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[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 227

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: 0.88.

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

The machine reads it as

  1. PRINOTDTA MATHEMATICA.
  2. t
  3. cibus (Data Squatione quotcunque Flventes quantitates involven. L. LDen
  4. le Fluxiones invenires es vice versa) eandem celarem: rescrip(IE SEConnOS.
  5. Vir Claristimus se quoque in ejusmodi methodum incidisse, ec mc.
  6. thodum tuam communicarie a mea vix abludentem praeterquam in
  7. verborum ex nocarum Formulis, ec Idea generationis quancitatum.
  8. Veriusque Fundamentum continetur in hoc Lemmate.
  9. PROPOSITIO VIII. TIEOREMA VI.
  10. Si corpus in Medio uniformi, Gravitate uniformiter agente, recta
  11. ascendat vel descendat, e spatium torum descriptum distingua-
  12. tur in partes equales, inque principiis sincularum partium
  13. Caddendo resistentiam Medii ad vim gravitaris, quando cor
  14. pus ascendit, vel subducendo ipsam quando corpus descendit
  15. collicantur vires absolutae; dico quod vires illae absolutae sunt
  16. in progressione Geometrica.
  17. Exponatur enim vis gravitatis per datam lineam AC; resisten-
  18. cia per lincam indetinitam AN; vis absoluta in descensu corporis
  19. per differentiam KCC; relocitas corporis per lineam AF (qua SIE
  20. media proportionalis inter R et AC, ideoque in subduplicata
  21. ratione resistentia;) incrementum relistentix data temporis particu-
  22. la Factum per lincolam R L, ex concemporancum velocitatis incre-
  23. mentum per lincolam PQ; ex centro C Alympeoris rectangulis
  24. C A. C HL delcribatur FIyperbola quaeris B NS, crectis perpendi-
  25. culis AB, R NV, L. O, F R, QS occurrens in B, N, O, R, 5. Ouo-
  26. niam AR CA ut APg. erit hujus momentum KL ut illius mo-
  27. mentum 2A P 9. id cA, ut AP in KC. Nam velocitatis incre-
  28. mentum F Q. (per motus L.Cg. II.) proporcionale est vi gencranti KC.
  29. Componatur ratio ipsius R I. cum racionc ipsius R N, ec het rect-
  30. anGUIUM RL XR N UE AF XKC. Z K N; hoc est, ob datum rect-
  31. ANGULUm RCZRN, uE AF. Requi arcae IIyperbOliCA RNOY
  32. ad rectangulum AL L Z R N ratio ultima, ubi cocunt puncta H d L,
  33. elt aequalitaris. Ergo area illa Ilyperbolica eranescens est ut AF.
  34. Componitur isitur area tora IIyperbolica ABO L. ex particulis
  35. KNVOL velocitaci AF semper proportionalibus, et propterca
  36. spacio relocitare icta descripeo proxorrionalis cst. Diridatur jam
  37. area illa in parres aequales AB M L, LMNK, XNO L, dec. de vi-
  38. 8
  39. red
  40. H.)PHSNIHIII
  41. NIHTIHIHHIMTHTITTIIHLNIHMTHHMHIHAMMIIMHNNEAMHIIMLINMNMMIMHIMEBMNIBIII

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 227. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0261?run=74