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. 133

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: 0.87.

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The machine reads it as

  1. PrOD. 166.
  2. Arithmetica Insinitorum.
  3. bel lX prOp. 138 nempe 1, 2, 6, 20, 70, _c. racio quam habet
  4. unicas ad numerum corundem primo e secundo incermedi-
  5. um, est ea quam habet Circulus ad guadrarum Diameeri: FF
  6. Ellipss ad Parallelogrammum circumfcripeum. Ic deinceps
  7. probabicur, ex prop. (c9.
  8. DROD. CIXVI. Theoremao
  9. Tleries infinica sequalium, Primanorum, Secun-
  10. danorum, aut Tertianorum, _c. respective du-
  11. catur in sciplam inverse politam; atq: cadem
  12. etiam in sciplam directe politam: erit aggregatum
  13. rectansulorumillorum, ad asgresarum horum; ut I
  14. ad 1, 2969 20, 70, ec. numeros diagoniales Tabellae
  15. PFOD. 132.
  16. Nam silerier Aqualium in seiplam (sive directe sive inver-
  17. Cc Poltam) respectire ducacur, tic leries AEgualium: cui con
  18. venie ratio LadI.
  19. Si autem Ceries Primanorum in sciplam dircece politam (10
  20. malciplicetur; Fer Peries Sccundanorum; Si Peries Secundano-
  21. rum sc ducacur, hec series ouarranorum; ( Peries Terrianorum.
  22. hec leries Sexcancrum; et c. Per prop. 73. Ouibus conveniunt
  23. rationes 3. 5. 3. 3. _c. Per PrOP. 44 vel 64.
  24. Si aurem Series Primanorum respectire ducatur in sciplam
  25. inverlam; (Duca Peries a b, c, _C. in Ceriem D = a, D= b.
  26. D C, RC.) Iem Ccries Secundanorum in sciptam invertam,
  27. (Duca Series a 2, b3 C2, _C. in Perie 9: D - a. d: D . b. d D C_C.
  28. vel D= = 2aD + a 2. D2 = 2bD +b2 V = = 2CD + c. _C.)
  29. Icem Ccries Tercianorum in sciplem inversam; (pura leries a
  30. b3,c3 _C. in Teriem C: D a C: D b. C: D C. _C. ) EC HC
  31. de reliquis; Raciones iplie ConvenicBe, 53 30, 1403 620, _C. PeK
  32. ProD. 133, 134.
  33. Racio igicur racionum harum sd rationes il-
  34. la8, ea est quam habet + ac nymerOS L, 2, 6,
  35. 205 70, uc. nempe numeros diagoniales tabet.
  36. 2) + C.
  37. D = C2
  38. 5. 36 6
  39. IX PrOP. 132. (UF ex calculO PaTEL) Ouod eraE 3) 1to20
  40. demonstrandum..
  41. 6630 (10
  42. SCHOLo

Cite

Qua Continentur De Angulo Contactus & Semicirculi, Disquisitio Geometrica. De Sectionibus Conicis Tractatus. Arithmetica Infinitorum: sive de Curvilineorum quadraturâ, &c. Eclipseos Solaris Observatio, fol. 133. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/824573315:0345?run=74