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[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 283

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. IIIIIII
  2. PRINOIPTA MATHEMATICA.
  3. 283
  4. Cum Figura BRV T a in puncto medio V, haec s ad partem al. L. IDEn
  5. cerutram BRV vel VSa excedic Figuram illam, deticiet ab cadem SEevuvVS.
  6. ad parrem alceram, ex sic eidem aequabitur quam proxime.
  7. PROPOSITIO ZXXI. THEOREMA XXV.
  8. Si Corporis oscillantis resistentia in sinculis arcuum descriptorum
  9. partibus proportionalibus aureatur vel minuatur in data ratio-
  10. ne; differentia inter arcum descensu descriptum et arcum sub-
  11. sequente ascensu descriptum, aurebitur vel diminuetur in eadem
  12. ratione.
  13. Oritur enim differentia illa ex recardatione Penduli per resi-
  14. Aentiam Mediis adeoque est ut recardatio tora cique provortio-
  15. nalis relictentia recardans. Un superiore Propositione rectansu-
  16. lum sub recta = a B ec arcuum illorum CB, Ca difterentia Aa-
  17. aequalis CTaE arCK BKT. Et arca illa, si maneae longitudo a B,
  18. ausetur vel diminuitur in rarione ordinatim applicatarum DK
  19. hoc et, in racione relictentia, adeoque es uc longicudo a B ee
  20. relstentia conjunctim. Proindeque rectangulum (ub Aa _ Z aB
  21. est uc a B ec relistentia conjunetim, et propterea Aa uc relisten-
  22. EIa. d. F. D.
  23. Corol. 2. Inde R resistentia sic ut relocitas, differentia arcuum
  24. in eodem Lledio erit ut arcus totus delcripeus: ec COntra.
  25. Corol. 2. Si relictentia sic in duplicata ratione velocitaris, difte-
  26. rentia illa erit in duplicata ratione arcus totius: C contra.
  27. Corol. 3. Ec universaliter, E relistentia sic in triplicata vel alia
  28. quaris ratione relociratis, differentia erit in eadem ratione arcus
  29. TOTIUS : dE COnETa.
  30. Corol. 4. EF E relictentia sic parcim in ratione simplici relocita-
  31. eis, partim in ejusdem rarione duplicata, difterentia erie parrim in
  32. ratione arcus cocius ex partim in ejus rarione duplicata: e contra.
  33. Eadem erit lex ex ratio resctentix pro relocitate, qua est differen-
  34. tiae illius pro longitudine arcus.
  35. Corol. 5. Ideoque sis pendulo insequales arcus successire descri-
  36. bente, inveniri pocest ratio incrementi ac decrementi differentix nu-
  37. jusprolonsicudine arcus desexipei; habebitur eriam rario incrementI
  38. ac decrementi relictentix pro velocitare majore vel minore.
  39. D02
  40. Scholium
  41. AI MIIMNIIIII
  42. NTMLITMHMIEMMAMNEMERIAMNI
  43. MipIIII

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 283. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0317?run=74