Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

[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. 378

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.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The machine reads it as

  1. A R PTEMETICA PFOP. XXXII.
  2. cem, ut 2 ad 3, nempe ut circulus bis sumptus ad eundem vel aequalem ter sum-
  3. Pcum;) hoc est, in reciproca ratione rectarum homolosarum M A, NI A. Nam
  4. MA in prima Cst Z rectx MIB, e MA in Sccunda = (aequalis rectae) MC; Tunt
  5. isicur M A in sccunda, ad MI A in prima, uC 3 ad Z, vel 3ad 3, vel 2 ad 3. Tdeo.
  6. que Figura M A BM in Spirali prima, ad tiguram M ABCM in spirali sccundu,
  7. uc recta M A in secunda ad rectam M A in prima.
  8. Acque idem similicer oltendetur, quaecunque sit ratio homologarum rectarum in
  9. distimilibus spiralibus.
  10. PROP. XXXII
  11. Corollarium.
  12. CT autem ejusmodi fieurae Spirales, lineis Spiralibus dissimilibus, e rectis
  13. item inaequalibus terminentur; erunt illae ad invicem in ratione quae com-
  14. ponitur ex triplicata ratione rectarum terminantium, ed reciproca ratione re-
  15. carum homolorarum.
  16. Seguitur CX PFOP. 30, 3T.
  17. eROP. AAACII
  18. Corduurium.
  19. quartan 6c. desrouut, sat ud norcemu ut 27 7, 29737, 649 66.
  20. nempe ut differentia numerorum cubicorum, quorum latera sunt Arithmetice-
  21. proportionalia.
  22. Nam (Der pr. 29.) Guae pra, qua Pa e secunda, quae prima secunaa c
  23. tertia, quae prima secunda tertia et quarta, ecc. describuntur: Tunt ut 2, 8, 27
  24. 64, +25, _c. ergo, quae prima, quae secunda, quae cerria, quae quarta, ec. deseri
  25. DOrro, Fieura Spirales, quae bialindus prima secunda, tertia
  26. buntur, Iut L, 6 = 1, 27 -8, 64. = 2p 2
  27. 27, 61, dc. nempe ut ditterentix numerorim cubicorum continue proximorum:
  28. 5 = 64, _c. hoc est, UE Y
  29. ATICLMCLICC PIDOIOnaleS: Nam X F 6 = 7. 7 F L um l9. 19 + 16- 31.
  30. 37 =24 = 0L. C.
  31. Ouarum quidem disserentiarum exceltis, sire ditterentiarum differentix, sune
  32. PROP.

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. 378. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0398?run=74