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[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 265

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: 0.90.

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The machine reads it as

  1. PRINCIPLA MATHIEMATICA.
  2. 265
  3. PrOP. ZIX, quod non mutabune sicum partium interNArUmM INEEF LIDEn
  4. Sc: proindeque, si Animalia imMErSANEUE, _ Senlatio omnis a MO- SECDNDOS.
  5. cu parcium oriatur; nec laedent corpora immerta, nec sensario-
  6. nem ullam excitabunt, nisi quarenus lxc corpora a compressione
  7. condenlari DoNunt. EC par est racio cujuscunque corporum Sy-
  8. Rematis Auido comprimente circundaci. SyHematis DartES OMMCS
  9. uldem agicabuntur motibus, ac E in racuo constituerentur, ac l0-
  10. Jam recinerent gravitatem Cuam comparaciram, nili quatenus Aui
  11. dum vel motibus carum nonnihil resictat, rel ad caldem comprelli.
  12. one conslutinandas requiratur.
  13. PROPOSITIO ZXI THEOREMA XVI
  14. Sit Fluidi cujusdam densitas compressioni proportionalis, e partes
  15. ejus a vi centripeta distantiis suis a centro reciproce proportio-
  16. nali deorsum trahantur: dico quod si distantiae illae sumantur
  17. continue proportionales, densitates Fluidi in iisdem distantiis e-
  18. runt etiam continue proportionales.
  19. Designet ATV Fundum Sphaericum cui Ruidum incumbie, S
  20. CenErUM, SA, SB, SC, SD, SF. Ec. distaneias continue prODOr-
  21. cionales. Frigantur perpendicula FI, BD CK, DL, F M, 8C.
  22. quae sinc ue densitates Medii in locis , B, C, D, F; St specitica
  23. graritates in isdem locis crunt ut 2FY BF CK
  24. perinde cAt, ut ITY BT CK
  25. AS BS C 5 ec. vel, quod
  26. AB BC C.∞ dec. Pinse pri-
  27. num has oravieaces uniformiter continuari ab
  28. A 2d B, 2 B 2dC, a C ad D, _cc. Factis per
  29. Eradus decrementis in punctis B, C, D, _EC. RF
  30. hae gravitaces ducte in alcitudines AB, BC,
  31. C D, Scc. consicient presiones AFI, BI, CK,
  32. quibus Fundum ATV (jUXEA THCOrEMA XV.
  33. ursecur. Suctinet ergo parricula A pressiones
  34. omnes AIL, BI, CK, D L. pergendo in
  35. intinicum; e particula B prestiones omnes
  36. praecer primam AFI; e parcicula C omnes
  37. praeter duas primas AII, BI; e Sic deinceps: adeoque parci-
  38. culae primae A densitaS AH est ad parriculae secunde B densi-
  39. Mtm
  40. eacem

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 265. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0299?run=74