Leibniz Legible

Machine transcription of the Leibniz Nachlass

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[Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis, fol. 548

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: 0.81.

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The machine reads it as

  1. DE SECTTONEDUS. Cap. III.
  2. aecoque + R 44 - 4 RgAq + A44 = E9 = +R9 - P4; et + R44 - AR 9A4
  3. + A99 = PGEq = 4 PgRg -P94. ErSO, P99 + A99 = + P4R4 + 4 AgR9
  4. =4R94. EL, Sumiliter, PrOPIeE
  5. R9 = P. 4 = A = Y: 4R9 -59: acteo.
  6. gue +R94 = + RAF 4 + E 44 = Ag = 4 R4 = 59; et 4 R49 = 4 R 9F4
  7. FF99 =SgAg = +R959- 599: Fres 594 + E. 49 = + R954 + ARGF4
  8. 4R99.
  9. 36. Sed cum A, P, cum F, S, concinene anoulum semiguadrantalem, Peu gra-
  10. duum 45. (Ve qui est angulus in peripheria insistens accui quactrancali.) Lt
  11. angulorum ad balin alter elt obcusus. F15O,
  12. 37. In crianeclo rectilineo, cujus aneutus in vertice est eraduum 45, seu recti
  13. semis, e ansulorum ad basin alter obtusus: Si auplum acoreeari quadratorum
  14. crurum (UC 2 Pg L 2 A 9) dempto quadrato basis (Og == 2R9) ducatur in
  15. quadratum basis (2 R 9:) Produetum (4. P 9R9. f 4. AgR9 - + H 99 = 2P9
  16. F 2 A 9 = 2R9 in 2R9) aequatur crurum biquadratis, (P49. F A94.) Si-
  17. milicer, 254 + 2P.9 2Rg in 2R4 = 45gR9 F 4 Li gR4 4R49 = 599
  18. + P 99.
  19. 38. Arque hrinc paret Alia methodus Radendi Biquadrata.
  20. 30. Trem: In tali trianculo, cujus anculus in vertico est graduum 45, an-
  21. eutorum ad basin alter obtusus: Si duptum aecrecati quadratorum crurum, duea
  22. cur in quadratum vasis: Productum aequatur Biquadratis omnium laterum. Nam
  23. proprer 4P9k9 F 4A929- 4R99 = P99. f Agg: tirgo P99 A99.
  24. +R99 =) 44 = 4 PgR4 + 4 AgR9 = 2P9 f 2Ag m (2 R9 =) 99
  25. EC, proxter 4S9R9 F 4FgR9 - 4R99 =-599 F F99; Frgo599. f E99.
  26. (4R99 =) 999 = 459R9 F 4 F. 9R9 = 259 f 2F9 in (2R9 =) 99
  27. 40. POrrO: Si circulo inscribatur quadrilaterum,
  28. cujus oppolica latera Finc S, A, e Q, Q; e diago-
  29. nales P, P, (ut in Schemate:) Fum, P4- (99=)
  30. 2R9 = SA. FrGO = 2= 2R4=5 = Y: 4R9
  31. A9. E, P9 - ZRa = A = Y: 4 Rg- 54.
  32. ErBO P94 = 4PgR4 + 4 R44 = 59 = 4R4
  33. 19. F, P49 + PgR4+ +R42 = 19 = 4 24
  34. =S9. EL, consequenter, P g9 - 4 P gR q. F 4 R94
  35. =A959 = 4 R9A9 - A99 = 4 R959 599
  36. 4T. Acque, eadem ratione, Si quadrilacerum inseribatur cujus opposica lacera
  37. SinE E, P, G, Q; e diagonales 5, S: Tum 59- (99 =) 2R9 = F. P.
  38. Frgo 54
  39. R
  40. = P = Y: 4Rg - E9. E, D9- 2R4 = F = 1: 4Rg - P4:
  41. Ere0 344= +5quq + 4RG4 - Cg - 4Rg- Pg. F, 394 45924 + + R94
  42. =P9 = 4 R9 = F g. ET ConSeqUentr, 599 = 4SgRg F 4R99 = PGF. 9
  43. qPgRq= egq = 4E9R9 -- 1.99.
  44. 42. FF uroquE modo concludetur, 599 F P99 = 45qR9 F 4 PqR9
  45. 4R49.
  46. 43. Sed P, S, continent semiltem recti anguli, seu angulum graduum 45;
  47. (ur qui est anculus in peripheria insistens areui quadrancali;) ansulique ad bâlin
  48. Tunc acuci ambo: F. r80,
  49. 44. In trianeulo rectilineo, cujus aneulus in vertice est eraduum 45, e uterque
  50. ad basin acutus: Si duplum accreeati quadratorum crurum (ut 2. 59 = 2 P 4)
  51. dempto quadrato basis (O 4 =. 2 L 9) duvacur in quadiacum basis (2 R 4) 210.
  52. ductum
  53. ti
  54. Iu
  55. C
  56. ae

Cite

[Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis, fol. 548. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851708439:0572?run=74