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. 369

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.

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

The machine reads it as

  1. exOp. X
  2. FINEFORUM
  3. PROP. A
  4. Corollarium.
  5. Tque in(uIper, Linea Spirales hae una duabus, cribus, quatuor, 33c
  6. circulationibus factae, (puta M A, N AB, M ABC, M ABCD,
  7. se habent ad invicem ut numerorum Prithmetice proportionalium quadrata;
  8. nempe ut 2, 4, 9, 26, 3c. Sive sunt in duplicata ratione rectarum M A, MIB,
  9. MTC, ATD, CC.
  10. Sunc enim recta M A, AB, BC, CD, invicem aequales (proprer aequabilemm
  11. progreltum puncti mobilis in recta MIA, etiam continuata, rantum in una circu-
  12. latione aequabiliter progrediencis quantum in alcera;) adeoque tam radii M A,
  13. MB, MC, ND, quam Peripherix (illis ractiis deseripea) A, B, C, D, FunE ad
  14. invicem uC E, 2, 3, 4. Si igicur sumancur peripheriae, prima lemet, secunda bis,
  15. texEIA TeT, quarra quater, crune illa mulcipla, (puta Y A, 2B, 3C, 4 D,) ut nu-
  16. MerI quadrati 2, 4, 9, 26, (VC LXI, 2X2, 373, 4X4. RC propterea etiam hO-
  17. rum mulciplorum lemilles, hoc est (per PTOP. 5.) Spirales M A, M AB, M ABC,
  18. M ABCD.
  19. Vel aliier, Si circuli primi peripheria ponacur A = p, erie secundi B = 2 p,
  20. TCrEII C = 3 p, quarn D == 4 P, _ SiC deinceps; e IA = E p, 2B = 2X2 p == 4 p.
  21. D = 4 X4 p = 26 p: _C. EL (per PrOD. 5.) Spirales
  22. et a = 3 p, t A B = EB =3B, M ABC = 3C = 2p, MABCD =3B = 18 p, _c.
  23. ideoque ad invicem UE F, 4, 9, 26, ecc. hoc est in duplicata ratione rectarum
  24. MlA, MB, M Cy MD, eec. (quae sunc ad invicem HC 1, 2, 3, 4, ec.) Quod
  25. erat demonstrandum.
  26. E ROP. XI
  27. Corollarium.
  28. universaliter; Ejusdem (vel similium) Spiralis segmenta quaelibet
  29. (a principio Spiratis exorsa) sunt ad invicem in duplicata ratione re-
  30. ctarum conterminarum.
  31. it
  32. Cum enim (per constructionem linex spiralis) cadem siE racio rectariim M. I.
  33. NI F, gyae est angulorum PM F, PM P, (anguli voce eo sensu sumpra qui
  34. Tupra InNUITUI pTOP. 5.) ratIO arCuU PF, PF, (quae ex duabus illis rationibus
  35. COMPONITE,) ut e spiralium MF, M F, (quae istorum arcuum sunE semilles,)
  36. erit duplicata rationis rectarum M P, M T, Peu VE M F9, M F9
  37. Sic V. 8. E recta M A (unius circulacionis) dicacur Fr, e peripheria circuli
  38. primi (eo radio descripra) E P, eric spiralis M A = Z P. Pgitur, in una circula-
  39. tione cum semisse, Aec recta contermina L Zr = Zr, e Decipheria concermini cir-
  40. culi 3B, quae ducta in 3 (numerum circulationum) AE Z X 3 X p = Z p: Ejusque
  41. semiltis - p = 8p est spiralis eodem tempore deseripra.
  42. Similes autem appello Spirales, si recta M A, MB, MC, Bc. in unam aequa
  43. les sint homoloeis rectis in alsera.
  44. PROC. LLL.
  45. Corollarium.
  46. T vero ejusmodi spiratium assu (Palco S. LA B In una tanta sit
  47. quanta VIC in alia) rectae conterminae sint aequales; erunt Spiralium il
  48. larum sermenta homoloeis sant tenm (patio a Alala B M A in altera)
  49. tel or 6b voblatted.
  50. Nam

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. 369. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0389?run=74