Leibniz Legible

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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. 444

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: 0.85.

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The machine reads it as

  1. ARITHMETICA PFOD. CLXXII.
  2. Denique, s timul addantur puncta siC InVEnL; nemBe 3 P et 3 = 18 p
  3. e
  4. 61. = 1514 1
  5. rum omnium: Hoc est, numerus criangularis cujus latus L. Tdeoque.
  6. ROP. CLZXII
  7. Theorema.
  8. Acus numeri cujutris Priangularis ad ipsum numerum, est ut
  9. 1 ad
  10. VE oltentum est in praecec.
  11. Adcoque, daco lacere l dabitur numerus Priangulacis illi lateri conreniens,
  12. puca n -
  13. Et Contra, Daco numero Triangulari, invenietur iptius latus.
  14. Nempe, resolvendo hanc Aquationem 2u = 1 + 1, erie Y: + + 2n: -
  15. P R O P. CLXXITI.
  16. Corollarium.
  17. T Fyperbolae Diameter cransversa sit L, e Lacus rectum :: sumpois
  18. diametris (puncto applicationis es vertice interceptis) 2, 29 3,4 5, 0c.
  19. Ordinatim. applicatarum quadrata erunt 1, 3, 6, 10, +5, C5c. nempe numera
  20. Trianculares, cujus latera sunt 29 27 3,4, 5, Bc.
  21. Probatue per 17 vel 33 prop. Con. Sect. nolE. Hyperbolam iptam exhribebie F.
  22. pura prop. leq.
  23. EtsitE
  24. eROP. CLXXIVI
  25. Torodarium.
  26. ADB; Sique ut X ad V = sa AD ad DB, C a D ad DB; es suman-
  27. tur aequales Aa = + = a D = DD e0c.
  28. Rectangula BDB, BDB, Cec. erunt
  29. ad invicem ut 2, 3, 6, 20, edc. numeri
  30. Trianculares, quorum latera sunt a D,
  31. a D, 530. Mediae vero proportionales in-
  32. ter BD, DB; BD, DB, CC. sunt or-
  33. dinatim applicatae in Fyperbola e, DF;
  34. cujus diamerer transversa Ao- e3 latus
  35. rectum aB, vel ipsi aequale.
  36. Lercium 3V = (4V 2- 6. Quareum 4 V 3X5V
  37. 10.
  38. Et lic deinceB. Suae lunc quadrata ordinatim applicatarum in Fyperbola, per
  39. praced. Ideoque Medixe proporionales pura Y Z, Y 3, Y 6, Y 10, _c. ipsae ordi.
  40. nacim applicatae.
  41. Tem, Si fiant ad eandem rectam A a D dua Triangula similia, a DB,
  42. Patet ex calculo. Nam rectangulorum BDB, primum erit V Z XZ V 3 = +
  43. BecunduM Z V 3X3Y3 =3
  44. dC. cbL. +VM
  45. Si aelem sumpta tuistent AD = DB, _ a D== DB, cum rectangula Fuistent
  46. XX2 = 2. 243 b. 34 = d 2. 4x5 = 20, _C. Cupla Mumerorit LHansula-
  47. ruul:

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. 444. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0464?run=74