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. 538

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: 0.92.

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

The machine reads it as

  1. CiTCLOIDF.
  2. De Dimentione Cycloidum Concractarum et PTOIALCaLEMI.
  3. Propturates quaedam Cycloidum.
  4. Eper eandem Balem CMI constituantur tres Cycloides genere tees, lcult
  5. D Cet Ca AMI Primaria, cujus genitor est AHID: C0OM Crclois quaedam
  6. Contracta, cujus genicor est OFD: _ GTCF. M, Csclb GuacaM Lrorracta, cu-
  7. jus genicor cAt F. K D
  8. Primo, quoniam Cyelois cujutris generis tc ex moc aequabili in peripheria se-
  9. nitoris, dum interim genitormoeu aequabili cranstertur, Cuver datam balem, donce
  10. punctum generans circulum absolrerir, a puncto contactus incipiens et ad idem
  11. rediens: Ergo utrique Mocus, tam circularis quam rectus, erunt ubique in cadem
  12. ratione. Duare in omni Cycloide, A ducatur Bali parallela d Genirore ad curram.
  13. ut FX, vel HP, vel RZ; erir ue mocus in arcu OF, ad mocum in semicireulo
  14. OFD, ica mocus rectus FX, ad semillem corius monis recti, scilicet femibalem
  15. DM. Similices uc arcus A HL ad semicireulum Tuum AHD, ica H Y ad semibalin.
  16. Idem dicicur de arcu P. R e recta K L
  17. Ouare policis in directum vunotis D K HF, quoniam areus OF, AH, F. R sune
  18. in eadem rarione ad semicireulos tuos, erunt rectae LZ, IIY, IZ, in eadem ra-
  19. tione ad communem balem DM: sunc ergo aequales, de puncta Crcloidum Z LZ
  20. in directum potica unc; rectae igitur X Y Z N F HKD, sunc aequales, de similiter
  21. lectae ee posiia: Sed F D ee OD similicer secta Tunc: erxd recta LLZ N, O AF. D
  22. similiter secta sunt a Curvis Cycloidum.
  23. Sccundo, quoniam aneulus ODF est ad rectum, ut arcus O F ad semicireulum
  24. suum, seu uE F X vel D N ad DM; erEO, ut M N ad DM, ita aneulus M NX
  25. ad Rectum.
  26. Fercio, juneanuur HIA, eique parallela dueatur Y9. Duoniam demonstracum
  27. est Y O canpere Cycloidem primariam in Y: ergo WY cadit normaliter in Cur-
  28. vam primariae.
  29. TheoremA.
  30. Curva Creloidis primaria est quadrupla Diametri: e portioni
  31. euivis assenatur recta aequalis.
  32. TC semiba lis CD dirita in parces aequales um indetinice minimas, et a punctism in.
  33. Dcidant ubiqi in primariam normalicer rectae ma, et in proxime majorem ma recta
  34. mu: ducantur Dn (subrenta genicoris) _ m2, Parallelx iptim à; ilem AB, à 2, a 8
  35. parallela: quare a 2 tansit Cyeloidem in a, de parallela de aequalis est iptim e Og0-
  36. niam isicur ipla ma l quum lins aequales ee parallela lubtenlis penicoris) sune tinus
  37. angulorum

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. 538. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0558?run=74