Leibniz Legible

Machine transcription of the Leibniz Nachlass

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Ps. 2, fol. 190

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. L F ML. C U R Y A R U N
  2. Y H E O R E M a VI.
  3. Proposirio 6.
  4. Recta per quodlibec IIrperbola punctum ad ueram-
  5. que Asymptocon ducta, qua in eodem puncto bita-
  6. riam diriditur, curvam ibidem contingit; de Contra,
  7. concinsens ad utram que Alymptocon producta in pun-
  8. eto contactus bitariam divila elt.
  9. Sit per punctum C in FIyperbola BCD, cujus ACympeotiAF,
  10. AF, ducta recta GCII, utrinque ACympeoris terminata, qux
  11. in eodem puncto C bitariam diridatur. Dico rectam OFICur-
  12. ram contingere in C. Secetenim, lihieri potest, recta OFIIIy-
  13. per 2C0r. perbolam in C _ I: eritque = III rectae C C, ideoque e ipsi
  14. C HI aequalis. quod est ablurdum. Non secat ergo C FI FIyper-
  15. bolam, sea eandem continoit. Dico porro conversim, (iC TI in
  16. puncto C. Hyperbolam contingat, candem quoque in C bitariam
  17. diridi. Hloc enim linon Cic, Cumatur in C HI majori parte ip(a FTI
  18. aequalis C C. Ilinc cum punctum C sic in FIyperbola, crit quo-
  19. per 4Cor. Gdc: punctum I in IIyperbola, totaque CI3 intra curram ca-
  20. dec, ideogne ip(aCFI Fsyperbolam non continget, led eandem
  21. Thujus. In punctis C X I lecabie, contra id quod ponebatur. NTon ergo
  22. OC ipsi C HIinaqualis est. Ideoque casu vtroque constat pro-
  23. policum.
  24. Corollarium T.
  25. Manifectum itaque est ex ancedictis, lingula rectangula, quae
  26. comprehenduntur sub parcibus cujuslibet rectae contingenti pa-
  27. rallelae, inter IIyperbolam ee ACymptotos interceptis, esse x-
  28. qualia dimidixe cangentis quadrato. TIE, ( tangenti CC HI aequi-
  29. distans urcunque ducta (IEB D, A(ympEOtiS OCCUETenS in F _ F.
  30. ver 2C0r. Ct. Crectangulum E B F Sire + BFD, UE_E FD F SIVCDF B aqua-
  31. shujus. le rectant, Id eA, ipsius C HI ret C6, dimidie
  32. Carcbo sllachal.
  33. S bujus.
  34. Shujus.
  35. 3 per 3 Cor.
  36. per S Bu-
  37. fus.

Cite

Ps. 2, fol. 190. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/175906937X:0214?run=74