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. 217

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: 0.90.

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The machine reads it as

  1. Cap. XLIII. MULTIPLTCATIONE, EEC.
  2. a - b (a + ac = b2 - bc (a + B +c
  3. Adeoque communis illius Divisoris ope reducentur exposiixe quancitates a2 f ac
  4. bc, e ab + af - b2 -bf, ad cerminos in cadem ratione minores a + b
  5. F6, _B + f. Adeoque a +ac = B2 - bc a + b +c
  6. ab.
  7. 5-
  8. b +f
  9. In hujusmodi iiaque casibus, acque hiscetimilibus, Pagacitate opus erit, et con-
  10. tilium in arena capiendum, ul ex posicae quancicases compolicae, ad simplicistimas in
  11. cadem ratione LCdUCaNEuE.
  12. Sed de Addicione de Subductione hactenus.
  13. Gi A P. XL III.
  14. Fractionum Multiplicatio Divisio: per numerum In-
  15. teerum; per numerum fractum. Multiplicationis, e
  16. Divisionis inversae, aequipollentia. Producti, e Quo-
  17. tientis, in minimis terminis exhibitio. Operationum
  18. praecedentium (Saditionis, Subductionis. Multipli
  19. Fractio-
  20. cationis. Divisionis) brevis Synopsis.
  21. CEquitur Fractionum Mulciplicatio et D vitio.
  22. D Si Numerus fractus per Inteorum mulciplicandus, Cit, nihil hrie disticulcacis nis per
  23. inest: Ouippe id sola Numeratoris multiplicatione peracitur. Sic 3X 2 = 2. Nam numerum
  24. bis duo sunt quatuor, quaecunque demum ea sint quae numerantur: Sive integea integrum
  25. Sinc, sive partes. Oua enimratione, bis duo homines, lune quatuor homines; bis Multi-
  26. dO COTPOTA, quatHOT COrPOTA; bis duo incegra, quacuor intesra; bis duo millia, plicatio
  27. quacuor millia, ecc. (nempe, quia bis duo Timpliciter, TunE quatIOT:) cadem, de
  28. bis duX PaTLES, quacOT parteS ; bis duo quadrantes, quatuor quadrantes; bis duo
  29. guintances, quacuor quincances, (live partes quinta.) Sec. Sic Z X A, vel ZA, exit
  30. Sic DX =, vel, Z xD, vel Z D, exie =. Et sic in aliis.
  31. Vel etiam, quoties id commodetieri pocest, pro Multiplicatione Numeratoris,
  32. Tublticui porerie Denominatoris Divisio. Ouippe idem ommino sic, quoad tractio.
  33. nis valorem, sire mulciplicemus Numeratorem, sire Denominatorem dirictamus:
  34. e Conra. Si enim verbi gracia, duplandus sic numerus Fractus Z: perinde cst lire
  35. duplicetur numeratOY, ut tatS; Cire denominator bisecetur, uc tiat 3: eadem enim
  36. urrobique prodibie tactionis quancitas, 5 = Z, quoniam eudem est iurobique nu.
  37. meratoris

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. 217. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0237?run=74