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[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 266

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. III
  2. 266
  3. PEITLOSODTITA NATURALIS
  4. DF MOEDEateM BF ut summa omnium AFP + BY + CK + DL, in intini.
  5. onronontum, ad summam omnium BY F CR f DL, _C. EE BI den-
  6. sicaS secundae B, CR ad C R densitatem tertix C, ut summa om-
  7. nium BT + CX + D L, Scc. ad summam omnium CH F DL, _C.
  8. Sunc isitur summe illae differentiis suis ATI, BT, CK, _EC. PrO-
  9. portionales, aeque adeo continue proportionales, per hujus Lem. 1.
  10. proindeque disterentia ATI, BI, CK, _c. Cummis proxortionales,
  11. Cunc etiam continue proxortionales. Ouare cum densicates in locis A,
  12. B, C, _EC. (INEUE A YH, BI, CK, eC. Crunt etiam hX COntInUC DFOPOr.
  13. cionales. PergaTUE per TaIEUM, _ (ex Xquo) in dictanciis S A, SC,
  14. SF continue proportionalibus, crune densitates ATI, CK, P. M
  15. continue proportionales. Ec eodem argumento, in distantiis qui-
  16. bulris continue proporcionalibus SA, SD, 50, densitates AII, D L
  17. GO erunc continue proportionales. Coeant jam puncta A, B, C,
  18. D, L, ecc. eo ut progressio graritatum speciticarum a Fundo A ad
  19. cummitacem Eluidi continua reddatur, ec in distantiis quibusvis con-
  20. tinue proportionalibus S , SD, SCi densitates AFI D L GO)
  21. semper existentes continue proportionales, manebunt ctiamnum
  22. continue proportionales. . B. D.
  23. Corol. Elinc si decur densitas Fluidi in duobus locis. puta ec
  24. En collisi potest ejus densitas
  25. in alio quoris loco 9. Centro
  26. S, ACrmpeotis rectangulis S9:
  27. SX, describatur FIrperbola sc
  28. eans perpendicula ALY, F. M.
  29. T in as e, q uc e perpendicu
  30. Ia FLX, MT, F Z ad ASmp
  31. eoton SX demista, in B, m EF +.
  32. Fiacarea Z YmF Z ad aream da-
  33. eam Zm B X UE area daFA F eg C
  34. ad aream datam P ea A; dc li-
  35. nea Z+ producta abscindet li-
  36. neam T denscati provortio.
  37. nalem. Namque Si linexe SA, SF, Cunt concinue proxortiona
  38. ICS, CFUNE arEK F eg Q F ea aequales, et inde arexe his prOPOr.
  39. tionales rm+ Z, Xhm L etiam equales, et lincae SX, SY, 5Z, id est
  40. ATL, F MI, QF continue provortionales, UE OPOTECF. EF Si linex
  41. SA, SE SQ obtinene alium quemris ordinem in serie continue
  42. proportionalium, linex AFI, F M, QT, ob proportionales arcas
  43. typerbolicas, obcinebunc eundem ordinem in alia serie quantita-
  44. cum continue proportionalium.
  45. C
  46. PKO.

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 266. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0300?run=74