. re, quae per data puneta transibit e rectas tans et positione datas.
  5. Cas. T. Dato umbilico S, describenda sit Frajectoria ABC per
  6. puncta duo B, C. Ouoniam Frajectoria datur specie, dabitur ra-
  7. cio axis principalis ad dictantiam:t
  8. umbilicorum. In ca ratione cape
  9. RB ad BS, _E L C ad CS. C CN- :
  10. eris B, C, interrallis BR, CL, dc.
  11. Tcribe circulos duos, ex ad rectam
  12. R I, quae tangat cordem in e
  13. L demitre perpendiculum SC, idemque C
  14. SA 2d AG _ 5 a 2d a G, ut CA SB ad BR, _ aXc
  15. A, a delcribatur Trajectoria. Dico Factum. Sic Cum E umbilicus
  16. alter Figurae descripex, ec cum sIC S Aad AC ue dd ad a Cr, crie di
  17. visim S a =S A sCu SFT ad a G - AC Ceu La III Cadlem ratione,
  18. adeoque in ratione quam habet axis principalis lsguta dlescribendae
  19. ad distanciam umbilicorum ejus; ee proprerca FIgura Clcripta cA
  20. ejusdem speciei cum describenda. Cumque SiInE R B dd ∞ _ L. C
  21. ad CS in eadem ratione, cransibit haec Figura per puncta B, C ut
  22. ex Conicis manifestum cst.
  23. Cas. 2. Dato umbilico S, describenda sit Trajectoria quae rectas
  24. duas T R, er alicubi concingac. Ab umbilico in cansentes demicte
  25. Derpendicula ST, S+ e produc ca-
  26. dem ad V, V, uc SInE TV, +V ∞-
  27. quales F5,+5. Bilcca V V in O.
  28. de erise perpendiculum infinicum
  29. DFI, rectamque VS intinice pro
  30. ductam seca in H ec R ita, UE (IL
  31. K ad IFS _ VK ad RS uE CA
  32. Prajectorix describendae axis prin-
  33. cipalis ad umbilicorum distantiam.
  34. Super diametro RR describatur
  35. circulus sCCanS OFY in FL; de umbilicis S, FZ, axe principali ipsam
  36. Il aequance describatur Prajectoria. Dico Factum. Nam biscca
  37. (Ck in X, ee junge IYX, TTS, LTV, IIV. Ouoniam eAt V X 2d 5
  38. AE V H ad LS; ee COmPOHICUEY L + Y h ad KS + kS: divisimque
  39. b il
  40. bus
  41. a
  42. F. IBFH
  43. P RI N BS

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 61. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0095?run=74