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[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 183

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.

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The machine reads it as

  1. PRINCTDTA MATHEMATIOA.
  2. Tam A linca P e sCCCE arCUM P F in g; &t recta
  3. arcu eranescente P.e coincidit, productâ occurrat rectae PS in Y; PnimOSI
  4. ex 2b S demictatur in P F normalis SCr: OD MMMa MtatGUIa
  5. OTF, a= es DFS; Crit D a ad L L al L L, leu L
  6. 1
  7. EIBER
  8. L dd
  9. FS; ex ob criangula F eg, F SG (per LCM. VETF, e COrOL. 3.
  10. Lem. VEI) Similia, crie FC ad eq sCu FF, UE FS ad SG; _ CX
  11. aequo, D d 2d Ff uE D F. ad SE; hoc est (ob similia criangula.
  12. PDE FG5) ut P F ad PS. Q. F. D.
  13. PROPOSITIO LXXIZ. TIIEOREMA ZXXIX.
  14. Si superficies ob latitudinem infinite diminutam jamjam evanescens
  15. FFFe, convolutione sui circa axem PS, describat solidum
  16. Sphaericum concavo. convexum, ad cujus particulas sinsulas aequa-
  17. les tendant aequales vires centripetae: dico quod Vis, qua soli-
  18. dum illud trahit corpusculum situm in P, est in ratione compo-
  19. ta ex ratione solidi D F. q X FF e ratione vis qua particula
  20. data in loco FF traheret idem corpusculum.
  21. Nam A primo consideremus vim Cuxerkcici Sphaericae FF, oux
  22. convolutione arcus FP generatur, de a linea de ubiris secatur in r;
  23. erie superficiei pars annularis, convolutione arcusr f genita, ut
  24. lincola D a manence Sphaerae radio P F, (uti demonstravie Ar-
  25. chimedes in Lib. de Sphaera ec Cylindro.) F.C hujus vis secundum li-
  26. neaS PP vel Pr undique in superticie conica sITaS exCrCIta, UE
  27. haec ipsa superticiei pars annularis; hoc cA, ut lineola D d veh
  28. quod perinde est, uc rectansulum tub dato Sphaerae radio P F. dc
  29. lineola

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 183. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0217?run=74