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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. 144

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. DE PROGRESSTONE
  2. et te
  3. A, M,
  4. NI, V
  5. 7 = 2. M -
  6. A = 2MI - V
  7. 34. Acque idem valet de tribus quatuorre terminis progrectionis Arichmeticae
  8. ueur non immediace proximis, modo aequalibus urobique incerralsis distantibus.
  9. Puta, (I a b,6, d, e, 538, 3. Cxit a f e ==26. NTam _Ca, C, C, = Der prOP. 14. Lrem
  10. a +5 = 6 + d. de d. F e = b + 8. FL GC alibi. Nam a,C; a, f. Vel a, d; 6, f. _ b, c:
  11. dy 8, Velb, d; cn 8. etC. Per PF. X2
  12. 35. Sed de praecedencium aliquor conversae paricer demonsrantur. Pura con-
  13. verla pr. 28. In concinua proerellione Rrichmerica, (excepta tantum progrestione
  14. aequalium, ubi exceltus ele ubique nullus, puta, 2, 2, E, L, _c. :=; qua _ deinceps
  15. aliquories excepta intelligatur,) Si duorum intermediorum cerminorum asoresatum
  16. acoregato extremorum aequetur, lune illi ab excremis aequaliter uerinque remot:
  17. (hoc est, quoc gradibus intermediorum alter ab alcero extremorum, cor religuus
  18. a religuo distac.) Puta in prosreltione an b, C, du e, f,8, == HIC F e = a L ∞, TOri-
  19. dem gradibus diltanca, c, aique e, s; item an e, aique c, 5. Cum enim quanco duo.
  20. rum C, en alter major elt quam a, tanto alier minor sic quams, (lecus enim agere.
  21. Sata non ellene aequalia,) distantia urobique aequalis crit, Per PFOD. 13.
  22. 36. Et converia prop. 29. Si termini alicujus intermedii duplum aequetur 28-
  23. Gregaco extremorum: aequalicer ille ab. viroque extremo diltat. Probatur uE Pra-
  24. Cedens.
  25. 27. TIeM COnVerS PrOP. 32. Si uniustermini duplum aequetur duorum agore.
  26. Bato, erit ille medius Rrichnccieus inter hos. Nam, nisi aequalibus disterentiis ho-
  27. rum cum alter major sic cum alcer minor, quam est exposuus, non constaret aequa-
  28. litaS.
  29. 38. Similiter et COnVKIa PrOP. 30. Si bini binis cimul sine aquales, crune illi
  30. quacuor termini Arithnerice (ut loguuneur) proporcionales. Puta li A F V =
  31. AI NI, quanto horum alter puta M, Luperar alterum illorum pUTa A, tanCO BO-
  32. rum reliquus ab illorum reliquo deticie; (nam nili excellus et detectus se mutuo
  33. perimane, non constabic asgresatorum aequalicas:) Fdeoque M - A = V --V
  34. F
  35. HrgO A, MI = A F L; N, V =- N V F. Vel lic, quia A. ] V, ==MI F N; crit V =- M
  36. + N- A, _ V = N = M - - A1 ErGO, per det. A, M; N, V. Sed e codem aro
  37. enEO M, A; V, N. vel V, N; MI, A. Item, cum sic V =M f N - A (uc dictum
  38. CAt) eric cciam V = M = N = A; Ideoque V, M; HI, A, ec M, V; A, N, vet A, B;
  39. M, V. Acque hinc sequicur, non camum
  40. 139. Si quamor termini line arichmerice proporrionales, Tunt ec inverse proPOr-
  41. tionales; (Incellige, si A, M; B, V. vel N, V; A, ML, CUM MI, A; V, N, vel V, N;
  42. M, A.) quod ex ipla detinicione sequitur. Nam S in alteris sE aequalis exceltus,
  43. in alteris erit aequalis detectus; adeoque utrobique prosrestio Arichmetica. Sed e
  44. 40. Si quatuor termini sinc Arichmetice proporrionales, sunt e alterne (permu-
  45. cacim, viciltim,) proporcionales. FIoC Ost, s A, ML: N, V, idCOqHC A F V = M f N
  46. eric A, N; M, V, uc ostentum est prOP. 38. Tcem N, A; V, M, ut ilidem, ec prOP. 39.
  47. 4T. Tiem si Arichmerice proporcionalium vel primus et cercius, vel secundus et
  48. quarcus, aequaliter vel augeanCuE, vel inuanEuT; manent achue Arichmecice pro
  49. Porcionales. Puta, l A, M, N, V, hoc est A, A ] P; NV, N. Y F; eric cciam A, NI ] B:
  50. NI, V + B, hoc cMt A, A Y R. Y B; N, N. J F J B; Nempe illic communis exceltus
  51. elt k, hic H, F B. Trem A F B, NP = A J Fi; N. F B, V = N + R, ubi commu
  52. nisexcestus elt F =B. FI, pari de cauta, A FB, M + C, N F B, V FC; Ex pariter
  53. in similibus. Ouippe qui pritis etat communis excellus, utrobique vet pariter au-
  54. secur, rel pariter minuitur, adeoque etiamnum urrobique aequalis; et propterea
  55. cermini Arichmeried proporcionale s; ecri CN CssiI
  56. 42. Icem, li Arichmeciee proporrionales (INCTM A, MI. N, V. cum aie; v,V; cum
  57. a m; n, un (cum, li placet, quaterni plures:) eryne irem cum aecregaca, tum dit
  58. Ferencia, terminorum respectire sumprorum, termini proporiionales. Puta A F a Fa-
  59. M F e. Fm; N F v Fn V F 0 F u. Nam si in primis excellus sit ubique F, in se-
  60. CunetiSE, In TETEIS =C; erit in quarcis P. + c L e. Or acdirione parebit.
  61. D111

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. 144. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0164?run=74