Leibniz Legible

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. 878

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: 0.88.

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The machine reads it as

  1. Cuamorr Cetcididudis.
  2. Cap. V
  3. P ROP. XXVII.
  4. A. B. Figura spHalIS (linea Spirali a principio Orta, et recta contermina,
  5. terminata) est contermini Sectoris Priens: Toties repetitis omni-
  6. busu quoties iterato describuntur.
  7. Sumprisque anoulis AMI T, A M P, ec. arichmetice proportionalibus;
  8. E Figura Spiralis primo conreniens ponatur F; eadem per duos con-
  9. FInUata CFIE B; DEF FrCS, 27; Per quatuOr, 64; e sic deincCPS,
  10. lecundum numeros cubos continue seguentes.
  11. Pocaque fgura circulationis primae, est contermini circuli primi Fri-
  12. ens; e, duarum circulationum (repetito quod in secunda iterato
  13. describitur, quod ubique intelligendum est,) ejusdem Circuli primi
  14. Octo trientes; Trium Circulationum, ejuldem Vixinti septem Tri-
  15. ences, (seu corius Noncuplum;) Suacuor Circulationum, ejusdem
  16. Sexaginta quatuor Frientes, et sic deinceps.
  17. Ft, universaliter, (polico R procirculiprimi Radio; P, pro ejusdem
  18. peripheria; ansulique circulationis quonsque libet continuatae pa-
  19. tione ad quatuor rectos; vel correspondentis arcus circuli Primi, ad
  20. inceoram ejus Peripheriam; ut à 2d P:) Fieurx Spirales sic
  21. descriprae srepetitis toties omnibus quories deseribuntur) Magnitudo est
  22. 522
  23. Adeoque, qua continuis Circulationum aneulis equalibus conveniunt
  24. fourx Spirales, sunt ut numerorum cuborum continue sequentium
  25. On 2, 8, 279649 T25, EC. differentia; 2, 7, 29, 37, 62, ec.
  26. Et speciatim quod Circulatione Prima describitur, est contermini Cir-
  27. culi primi Friens; quod secunda, ejusdem Primi Circuli Septem
  28. trientes; quod Tertia, ejusdem Prientes Novendecim; quod Duar-
  29. ta, ejuldem Frientes Frisinta septem; quod Oninra, ejusdem Iri-
  30. entes nus et sexaginta. Fit sic deinceps.
  31. Figurx Spiralis (a Principio orCX) quousque libet concinuatae, cories
  32. repecitis omnibus quoties iterato describuntur: (positospro linu
  33. recto anguli circulationis, ad Ractium R; ex pro sinu complemen-
  34. ti; iploques, pro Semicirculis secundo, quarto, (exto, Octaro, Cx
  35. cerisque in locis paribus, per contrarium signum semper expolito,
  36. urpore ad concrarias diametri partes posito:) Momencum respectu
  37. RECtR PMP, est a R = 65R =6av R - a P + 3ais + a v; Cenrrique
  38. 22aR + Z25F = +2aVR 2a +6a5R = 2~VR
  39. Et quidem vel ad partes P. vel ad parres C, prouc sienum F, vet
  40. Pravaluerie.
  41. H. EiusquE MOmEnCUm respecta rectX F. MC,
  42. v + 32 P. = bas Re -3a v + asR. Cenerique eravicatis inde di-
  43. Rtantia,
  44. 22VR1 = 6a 2 R3 - + 245P3 =6a 2 V R 2 + 2 a35
  45. vel ad partes P, rel ad parces F. prout sienum F, vel -, praeralue
  46. 2
  47. 2

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. 878. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0898?run=74