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[Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ, fol. 41

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: 0.89.

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

The machine reads it as

  1. V E C F. V.
  2. eric. Sin punctum T extra datum angulum exictat, evidens est ran
  3. cum uno modo problemari lacistactum iri; quodque per alceram in-
  4. ersectionem, e Y, ducca recta ad angulum pertinet dato verricalem.
  5. hiaec, inquam, tantillium actendenti manifeste constabune; nihil ut CIE
  6. opus hic plura verba consumere. verum ut in horum caluum primo
  7. constet (id quod pro sequentibus ex usu erit cognoscere) quando
  8. dictus circulus hrperbolem continoit; seu quando tantum una per
  9. Y recta quancicaris ejuldem incerseri poltir, hoc adrectemus Thco-
  10. rema.
  11. IX. Si a puncto quovis Y intra rectum angulum X P F existente F18. 54.
  12. demitrantur ad ejusdem anguli lacera perpendiculares YB, YD; ac
  13. inter YB, YD proportione medix sInE reCtX BH, GD; Per pUnCta
  14. N, E, Co cranlibit recra cunctarum minima, quae per Y ducex ansu
  15. lum X P F subrendere posune.
  16. Ouod HYO CIEuna recta patet, quoniam est YB. BH:: GD.
  17. D Y (ex constructione nimirum) porro per P eranseat alia quxcunque
  18. reCT L YM; _ N Had C N, M H ad P F perpendiculares concur-
  19. rant in HI. item HI A ad NVC parallela ducarur; _ C S ad P F
  20. denuóque connectatur GHI. Jam pacettriangula CDY, YBH;
  21. HIMN, AIM _ Cimilia Fore; quodque proprerea est MH. MR::
  22. MNg. MHq:: DCg. YDg. irem (ob BH, DC, YD..
  23. eABH. YD:: DCg. YDg. hoc est YN. YC (vel MNI. 6S)
  24. :: D6g. YDg. ergo eAt MN. MR:: MN. CS. adeoque M H
  25. =65. itaque major eAt CS ipsa M T; abeoquerCCEX OHI, L. M
  26. PTOTTACEX COnCurreNE; puta ad Z. ergo LM. GH: : LZ. 62.
  27. rerum proxter angulum L G HI recro P majorem, cA L. L. L 62.
  28. quareL ML GHI. ast ob angulum rectum C NH eA CHIC ON.
  29. quare magis est LM E CN. codemque modo quaeris per P ducta
  30. major ostendetur ipsa OH: Q. F. D.
  31. Z. Ilinc etiam Si C N sic in ratione T B ad Y N quarca proxortio-
  32. nalis; erit C NI minima. nam inde consequetur Fore YB, BN, GD,
  33. YD -:. Frenim erit TNg. YBg:: GN. YN. _ dividendo
  34. BNg. YB9:: GY. YN:: DY. BH. ac inde ZBGKDY =
  35. BNcub; velDY=
  36. BNI cub
  37. tione YB ad BN.
  38. B9. IEaque D Y est quarca proportionalis in ra.
  39. ate ant F Anceo hetudt.A Edtat
  40. rioribus

Cite

[Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ, fol. 41. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/797435492:0073?run=74