Leibniz Legible

Machine transcription of the Leibniz Nachlass

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Qua Continentur De Angulo Contactus & Semicirculi, Disquisitio Geometrica. De Sectionibus Conicis Tractatus. Arithmetica Infinitorum: sive de Curvilineorum quadraturâ, &c. Eclipseos Solaris Observatio, fol. 41

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: 0.87.

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The machine reads it as

  1. is o
  2. PxOD. SL.
  3. Arithmetica Infinitorum.
  4. merice proportionales. Vel eciam, quia si recta sinE Serics
  5. Ouarcanorum, Ouincanorum, _c. Plana timilia ad has LCccas
  6. timsilicer polica, crunt leries Octaranorum, Decimanorum, _c.
  7. quibus conrenit racio 3 ad9, 1 ad 11, _C.
  8. SCAOLLV M.
  9. Acq: hoc pacto Rsurarum solidarum superficiebus curris
  10. comprehenlarum insens mulcicudo recuci poltune ad aliasu.
  11. Superticiebus planis comprehenlas; corpora non modo conic:
  12. (quod docuerunt rereres) sed _ alia quamplurima conoidica,
  13. ad eylindrum reduci. Guod vescio an quilpiam alius ancehac
  14. ostenderit.
  15. PROP. LI. Lemma.
  16. Exta eandem regulam (prop. 46, 47.) Si expONA-
  17. tur series quancitatum quarumlibet, juxta quam-
  18. libet Tabellae Seriem; de illarum radicibus qua-
  19. draticis, cubicis, ac. aut quibulris intermediis pore-
  20. Ctacibus, paricer inguirendum exit.
  21. Exlempli gracia; s exponantur infinica ouadrata (rel quae-
  22. libec plana similia) juxca seriem Cmartanorum; (cui astigMaCUT,
  23. in Tabella, racio 1 ad 5:) series lacerum (vel rectarum in illis
  24. similicer politarum) racionem habebit (ad leriem aequalium)
  25. 2ad 3: quia 1, 3, 5, lunc arichmecice proportionalia: vel eci-
  26. am, quia ubi plana tunc series Ouartenorum, eorum lacera
  27. erunc series secundanorum, quibus assignacur in TebcIla racio
  28. 1ad 3.
  29. Sic, s exponantur cubi infinici (vel ouxlibec similia Colida)
  30. suxca Ceriem sexcanorum, quibus in Pabella consruie racio 1ad
  31. ; eorum laceribus cubicis (vel rectis in his lmilicer poticis)
  32. conreniet racio 1 ad 3; e horum lacerum quadracis (vel planis
  33. in cubis illis similicer posiris) rario 1 2d5; quia euarum medi-
  34. arum arichmecicarum incer 1 _ 7, minor cR 3, MajOrS, (LUINE
  35. enim 1, 3, 5, 7, arictmetice proporcionalia: duns aucem medias
  36. Arichmecicas interxono incer 1_7; quia colidem supponimus
  37. medias Geomerricas inter unicacem _ cubUM, MEnIPC LACUIS
  38. 8

Cite

Qua Continentur De Angulo Contactus & Semicirculi, Disquisitio Geometrica. De Sectionibus Conicis Tractatus. Arithmetica Infinitorum: sive de Curvilineorum quadraturâ, &c. Eclipseos Solaris Observatio, fol. 41. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/824573315:0253?run=74