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. 838

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.

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The machine reads it as

  1. Calculo Centri Cravitatis. Cap. V.
  2. Polsunt etiam ex Crcloidum Secundariarum (Contractarum scilicet 8
  3. Crotractarum) Tansences exhiberi; carumque Curris semtpe
  4. aequales; d partes partibus respectire lumptis.
  5. COmpto, in SeMmeyeloidis curva R7, puncto quoris B; aIICL WHLCHIZACUII Bai
  6. 18. 177. Vra, Parallela bB, Circulo genitori, cirea Cxcloids ase La Coc,
  7. curreus in B: Junetaque Chorca AB; ducacur hiuie paraltela, per punctum b, recla
  8. Sbh. Dico rectam sbh,
  9. Semieycloidem in b comringere.
  10. B
  11. Sumpiis in recta sbh, supra b, puncto 8; ec, intra, puncto h: ducancur, ipsi
  12. BB Parallela, recta 8 x X C, hd HD, Semicycloidi occurrentes in X, d; Semicir-
  13. culo in Z, D; chordaeque AB (producta) in G, HI
  14. Otentum est (S A. prop. 20.) arcui BA, aequalem elte rectam bB; adeogrie de
  15. (propier parallelas) sG, e hHI. (Trem arcui Z A, rectam XZ; e arcui D A,
  16. rectam dD.
  17. Cumque ibidem demonstracum sit rectas BP, (tic. 167, 20B, 288.) areubous
  18. BX, ubiqueminores esse; rectasque B F, arcubus BD majores: Similiter osten-
  19. detur, (Hig. 777.) rectam Z C minorem arcu B X; rectamque HI D, majorem este
  20. arcu BD. (Nam Cimilicer, hic, ducitur AB, ab A; atque illic, a B, ab a.
  21. Adeoque; propter cotam p CE rectam, tori B A currx aequalem; e ablatam ZCI,
  22. ablata XB minorem: Frit reliqua X 8 recta, major quam reliqua X A curra, leu
  23. recta XX. Erpropterea, punctum g, extra Cyeloidem cadet.
  24. Icem; propter hE rectam, ipsi B A currae aequalem; de FID adjectam, majo-
  25. rem adjecta BD: Frit cota Dh recta, major quam tora curra D A, leu D d recta.
  26. FC, propterea, punctum h est extra Cycloidem.
  27. Cum iraque, cum 8 (punctum quodris supra b,) cum h (punctum quodris
  28. intra B,) sic extra Cycloidem; (adeoque unicum b punctum Cycloidi commune;)
  29. recta sbh Cycloidem in b cangit.
  30. EIIque (propier parallelas) b8 = BC, bh = BHI, gH = CH; e (producta
  31. b8. donec tangenti verricis A P OCCUETat in T,) bY = BA = C = V 2VR.
  32. PFODEEE AV, AB, A~ hoc cllu V. c. 2. R. continue proportionales; ut CaepC
  33. dictum est.) Irem, (ductis BXO, bBV, hDC, ipsi F A parallelis, AXi Aa
  34. occurrentibus in O
  35. C rectam VO, vel CO, incercipiencibus; quam dicamus
  36. B;) eri uE AY = v, ad A B = Y 2~R; siC VO, vel CO, = B; ad BC, vel
  37. HC; hoc Cst, ad b8, vel H8,-
  38. 8120 =B,
  39. FiB. 177, Si ieaque intelligatur recta A a = 2 R, in partes aequales numero infinitas, di-
  40. ridi, quarum una incellisatur VO, vel OC; adeoque omnes AV, hoc est om-
  41. nes v, eo spectantes, arichmerice proporrionales: Oux his respondene subren(x
  42. toridem AB, hoc elb, toridem V 2V R correspondences; (series urique Tubsecun-
  43. AanOruM;) Tunt ur coridem rectae Vp semiparabolam AP P a (H5. 278. ) com-
  44. plenres; cujus cum AIS Ao cum batis a P, (adeoque de lacus rectum,) it
  45. Rectaeque b8, seu eh, cangences; hoc est, (in parcibus intinice exieuis) ipsa
  46. DX
  47. 1d.

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. 838. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0858?run=74