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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. 169

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. CaP. XXXIII. DE PROGRESSFOHE, SEC.
  2. LLL. XXXTII.
  3. Proeressio Geometrica fusuls rcut.
  4. STCUL TUPCrIUS Cap. XZVII C XXVIII, Frogreltionis Prichmeticae doctrinam
  5. DFulius prosecuri lumus, libet eadem Meodo e Prosrectionem Greomecricam
  6. tunco quibus Cum uturus Symbola.
  7. Terminus minimus, quem primum appello, sic A; MaxiuS V; extremorum
  8. rectansulum H == V X A; maximi ad minimum ratio Z: Rcclangutorum (iptiM
  9. aequa) Celnis reciproce sumpeis CompMeMOru ASGrESaTI, Z; mIeTUS
  10. termnorum, T; communis racio R (incellise, Rationis communs xponentem)
  11. ducanlia termini cujutris à dato, D; Lumi progretionis, S. Termini ipli, a mi-
  12. agcredi, sequencibus propolicionibus explicandam. Ouod quo rectius tat, haec
  13. nimo inchoando, dicaneur. a, B, c, a e, _c. d maximo vero inchoando, dicantur
  14. en B, 7, d _C. Numeros qui cujusque termini d primo distanciam indicane Indi-
  15. ces axpello; puta 0, L, 2, 3, dc. LHS praemullis, lequuntur propoliciones.
  16. 8
  17. AL
  18. (3T22
  19. L+
  20. AL
  21. 30366 AR3 k. 0
  22. T. Si SCa = A, erit B = A R, C = AR2, d = AR3, dc. Ouitibet enim termi-
  23. nus in communem rationem ductus, producit terminum proxime sequencem, per
  24. det. Prosressionis Geometrica
  25. 2. Omilibet erso terminus producitur ex mulciplicatione termini primi in
  26. Rationis communis porestatem Indici cognominem; vel (quod idem eAt) cogno.
  27. minem distanciae iptius a cermino primo, iptum primum non compucando. Nempe
  28. ARd. Sequitur ex praeced.
  29. 3. Datis igitur Termino primo seu minimo, Racione communi de termini quae-
  30. fici distancia d primo; A, R, D; habEEuE terminUIS quasicuS, nempe ARd. per
  31. praeced. Pura terminus sextuS f, cujus index live distancia a primo 5, fic ex ductu
  32. primi in rationis communis poteltarem sun diltancia D =5 coenominem.
  33. = AR3.
  34. 12t 1
  35. 4. Si cerminus maximus tire ulrimus lc V, eric pemulrimus vel R) V; an.
  36. cepenulcimus = L vel R =) V; hinc proxime minor R.) V; de sic deinceps; V = a,
  37. R) V =B, R2) V = y R3) V = 5. Sc. Ouilibet enim terminus per rationem
  38. communem dirisus, dac terminum proxine minorem. Per det. proBr. GeOM.
  39. 5. Duilibet isicur cerminus aequalis ell, termino maximo per rationis commu
  40. nis poceltarem distancia ab ultimo cognominem diriso. Nempe R d) V. per praeced.
  41. 6. Dato ergo termino Maximo, cum Ratione communi, et Distancia cermini
  42. quaesiti a maximo; V, R, D; habetur terminus quasituS. Puta sextuS a fine, Sive
  43. anee ulcimum quincus, s = R3) V. Per Praced.
  44. 7. Daco cermino quovis, (uc f) cumratione communi, de cujusris altienati
  45. majoris distancia a dato; f, R, D; inrenitur terminus altionatus (pura J.) nempe,
  46. mulciplicando terminum dacum in Rationis communis poceltatem distantix cogno.
  47. minem. HOc Ci = fRd = sR3. Nam per det. vel prop. 1. pro fingulis ct
  48. S
  49. Stanciae

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. 169. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0189?run=74