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. 106

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: 0.82.

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The machine reads it as

  1. De Sectionibus Conicis.
  2. PROP. XL. VI.
  3. PROP. 46.
  4. De recta Paraboloides Cubicale contirgente.
  5. Y Parabo oides Cubieale Aa, in puncto quoris
  6. a continrae recta aF, diamCtRO PA OCCUETeNS
  7. in F, Ccq; eidem diametro ordinatim- applicata
  8. aD: erit recta AF Cdinmetri continuatio) dupla di-
  9. ametri interceptae PA: hoc elt, diameter continuota
  10. PE, tripla dianceri PA.
  11. Nam, Cumpeoubiris (in caden diametro) punctoD, cui
  12. ordinacim applicetur DO, cangenti e F’occurrens in T: Pun-
  13. Atum T (DrOPterFangentem) vel eric idem cum punctó a, (sI
  14. nempe P, D, coincidane;) vel CE (CCUS) erit P exCra curram:
  15. E (pTOPFCrCA) DF = DO (nempe aequales, A D, P, coinci-
  16. dant; vel, A lecue, DY longior erit.)
  17. Ponamus aurem (ob commodiorem calculum) Pa =P, PA
  18. =d. PF = f, PD = a. Prit ergo (per det. praeced.) Pd. DA
  19. : PaC. DCC. hoc est d. d = a:: p.
  20. du
  21. p. =- DOc. Icem
  22. (Dropcer similia eriangula) PF. Po:: DF. DT. hoc est f. p::
  23. a. F
  24. a
  25. P = DT. Pjalq; cubus
  26. (=-DTC) (DOC =
  27. 2
  28. f2 a + 2 f a +
  29. p5
  30. d P. Ec Cuerinqe mulcipii
  31. cendo per f. d, e dividendo per p2) erie f. d L 3F2da +
  32. 3faa = d a 2 = f3d +f a. Tum Cauterendo verinq: F. d, &
  33. diridendo per a) erie 3 f2 d =+ 3fd a Y da = = f. Denia
  34. vonendo puncta PD coincidere, CHe eranelcac quencicas a,
  35. adco9; ee ipsus molciplicia + 3 fda, Y d a 2 0) eric 372 d = f.
  36. hoc cA3d-- f. Duod crac demonstrandum.
  37. R

Cite

Qua Continentur De Angulo Contactus & Semicirculi, Disquisitio Geometrica. De Sectionibus Conicis Tractatus. Arithmetica Infinitorum: sive de Curvilineorum quadraturâ, &c. Eclipseos Solaris Observatio, fol. 106. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/824573315:0190?run=74