Leibniz Legible

Machine transcription of the Leibniz Nachlass

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[Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica, fol. 404

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.

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The machine reads it as

  1. AREPEMEETCA PEOD. LACLLELVELI.
  2. proreniens seriei Secundanorum reciproce proportionalis. Lula
  3. (quod tancundem valec) series Aqualium per seriem Secundanorum; erir Peries
  4. Et pari modo in omnibus ejularot c sons conc
  5. 02 2 242 4a2 9a 2 16a2
  6. LROP. LZXXVIII.
  7. CorollatEum.
  8. Tinfinita numero plana (parallela) Paralle lepipedi, ad totidem rectas Ld
  9. venientium erit reciproca seriet Primanorum, quae quidem rectae sunt suis a
  10. vertice distantiis (vel, si placet, diametris interceptis,) reciproce proportio-
  11. nales.
  12. Esto enim Parallelexipedum, cujus infinica plana equentur quadraris coridem
  13. rectarum Parallelogrammi ADt, quae l applicentur ad rectas Prianguli ADB,
  14. prodibunt rectae (rectis triansuli et Parallelogrammi certiae provorcionales) tigu.
  15. anculi (aequealti) applicentur; (vel si respectivis rectis Triansuli, C la
  16. ralleloerammi. sumant a proporoales;) series rectarum pro-
  17. 5
  18. nam ADB mixtam consticuentes, quae reciproce proportionales erunt tam hom-
  19. Jogis rectis Trianguli (quia nempe cum illis conttituune rectansula aequalia,)
  20. quam Diametris incercepiis, seu distantiis à vertice, quae (proxter Similia Frian-
  21. sula abscicta) Tune illis criangul rectis proportionales.
  22. L RO P. LXXXIX.
  23. Corollarium.
  24. Dem contineet, si Plana Pyramidis (quadratis rectarum Frianeuli ADF.
  25. aequalia applicentur ad totidem Rectas Complementi Semiparabolocidis
  26. Cubicalis ADBC.
  27. Patet ex PrOP. 87. Nam (UE In DCOP. praeced.) series primanorum ex quibue
  28. contlatur Friansulum, est uno gradu Luperior, quam feries N quatium ex quibus
  29. constat Parallelepipedum: Sic (in hac Prop.) Series Fercienorum in complemento
  30. semiparabolocidis cubicalis est uno gradu superior quam series secuncanorum ex
  31. quibus constat Pyramis. Verobique igieur provenir series seriei Primaniorum
  32. reciproca.
  33. P ROP. ZC.
  34. Corollarium.
  35. Dem co si Plana aladoeidis Parabolici (hoc est, series Pri-
  36. manorum,) aequalia, quadratis rectarum semiparabolae A. L. respective
  37. applicentur ad rectas complementi semiparabolae AD BP. (Seriem nempe
  38. Secundanorum.)
  39. Nam e hic index seriei dividemis unicace superat indicem seriei dividendae.
  40. P RO P

Cite

[Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica, fol. 404. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0424?run=74