Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

[Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ, fol. 54

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: 0.83.

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

The machine reads it as

  1. SiB. 56.
  2. 15. 57
  3. 218. 58.
  4. L. E C Y. VY
  5. Corol. Si ZS cangaE hyperbolam DYY; CxIEP M 9. PY 9::
  6. P A. PS.
  7. Nam eAt PMg. DB9:: P Ag. ADq:: P A. AS. ergo per
  8. rationis conrertionem est P Mg. P Z q:: P A. PS.
  9. ZXIII. OuodR reliquis similiter posiris, Sic jamF Y = V PMG
  10. ) D B9; erit eriam linea YY Y hyperbola; cujus nempe Cen-
  11. erum A; Semidiameter A F (parallela _ aequalis ipti DB) Semi-
  12. parAmEtOr aUTEM P, SI HAE AF. AD :: AD. P.
  13. Nam ducatur Z K ipsi A P parallela cum A F conveniens in R;
  14. Sirgne F T = 2 F A; CAque A F. P:: (AFg. ADq:: DB9.
  15. ADg:: PMg. APg:: FY9- DB9. APg:: AR9- AFg.
  16. RYg::) LRXEK. KY9:: AF. P. unde constat PropolI
  17. EUIM.
  18. Corol. Ruxsus, Si recta Z S Byperbolam F Y Z FaNBAL, exIt P M 9.
  19. PYg:: P A. PS.
  20. Naim A D est Semidiameter ip(I A F conjugata. unde P A. AS::
  21. P Ag. ADg:: PMg. DB9. ergoP A. PS:: PMg. PM 9
  22. ) DBg:: PMg.PY9.
  23. XZIV. Sicrriangulum A D B, rectur habens anguluM ADB.
  24. d curra CCDralis, ut duet ầ quicunque recta F F C ad D B paral-
  25. lela (quae lineas expotitas secet ut vides) sic asprepatum quadrato-
  26. ruM ex F F, F C aequale quadrato ex D B; erit CurVa C C, D Ellip-
  27. sis cujus Temiaxes AD, AC.
  28. ETaM SIE AV = AD. FAtque ADg. DB9 (AC9):: AF 9.
  29. EFg:: ADg - AFg. DB9 - F Fg. HOC CAADg. AC9::
  30. V EX ED. F. C9. unde liquet ProDOCIum.
  31. Nota, TanBat CY ellipsin C CD; eA FFg. EC q:: F A.
  32. F T.
  33. Nam ob AF. AD:: AD. A F, CA A Fg. AD9:: AF. AT.
  34. unde AF g. AD9 -- A F 9:: AF, AT - AF. LIOC CA F P 9
  35. DB9- EFq:: AE. ET. hoc esF Fg. EC9:: AF. ET.
  36. Sit Angulus rectilinens D TH, in cujus latere F D SIGMeTUF pUN-
  37. ctum A. Sic item curra V CC proprietate talis, ut duet a rect â qua-
  38. Piam F FC ad T D perpendiculari (quae lineas TD, TFI, VCC
  39. Iccet punctis F, F, C,) connexaque recta AF, CIC EC = AF.
  40. erit linca V C.C hyperbola.
  41. Nam ducaneur AP ad TH ec V PC ad =D perpendiculares;
  42. Iem
  43. 1
  44. CI
  45. mlum
  46. un

Cite

[Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ, fol. 54. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/797435492:0270?run=74