Leibniz Legible

Machine transcription of the Leibniz Nachlass

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Qua Continentur De Angulo Contactus & Semicirculi, Disquisitio Geometrica. De Sectionibus Conicis Tractatus. Arithmetica Infinitorum: sive de Curvilineorum quadraturâ, &c. Eclipseos Solaris Observatio, fol. 105

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: 0.81.

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The machine reads it as

  1. PROP. 47.
  2. De Sectionibus Conicis.
  3. l
  4. duCatuT recta C (diREErO AP OCCurrenS in C) Paralscta
  5. cansenci at (quae eidem diamerro occurrie in t.) Wico aX
  6. ejuldem Paraboloideoo diameerum esse, eigi ordinacim poli-
  7. EABL NC.
  8. Diametro AP ordinacism opplicetur oe, eiq: parallela du-
  9. Catur rp (eidem dismeero occurrens in p.) Ec lunco Cymbola
  10. Pa = p. PA - d. FC - a = PD- 5.
  11. Tum Cumantur in diamecro, ucrinq; a puncto p, aqualesre.
  12. AXPD =PD =-9 VETAG; nempe canca, quonra est radix hujus
  13. aequacionis 9d92 -+ 92 = 27d 8. PF punctis D, D, ordina-
  14. EIMI DOnANEUE reCCA DO, DO, reCtE X G OcCurrenceS in C, O:
  15. quae cum para Hlela snC reCta P, GICNE reCtA VD (ex constru-
  16. ctione) bilceatur in D, eric ideo OO (propcer Parallelas) bi
  17. sectainn.
  18. Superestigitur ut octendam rectam OO (bilectam in x) ea
  19. raboloidi inscripeam esse (nc nemve ax recta bisecans sit dia-
  20. meter) hoc eA, puncta C, , elle in Paraboloideos curra; nem-
  21. De rectas DO, DO, (diamecro A P ordinacim. BOLEAS, Cx CON
  22. Fructione,) ordinacim applicatis c’ad eadem diameeri puncta)
  23. aequales elle, adeoq; in cu. ra terminari. Ouod sic ostenditur.
  24. FA PA = PA + PP- -d F C. DA - PA + PD = d t 3 + g. DO
  25. =-DF = 3d. DO - DC + DI - 3d + 9.
  26. Tum (propeer Paraboloides cabicale) at PA, ad DA; SIC Cu-
  27. busrectae Pa puncto P ordinacim applicaca, ad cubum ordi-
  28. nacim. applicacae puncto D. Hoc eA d. d F 8 +, 9:: p.
  29. quiisitur cutrus est ordinatim applicatx puncto D.
  30. NB 9, 2
  31. Scd _ cancundem est cubus rectae DO. Nam Cpropeer hmi-
  32. Lia criangula) PF. Pa :: DC. DV. hOC eA 3d. P: : 5d, + 9.
  33. 3 d
  34. -
  35. Ba
  36. P=-DO. Ejulq: cubus DOC-
  37. 274 + 27a 9t 9d9 = 4
  38. 274
  39. D2 Vel (PrO gd g = = 9=, lubRicuendo 27d 8, QuX Per CON
  40. dructionem lune aequalias)
  41. 2 7d3
  42. L. 27d 9+ 272
  43. 27a
  44. vel deniqi (abbreviando trachionen per 27 d
  45. a -= 9+B, 3
  46. =DOc. 2d209; rect+ DO, DO, ordinarim- applICALE TunE
  47. puncis. D, Iad Paraboloideos curram cerminatae in C, ;
  48. et
  49. de

Cite

Qua Continentur De Angulo Contactus & Semicirculi, Disquisitio Geometrica. De Sectionibus Conicis Tractatus. Arithmetica Infinitorum: sive de Curvilineorum quadraturâ, &c. Eclipseos Solaris Observatio, fol. 105. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/824573315:0193?run=74