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. 349

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: 0.82.

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

The machine reads it as

  1. Cap. L XXXI.
  2. A E G F B R A.
  3. Si ACF Semisesmencum Circuli (cujus Radius AC, Diame.
  4. teT AS,) FOTEUE CIrCA A F: produCETIX Spharx Segmentum
  5. cujus Flementa func O HIB, O D l ac. Scd DHB = D AB
  6. OAHI, eCD DE =O AV. = D AD. e d HC ==C AC
  7. () A F. AF serieS (O AB, O AF, O AG:: AB 9, AE9.
  8. AG9:: ASXATT, ASKAD, ASXAF:: A LB AD, AF, hoc est sC
  9. ries Primanorum: ideoque =O AG X Z A F. HC O AFI, G) AD,
  10. AF, Scc. Clt series Secundanorum: ideoque elt =- AFX ZO AF.
  11. tergo Segmencum Sphaerae cst ; A F X: A G = 3O AF: =
  12. E A F X: O FG F 3O A F. (Id quod elt cheorema jam ulur-
  13. Dacum in menturanda Corona Aheui Cerrisiarii.) = 3 A F X:
  14. C
  15. OFC F IAFH X, LSOFC =IOF Cn AF~ (3Vd f AP)
  16. quod ipsum cst Theorema Archimedis, cognita diametro. Mnod tamen (cum
  17. praesimat diametrum cognitam) minus est ulii accommodum quam iliud alterum.
  18. De Erusto Eyramidis eet Coni.
  19. Sunto A, B, C, D, F, _C. Flemenca Segmeni Frianguli Rectan-. r. . 7F. - - - . . .
  20. suli Parallela bali: Elemeneorum Ouadraca constimune trultum:
  21. F
  22. Pyramidis Ouadrara. Sincb, c, d, X esc. complementa legmenci .. . d . . ... -. 7..
  23. ad parallelosrammum. Sitque A L P = Z. Fum
  24. B9 = AA - 2 Ab F Bb, Scd Series AA, AA, AA, est AEquali- 1. C. . C...
  25. Cq = AA - 2Ac = cc C um, ideoque = p AA. Series Z. AB, ib - - . - - .
  26. Oc. usque ad E 2 AC, ec. Cst Primanorum ideoque
  27. F9 = AA 2AX + XX) = 2p A Z = pAX. SeriCSBB, CC, dec. eAt
  28. Sccuntanorum, Ideoque =-5p XX. ErgO Frultum Pyramidis
  29. e
  30. Ouadratae est = p X: AA - AX f G ZX = pX: AF. + SXX (quod FIL THCOreMA
  31. DrIMUM) = SpX: 3AE + XX = (prOPIEE XX = A A - 2 AF f LF) 3PX: A9
  32. FAF F Pg (Theorema Sccundum) = SpX: Z. A f P. 9 (Fheorema cerrium)
  33. =3PX: LF + A9 (TheOremA quarII) 5 pX Z9 = AE. (T heorema quincum)
  34. vel = : p, 2 44 + 2E2 + 2AF = 1 pr. 29 + A9 L E9 (heorema Sextum.)
  35. Si Fructum Fueric Coni, positis A, P. diameeris Balium: Coliditas per Pheorema.
  36. cum superiorum quodris inventa ducatur in 253. Pariterque mulciplicando per 2
  37. LiOS aPEOS NUMETOS, Pheoremata applicentur Pyramidlibus quamlibet Polvedris. V).
  38. tiigue crunt in Menturandis ratis Cerrisiariis (Anstis Fonnis dictis,) ec Arbo.
  39. rum cruncis.
  40. De Trusto Sphaeroidis:
  41. Sit CBF quadrans FMip(COS, cujus semiaxes CB, CF, ee semipara.
  42. ODt
  43. 1OCB- DCD
  44. metri ad CB racio lic uE L act L, FrGOC NIE =, K CCB GCN E
  45. OCiII)
  46. OCB dC
  47. Erxo Frullum Sphaeroidis cst = =- pr: D CB - ; D CC -
  48. = +2OCB. + =OCB - =O CO = 5 pr: 2OCF + OHC
  49. Ouod ipsum est cheorema ab Ouchereso primo, jamque ab aliis adhibicum invenienda
  50. capacitaci Doliorum.
  51. De Trusto Fusi Parabolici.
  52. Sic Parabolae axis A, et ad axem Axplicata P divisa in parres aequa.
  53. les innumeras; pes rectas B, C, F, ec. axi paralelas; quarum disse.
  54. rEnEIX ab A CIMC n, 2 Bcc. uIque ad X.
  55. EroO B9 = 19 = 2 A1 F B n
  56. C9 = A9 = 2 Am = m m
  57. _c. ulque ad
  58. F.g = A9 - 2 A N + N X
  59. Sed series Aq, Aqe ecc. Cs Aqualium, ad eoque = p Ag. F.1
  60. 2 A m, ec. eA Secunctanorum; proptet rectasn, m, dec. in dupli
  61. co

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. 349. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851708439:0373?run=74