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[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 84

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.

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

The machine reads it as

  1. PFTTLOSOPHTA NATDRALIS
  2. LE MIMIA XXIV.
  3. Si rectae tres tangant quamcunque Conisectionem, quarum duae pa
  4. rallelae sint ac dentur positione; dico quod Sectionis semidia-
  5. meter hisce duabus parallela, sit media proportionalis inter ha-
  6. rum sermenia, punctis contactuum e tangenti tertiae inter-
  7. jecta.
  8. SunEo AF, G BP2-
  9. rallelae dux Conilee
  10. tionem AD B Ean
  11. gentesin Ae B; L.V
  12. recta certia Conitee.
  13. cionem tansens in L
  14. et OccurrenS prioribus
  15. cansentibus in le G;
  16. scque C. D Cemidiame-
  17. ter Ligurae tangenti
  18. bus parallela
  19. quod AF, C D, B
  20. fune continue proporcioaus.
  21. Nam s diametri conjugatae AB, DM tangenti FG OcCUrran
  22. in F: e TI, leque mutuo secent in C, ec compleatur parallelogram-
  23. inUm TKC L; erie, ex natura Sectionum Conicarum, ut L.C 2d
  24. CA ita C A ad C L, _ ita dirisim F C =C A ad C A - CF, Ceu
  25. E A ad AL, e compoMItC F. A ad F. A + AL TCU F. L UE F. C 2d
  26. F.C + C A Ceu FB; adeoque (ob similitudinem trianzulorum P. AF,
  27. EL B FCHI EBG) AF 1d L. TUE CFF 2d BC. FA icidem.
  28. ex natura Sectionum Conicarum, L. Y (Ccu C) 2d CD ut CD ad
  29. CFT; aeque, adeO CX aQUO PeRTUrbaTC, F ad CD ut C D ad BC.
  30. d. F. D
  31. Corol. 2. Ilinc A tangentes dux FG, P Q cansentibus parallelis
  32. AF, BC OCCurranE in F e G, P e Q. seque mutuo secent in O;
  33. erit (ex aequo perturbace) AF ad B a uE A P ad B C, e divisim
  34. Ut F P ad G ∞ atque adco uE FO adO.
  35. Corol. 2. Unde etiam rectae duxe PC, F per puncta P ec C
  36. F ex _ ductae concurrent ad rectam AC. B per centrum Figurx &
  37. puncta contactuum A, B tranleuncem.
  38. LEMI
  39. L
  40. DE MOTD
  41. EORPOKVM

Cite

[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 84. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0118?run=74