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. 150

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.

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The machine reads it as

  1. Arithmetica Infinitorum.
  2. PrOP. 182
  3. Oux estigitur summa Ceriei Mmartanorum cujuo terminus
  4. ulcimus eA lE numerus cerminorum l F T.
  5. Vel, si pro numero terminorum lF 1, Tubsticuatur n, a
  6. provcerea Ceries r qualium n1o; erit series Ouareanorum Znl
  7. 15n1 + 30nt= = 26RI. (Einempe terminus primus HC O,
  8. Eccundus 1:) vel.
  9. nIL
  10. n12
  11. 101 = 3012
  12. 30t
  13. 9. Adeoq; Peries finica Ouartanorum ad seriem coridem max-
  14. EMO AE qualium eAUC Z X
  15. rac inquirendum.
  16. 101 + 301= 3015 ad T. Ouod e.
  17. Ecpari modo, his cognicis, ratio quam habet ad seriem A-
  18. qualium Peries Ouincanorum, inremietur ope characteris in
  19. proxima praelentis cabellae serie: PF deinde, quam habec feries
  20. Sexcanorum, opc characteris seriei proxime sublequencis in hac
  21. eabella; ee hc deincepe quoulq: libet.
  22. Ouo melius aurem hoc intelligarur, operae Forcasse prerium
  23. eric, qua jam cradica lunc, paulo distinctius aperire: Elcuc enim
  24. ea Caris aperee rradidisse nos nobis videamur, heri tamen porest
  25. uc leccor illis minus assuecus nonnunquam Corlan hxelitet.
  26. Nocandum ixicur eA, nos hic (ut de alibi Ccmper, ubi de A-
  27. nita Cerie rerba hiune, ) numerum cerminorum altienare l+ L
  28. (nempe literminus primuso, sccundus dicatur L, 3 nimirum
  29. unicare majorem quam eAt numerus parricularum ex quibus
  30. conslacur cerminus maximus, hoc es, omnium differentiarum
  31. terminorum continue policorum, quarum omnium agpresaro
  32. terminus maximus aequacur; sire differencix illae sinc aequales,
  33. ue in serie primanorum, (DUTA L, F, F, T, _C, differencire nume-
  34. rorum arichmecice proportionalium,) sire crescentes, ut in le-
  35. rie lecundanorum, cerrianorum, _C. (PUta T, 3, 5, 7, dec. dit-
  36. terencix numerorum quadracieorum, vel 2,7, 19, 37, _c, ditte.
  37. rentia numerorum cubicorum; _C:) sire eciam decrelcentes,
  38. ut in Cerie subsecundanorum, Cabcertianorum _C; (nam verbi
  39. sracia, difterencia N3- N2 minor est quam ~2 = ~ T, 219:
  40. baeC minor quem VFi VO; e sic in caeceris.) Harum omni-
  41. um differenciarum (in qualibet Perie) numerust, unitate min
  42. nor ell quam numerus terminorum, uc paree; carumq; omnium
  43. dexresacum (proprer cermini primio nullitarem) cs Ip(e rer-
  44. inus
  45. asrue

Cite

Qua Continentur De Angulo Contactus & Semicirculi, Disquisitio Geometrica. De Sectionibus Conicis Tractatus. Arithmetica Infinitorum: sive de Curvilineorum quadraturâ, &c. Eclipseos Solaris Observatio, fol. 150. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/824573315:0362?run=74