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[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 65

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: 0.89.

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

The machine reads it as

  1. PRTNOTPTA NATHIEMAEICAS
  2. ces TR, vel plura puncta P, derenietur semper ad lincas tor L IBEU
  3. rTP vel P HI, 2 dictis punctis Y vel
  4. P ad umbilicum II ductas, qux vel
  5. aequantur axibus, vel datis longitu
  6. dinibus SF disterune ab iildem, at-
  7. que adeo quae vel aequantur sibi invi-
  8. cem, vel datas habent differentias; e
  9. inde, per Lemma superius, datur umbi-
  10. licus ille alter FI. Hlabitis autem um-
  11. bilicis una cum axis longitudine (quae
  12. vel est YHI; vel A Trajectoria FIlipsis eAt, PTY F SF; Cin LY.
  13. verbola, P H -SP) habetur Trajectoria. 8. F.. 1.
  14. Scholium.
  15. Catus ubi dantur eria puncta sic solvitur expedicius. DenEUE
  16. puncta B, C, D. Junctas BC, C D produc ad F, F, UE SIE F B ad
  17. FC uE SB adSC, eE FC ad F D AE SC ad SD. Ad F. F ductam
  18. ex productam demitre normales SG, BII, inque CS infinite
  19. producta cape C ad AS e G a ad aS ut eAt HB ad BS; de crit
  20. A vertex, e Aa axis principalis Trajectorixe: quae, perinde ut Ci
  21. major, aequalis, vel minor tuerit quam A5, erit EIlipsis, Parabola
  22. vel Hyperbola; pun-
  23. eto a in primo casu
  24. cadente ad candem
  25. Partem lineae G Y
  26. cum puncto A; in
  27. secundo casu abeunte
  28. in intinicum; in certio
  29. cadence ad concrari-
  30. am partem lincae GF.
  31. Nam (I dCMIETANEUE?
  32. 2d C F perpendicula
  33. CT, DK; erit TC ad TYB UE F C 2d F B, hOc eH, uESC ad SB; de vi-
  34. cissim TC adSC uETIB ad SB SIvC UEC A adS . EE Simili aEBUMCNEO
  35. probabitur ene RD ad SD in cadem ratione. Pacent ergo puncta B,
  36. C. Din Conifectione circa umbilicum Sita delcripta, ut rectae omnes
  37. ab umbilico S’ad singula Sectionis puncta ductxe, sint ad perpendicula
  38. a punctis iildem ad rectam G F demissa in data illa ratione.
  39. Mechodo haud mulcum dissimili hujus problematis solutionem
  40. cradir Clarissimus Ceometra de la Flire, Conicorum luorum L. ib.
  41. E
  42. VIIL. PFOD. ZZV
  43. PRIOS
  44. SE CTI

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 65. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0099?run=74