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[Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ, fol. 43

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. L B C F.
  2. jam aliquories insinuara; Scilicet uF SE AB. FB: : V I9 =Rg. l;
  3. ee delignetur quilibet refraCruS R H, Tum continuerur ratio YB ad
  4. BN, uc sir ad has proportione quarra BP, per punctura P du. 418. 57. 38.
  5. eatur recta PZ ad A B parallela; retracto R N occurrensin L; dico
  6. nullum alium retraecum per Z transire. Nam Si Reri porek transeat
  7. alius LR; _ per PtraduCantuY reCIX NYC, RYS; e pramon-
  8. Ctratis apparet quod sit RS F = NC. item e praedieris manitestum ett r 12. L oct. 4.
  9. quodRS+E NC, QuX RepUBNANE.
  10. XVI. Non dispari rarione, quoad casum secundum, designetur quilibet
  11. retractus RH; _ Aat RB. GB:: N RG - Ig. R; tum adnexa
  12. GH, ad iplas NC, C B sumatur tertia proportionalis V; e hat
  13. NO. V:: BN. NP; _C pex pUNCT P duCREUE P Y ad B A Pa-
  14. rallela retractum N K decussans in Z, dico nullum alium refractum
  15. per iptum Z meare. Ilam, si neges, transeat alius Z R; _ per
  16. Y trajiciatuE RZS; _ quoniam Z P. XP :: RB. GB:: N R9
  17. =Ig. R. ex antedicris apparet Fore RS =NC. quinetiam ob + 1g. Lett. 4i
  18. NOg. GB9:: NC. V:: BN. NP. erit diridendo NB9.
  19. GB9:: B P. NP. hoc est NPg. P ZG:: BP. NP; inde Facile
  20. deducitur esse B P quartam proportionalem in ratione Y P ad PN.
  21. consequenterque fore R S minima N C majorem. Quod adver-
  22. Pacur octensis. itaque porius per Z nullus alius transi retractus:
  23. Q.F. D.
  24. XVI. Prxrerea, Si retractum NK Z intersecet alius quilibet M I,
  25. ad rectiorem perrinens incidentem (hoc est ur incidentix punCtu M
  26. inter B, NI jaceat) intersectio Z Tolicario puncto Z cirerior erit
  27. (seu perpendiculari R B propinquior). Nam ab X demittatur per- F18. 59, 60
  28. pendicularis X O. ipsam NC secans in V; e (in primo catu) per
  29. M, PETAdUICATUT RCCEA MYHI. CrEOMH --NV. quare minima earum
  30. quae per X angulo X QP interseri poltuncinter puncta M, N cadet
  31. uri nuper admonitum, e adstruCEU). Puta ad p. ergo quum sIc
  32. B L quarta proportionalis in rarione YB ad B NY; e B O quarra
  33. proporrionalis in ratione YB ad BP, erit PBC OB; adeoque
  34. reCtA X G reCtSZ P, R B interjaCeE: C. F. D.
  35. In secundo calu, per y trajiciatur recta M v HI. ergo cum sIF
  36. DX. QV:: PZ. P Y:: V R9 - Ig. R. eriE HIM =- ON. ergo
  37. minima per 2 ducibilium angulo A B F incercipienda punctis M, N
  38. intercidet; puta ad p. quare B quarta proportionalis erit in ratione
  39. adP; et cAr . OPC. (rQ. N.):: YP. PN. e
  40. CIm.
  41. 3 haejus Let.

Cite

[Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ, fol. 43. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/797435492:0075?run=74