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. 445

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: 0.86.

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

The machine reads it as

  1. eet
  2. LHL LALEOR UN
  3. e
  4. rium: e Media proPOrtONaleS V2, V 6, V (2, V 20, _c. ellenE Ordinatim. a
  5. plicata in EIyperbola, cujus tam lacus rectum quam lacus tranlversum sIC T. Ut
  6. ex dietis, contideranci parebic. Ouod aluis rarionhus Lateris Recti ad Diametrum
  7. Lcumtrectam, tacile accommodaBIEIII.
  8. PROP. CLX LV
  9. Theorema.
  10. Fries numerorum Priancularium, in praemista tabella, commode
  11. interpolari poterit, s ipsorum numeris lateralibus tor interponan-
  12. tur media Arichmetica, quoE opus est, et ex iis formentur numeri
  13. FriangulaTeS, JuXIA PFOP. 172.
  14. Puca si in serie numerorum criangularium F, 3, 6, 20, 15, dcc. unus ubique
  15. interponendus est numerus; eorum latera 1, 2, 3, 4,5, ec. mediis Arichmericis
  16. debite incerpolara, erune 3, F, 23, 27 2. 4, 3, 3234 427 5, c. quibus laceribus
  17. (DEF PrOP. 172.) respondenc numeri criangulares, 8, L, 18, 5
  18. 4876, 78, 1C
  19. 1287 25, 176, 2. Fy c. Vel 83 E, 87 3, 8,6, 8, 10, 8, 25, 8, 24, _c.
  20. denique 8, 8,
  21. rentice lunt Arichmerice proportionales
  22. Ve
  23. 8, 18, 150, 8c. quorum quidem disse.
  24. Pari modo, li incerponendi sinc in lingulis interrallis duo loci; prodirent nu-
  25. Meri, 3, 3, 1, 3,3, 3
  26. 5367 3, 13, 20, ec. Vel 3, 37373357 3, c. quo
  27. rum iem ditterene luue Aciclumerice proporcionales.
  28. Bo s: P R O P. CFZXVI
  29. Lemma.
  30. DRoposium sic inguirere quam habeane rationem numeri Prrami-
  31. dâles, ad latus suum.
  32. Liceret de hanc proxolicionem pari propreltu inrestisare, quo in prop. L7F.
  33. utus Cum: (obserrato incerim diserimine quo disterr debua numeri Pyramidalis
  34. dispOL
  35. Verum cum non ita facile elter lectori concipere debicum punctorum licum in py-
  36. ramide, (ue quae non omnia supponenda tunc in eodem plano,) et ansulorum (o-
  37. licorum ad ea puncta politionem: Cacius ridetur illud hac qua sequitur methodo
  38. praeltare. (Oux quidem, nisi mallem urrumque modum oltendisse, adhiberi Do-
  39. ruisseo etiam ad DEOP. L7F. )
  40. F. Numerus Pyramidalis aequatur asgregato numerorum Friangularium (uE p2
  41. rec ex dietis ad prop. 130. es 132.) nempe ab Onitace ad numerum Triangularem
  42. sibi collaceralem inclusire: (heut et numeri Priansulares hunc aggresarione L. a-
  43. reralium; et Lacerales, Monadicorum; ur e Friansuli eriansulares, Pyramida-
  44. lium; et sic deinceps.)
  45. 2. Est aurem lateris h numerus quiliber Friangularis
  46. 3. Ergo, sumpris lateribus F, 2, 3, 4, ec. Yel (corum l0c0)
  47. ag b, C, due dec. summa horum a an b = B, 6 + 6, d2 + a
  48. Scc. erit duplum acoregati Friangularium; (quorum numerus
  49. exit aequalis lateri maximi;) e hujus proprerea lemissis, erit
  50. numerus eramidalis, cujus lacus aeguatus laceri maximi Pri.
  51. angularium.
  52. C.
  53. 4. PIE ivicur numerus egramidalis, semiltis aBerexaci dua Num Pyramid.
  54. rum serierum; cousque ab unitare continuatarum, donec numerus locorum xove
  55. cur laceri numeri Pyramidalis quaesiti, quod supponatur l: Onibus Si praeponatur
  56. locus alter 0 f O, (ur series incelligantur ab 0 inchioacae,) Het HaruM nuMeTUS
  57. FF. Ec ucriusque seriei summa scorlim innoteleet Per pFOP. 2 C 20.
  58. 5. Nempe, summa seriei Peimanorum 0 f a + B. F C, dec. quorum ulcimum est
  59. 3 numerus locorum L F E; erie =L. per proP. 2.
  60. PEF DEOP. 271.

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. 445. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0465?run=74