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[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 269

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. PRTNOTPTA MAEETEMAETC A.
  2. cur jam distantix quaelibet, puta S A, SD, SF in progrestioneMU. LIDEn
  3. lica, e disterentix Aa =D de D d = F f erune aequales; e PFOPECE. SECoND.
  4. ea difterentiis hisce proportionales arex thla X In Z aequales CrUNE
  5. inter se, _ denstates S+ Sa, 52, id cA, AFE, D L FN, conci-
  6. nue proporcionales. D. L. D.
  7. Corob. Hlinc A dentur Fluidi densicates dux quevis, puta AII
  8. Ee CR, dabitur are Fhkr harum disterentixe + re respondens; et
  9. inde invenietur densitas Si N in alcitudine quacunque SF, sumen-
  10. do aream thn Z ad aream illam datam shkwe ut est disterentia
  11. Aa - Ei fad difterentiam Aa = C c.
  12. Scholium.
  13. Simili aroumentatione probari porest, quod si Graritas partieu-
  14. larum Fluidi diminuatur in criplicaca racione distanciarum a CCNErO
  15. ec quadratorum distantiarum S , SB, SC, Scc. reciproca (nCm-
  16. De dAcub: S Acub. SAcub.
  17. SA
  18. dB9
  19. Sc q Cumantur in prosressione Arichme
  20. tica; densITateS AFI, BL CK, ec. crunt in progrestione Geome
  21. trica. FC E gravitas diminuatur in quadruplicata racione distan-
  22. tiarum, de cuborum distantiarum reciproca (puca
  23. 5 Agq
  24. SCcub
  25. SAg9 SAgq
  26. SACub SBCub.
  27. ecc.) Tumantur in progrestione Arithmerica; denlitates
  28. AH BB CK, _c. erune in progrestione Gcometrica. Ex sic in
  29. intinicum. RursuS S graritas particularum Fluidi in omnibus di-
  30. sanciis eadem sc, ec distantixe sine in progrectione Arichmetica
  31. densitates crune in progressione Geometrica, vri Vir CI. Lamundus
  32. Flalleius invenie. Si graricas siE ut distantia, ec quadrata distantia-
  33. rum sinc in progrectione Arichmetica, densitaTeS crunt in progre
  34. sione Ceometrica. FE sic in infinitum. Flxec ica se habent ubi Fluidi
  35. comprestione condenlati densitas est ut vis compressioniss vel, quod
  36. perinde est, sparium a Fluido. occupatum reciproce ut hrC Vis.
  37. Finsi portunt alix condenlationis Leses, uc quod cutus ris com
  38. primeneis sE ue quadraco. guadratum densitatis, scu criplicata ra-
  39. eio Vis aequalis quactruplicatae rationi densitatis. Duo in casu, ( GFa-
  40. vitas est reciproce uc quadratum distantix a cenero, densitas crie
  41. reciproce ue cubus distantix. Fingatur quod cubus ris compri-
  42. MenEiS SIE UE quadrato cubus densitatis, _ Si gravitas est reciproce
  43. ux quadracum distancireo densiras exir reciproce in sesquiplicata ta
  44. tione
  45. aC

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 269. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0303?run=74