Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

[Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica, fol. 446

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. ARTTAMETICA PFODCLXXVII.
  2. 6: FE summa Perici Secundanorum o- f a 2 f B2- f 02_c. quorum ulrimum est
  3. -
  4. P, ee numerus locorum L. L. L; cric F L P + , P, vet = = +
  5. PrOB. 20.
  6. 1. Per
  7. 7. Viriusque isicur summae aexrexaum, (pura F = 1 f. L = 2 p. 1 1 +
  8. nempe 3V = 31 + 2.P + 21 +1 + 7 213 +61 +4 es aexrepacum dua
  9. cum serierum; cujus aeprepui semistis P + 3 V +
  10. jus latusV. Ideoque-
  11. et
  12. est numerus P pramidalis eu-
  13. P RO P. CLXXVIL Theorema.
  14. Atus numeri cujulris Prramidalis ad ipsum numerum suum, est ut
  15. 1 2d - + 31 + 21
  16. Or ollendicur in praeced.
  17. Acq daco numero Pyramidalin, non innoreleic iptius latus, nisi resolvendo A-
  18. quationem Cubicam 6n = 13 + 312 F 21.
  19. P R OP. CLXXVTTI.
  20. Theorema.
  21. CEries numerorum Pyramidalium, in praemissa cabella commode in-
  22. terpolari poterit; si ipsorum numeris lateralibus tot interponan-
  23. tur medix Arichmeticae quot opus est, et ex iis formentur numeri er-
  24. ramidales, juxta prop. Praeced.
  25. E csosue lois cst
  26. Duta, si numerorum Pyramidalium 1, 4, 20, 20, 35, 56, lacera F, 2, 3, 4,5, 6, etc.
  27. Sic interpolata LInC Z, 2, L3, 2, 23,3,32743 423535336, ec. hisce lateribus re-
  28. spondebit series Pyramidalium 26, 1, 2 16, 4, 676, 20, 24 16, 20, 26 16,35, 44 16,56,
  29. Ac. vel etiam 26, 1, 28, 43 183 20, 767 20, 187 35, 76,56, _C. Vel pOrivS, 183 L, 2834
  30. a8310, 28320, 98,35, 18, 56, eC. 11111
  31. P R OP. CLXXIX. Lemma.
  32. D Ropositum sic inguirere, quam habeant rationem numeri Frianguli-
  33. eriansulares ad latus fuum.
  34. Praestabicur hoc eadem methodo qua prop. 1, 6. Dempe,
  35. T. Numerus Frianguli criangularis aequacur agoregato numerorum omnium Py.
  36. ramidalium, (incellise quorum latera sunt numer inceori, nam de incerpolacis tic
  37. non agicur,) ab unicace ad numerum libi collareralem, inclusire.
  38. 2. Est aurem laceris I, numerus Pyramictalio L F 31 F2. per prop. 177.
  39. 3. Freo, sumpris laceribus L, 2, 3, 4 c. vel (eorum
  40. 10c0) a, b,6, a, Sc. Cumma horum a3 f 3 a f 2 a, b3 L
  41. b = 2b,63 f 302 + 26, 23 4 3a2 + 2 d, ec. exit
  42. Texcuplum asoresati Pyramidalium, (quorum omnium
  43. nUMerUS exiE aequalis lateri eorum maximi, ut patet:
  44. e propterea hujus asgresati sextans erir numerus Pri
  45. Num. Prianguli crians. anguli criangularis, cujus lauls idem exie cum latere
  46. maximi Pvramidalium.
  47. 4. Adeoque numerus Frianeuli triangularis est lexta pars aggregaI irium Perie
  48. rum, cousque ab unitate concinnacarum donec numerus cerminorum sC aequalis
  49. lateri numeri Friansuli criangularis propoliri, quod dicaturl: adeoque si iplIS prXe
  50. ponatur terminus alter 03 + 52 f0 (uc series intelligantur ab 0 inchoatae,) fict
  51. numerus terminorum l.+. 1. Fclingularum serierum illarum lumma scorsim inno.
  52. teICet Dex PrOP. 2. 20. et 40.
  53. 2a 30
  54. 5. LCai DC.
  55. F 3
  56. 13 + 322
  57. etC. e. lC.

Cite

[Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica, fol. 446. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0466?run=74