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[Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ, fol. 146

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: 0.85.

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

The machine reads it as

  1. E B C F: ZIII.
  2. verx radices propolicae talsas exhibent. Hlic insuper modus aequatio.
  3. nis propolicae, quatenus illa ex aliarum in se duetu provenie, constiturio.
  4. nem ostendit.
  5. 4. Radices maximx Ee minimxe deprehenduntur in quacunque se.
  6. rie ponendo (quoris in gradu seriei) Fore n=o; ut in octara serie sIt
  7. ba- aa c0 = 0; adeoque 50 = 44- ba, exic a (L . . V --
  8. cc) maxima radix; item in Serie duodeci a CiE Aa ba -66 = 0;
  9. unde c0 -ba- aa; exit et (=
  10. - - 66) redix MBaXMa;
  11. d a (= = = V =cc) radix minima.
  12. 5. Curvaram nodi, vel intersectiones innocelcune, cujulris in Seriei
  13. quoris gracu, ponendo fore a =n; ut in octara Serie, ubi b3 -a
  14. . 6C= n, HE a = n; er∞d ba aa ) c0 = aa; vel c0 = 2Ba ba;
  15. vel = aa - =; quare a = ) V--
  16. 6
  17. rie duodecimia, ubi aa - ba 60 = nn = a4; erit ide060 = ba; ac inde
  18. 2=
  19. 6. Ordinaca maximae, minimeque variis nodis, methodisque pas-
  20. Cim nocis investigantur; e80 simul illas atque curvarum tangentes
  21. una opera sic determino. Sit curra A V HI, ad Seriem unelecimam
  22. pertinens, ejusque sradum, cujus aequario eAt cCA- baa - a3 = n3:
  23. Polito T curram tansere, ∞, P ad AHI ordinari, reperio (de su-
  24. pra monstratis) fore P I-
  25. 3n3
  26. 3aa 2ba- ec tum contidero, si Or-
  27. dinata P sit maxima, fore tansenrem ips HI A Parallelam, seu rectam
  28. P T esse infinitam; quare cum (IE n3 =PPX : 3a4 ). 2b4 - C6; BEn
  29. Sit Enica, Pacet esse 3a4 ] - 2b4 - 66 = 0; vel as 7ba =; adeo-
  30. que a:=-
  31. 6
  32. dL0
  33. 7. Adnoro demum e maximis de minimis ordinatis radicum li.
  34. mites derirari; nempe si reperiatur ad maximam ordinaram pertinen-
  35. eis radicis (veluc ipsus A P in exemplo proxime luperiori) ralor, e
  36. is ubique in xquatione proipsâ a substienatur, si quod provenit, de
  37. ticiat ab homzoseneo (quod vocan) comparationis, problema construi
  38. requiF
  39. E18. 220.

Cite

[Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ, fol. 146. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/797435492:0400?run=74