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Machine transcription of the Leibniz Nachlass

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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. 476

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: 0.89.

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The machine reads it as

  1. ARTTAMETICA LTOP. CiCI.
  2. Acque tractenus Nobilissimi Viri mencem, quanta pocui brevicace simul acque
  3. perspicuitate exposui; quaque de iplins mechodo dicenda habus breviter indicari.
  4. P R OP. CXCTI.
  5. Theorema.
  6. Tse aegnabilis Curra (non hrinc inde Cubsultans) V C, cujus Axis
  7. DVX, et Pansens in rertice VP: unde ductis ad curram rectis axi
  8. parallelis, et ab invicem aequalibus distanciis remoris, harum Secunda,
  9. Duarta, Sexta, Octara, etc. (in locis paribus,) sine uE T, 6, 30, 540,
  10. _C. (qui numeri tiune ex continua mulciplicatione hOrUM, ZXEX 13, X 15 X ,
  11. eC.) Frit, ur Secunda ad Tertiam (hoc est, ue xad numerum ipsIS I,
  12. s, incerponendum,) sic Semicirculus ad Ouadeatum Diametri.
  13. Sequitux ex PrOP. 139, et 135.
  14. P R OP. CXCITI
  15. Theorema.
  16. L exponatur aequabilis curra VC, cui occurrat in verrice VY.
  17. unde ductis ad curram quoclibet rectis parallelis et aequaliter ab
  18. invicem remotis, harum Secunda, Ouarta, Sexta, Octara, Decima, _c,
  19. (in locis Paribus,) sint uE 2, 233, 583 3 ec. (qui numeri Aune ex
  20. continua mulciplicatione horum, 2, X3X3 XZXZ etC.) Frit, ut Secunca
  21. 2d Tertiam, (hoc est, ue r ad numerum ipsisL, 3, interponendum,)
  22. sic Circulus ad Ouadratum Diametri. (VF autem Sccunda ad Ouin-
  23. tam, sic Triplum Circuli ad Ouadruplum istius Ouadratiu _c.)
  24. Sequicur ex PFOP. X18, 12T, e 285.
  25. P ROP. CXCIV.
  26. Theorema.
  27. Tsic aquabilis CuerX V C, axis VX tangens in vertice V P, un-
  28. de rectae ad curram ducta (axi parallela e aequalibus interstuiis
  29. dissita) lccunca, quarta, sexta, octara, decima, ec. (in locis paribus)
  30. lint uE 2, 238,18, 23 ec. (qui numeri hiunt ex continua multiplica-
  31. tione HOTUM FXZX ZX3X B _C.) Prit, uc secunda ad tertiam (hoc est,
  32. ut c ad numerum ipsis F, Z, interponendum;) sic Circulus ad 3 Oua-
  33. drati circum (exipei(sire Ouadrati ex Diametro;) Sire Triplum Circuli
  34. ad Ouadruplum Ouadrati circum scripei. (Oc aurem Sccunda ad Ouin-
  35. cam, sic Friplum Circuli ad Octuplum iltius Duadeati _c.)
  36. PateE ex praesed. _ Tabella pFOP. 189.
  37. dC FOT. L M
  38. Ec quidem hujulmodt alla propotitiones innumera ex eadem Labella (prop. 180.)
  39. deduci pollime: Formaris scilicet aliis acque aliis ejusmodi curris juxra istius LL
  40. bellae tenorem.
  41. Ouales aurem futurx sine illae omnes curra non adeo Facile erit juclicare.
  42. Hloc incerum de quibuldam observare licer. Nempe; In terie serta, numeri (Pri
  43. angulares) F, 3, 6, 20, _c. (qui tiune ex continua musriplicatione horum
  44. TXEXZ XIS _C.) Sune uc quacdraca ordinacim applicacarum in Hyperbola; ue di.
  45. ctum est prOD. T73.
  46. In serie Ouarta, numeri (arictmerice proporcionales ) 1, 27 3, 4, 8c. (qui Fi
  47. une ex concinna mulciplicatione horum FX3 X E X E eC.) Luneue quadrata ordina-
  48. tim applicatarum in Parabola: sire ut rectae in Friangulo: ut patet.
  49. T2

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. 476. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0496?run=74