Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 285

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: 0.91.

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

The machine reads it as

  1. III
  2. PRINCTPTA MATTIEMATICA
  3. 28)
  4. Designer jamr V velocitarem maximam in oscillatione quavis, LIVEn
  5. Cintque A, B, C quancitates datae, ec finsamus quod difterentia SECVNNOS.
  6. arcuum sIE AV +BVZ + CV.. Cum relocicates maximae sinc in
  7. Creloide uc semisses arcuum olcillando descripeorum, in Circu-
  8. l0 vero ut semissium arcuum illorum chordae; adeoque paribus
  9. arcubus majores sint in Creloide quam in Circulo, in ratione
  10. lemissium arcuum ad corundem chordas; tempora aurem in Cir-
  11. culo sint majora quam in Crcloide in velocitacis ratione reci-
  12. proca; patet arcuum differentias (quae lune ue resictentia d qua-
  13. dratum temporis conjunctim) casdem Fore, quamproxime, in vera-
  14. que Curra: deberent enim difterentiae illae in Creloide augeris una
  15. cum relistentia, in duplicata circirer ratione arcus ad chordam, ob
  16. relocitatem in ratione illa simplici auctam; ex diminui, una cur
  17. quadrato temporis, in eadem duplicata ratione. ltaque ut reductio
  18. hat ad Creloidem, caedem lumendae lunt arcuum disterentia quae
  19. Fuerunt in Circulo obserratae, velocitates vero maximae ponen-
  20. da sunt arcubus dimidiatis vel inceoris, hoc cst, numeris 23 Y, 23
  21. 4. 8, 16 analogx. Scribamus ergo in casu secundo, quarto et lex-
  22. to numeros 1, 4 ec 16 pro V; ec prodibit arcuum disterentia
  23. T2F
  24. A +. B + C in casu secundo;
  25. 25+ = 4. A + 8B F T6C in casie
  26. quarto; e = = 16A + 64 B + 256C in casu sExIO: FF ex his X
  27. quarionibus, per debitam collationem ex reductionem Analyticam,
  28. FE A = 00000976, B =0,0010847, & C, = 0,0029558. FA igitur
  29. difterentia arcuum ut 0,0000926 V +0,00r0847 V3 +0,0029558.
  30. ec proxrerea cum (per Corollarium Propositionis XXX) relictentia
  31. Globi in medio arcus oscillando descripti, ubi volocitas eAt V,
  32. SE 2d ixEuS pondus uE Z AV + 23BVZ + = CV. ad longicudinem
  33. Ponduli; sI prO A, B ec C scribantur numeri inventi, het relistentia
  34. Crlobi ad ejus pondus, uc0,0000585V +0,0007545V2 + 0,0022169V
  35. ad lonsitudinem Penduli inter cenerum suspensionis et Regulam
  36. id cA, 2d 121 digitos. Unde cum V in calu secundo designet 1.
  37. in quarto qu in sexto 16: crit relistentia ad pondus Globi in casu
  38. secundo uc 0,0030298 2d 22Y, in quaYEO UE 0,0417+02 ad 1217 in
  39. TCXTO Ut 0,61675 2d 125.
  40. Arcus quem punctum in silo norarum in catu sexto descripsics
  41. CFaE 120 - =- seu. 119,3 digitorum. EE propterea cum radius cAec:
  42. 222 dixitorum, ec lonsicudo Penduli incer punctum suspensionis
  43. de

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 285. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0319?run=74