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. 422

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: 0.79.

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

The machine reads it as

  1. 219.
  2. 2dC 2L LLL1 L L LC A
  3. PrOP. C XXIX
  4. PROP. CXXIX.
  5. Corollarium.
  6. PPTOPterCa, Conceides (vel Pyramidoeides) Complemento semiparabou
  7. circa ipsius ordinatim applicatam, est ad Cylindrum (vel Prisma) ejus-
  8. dem basis eo alticudinis, ut 2 ad 6.
  9. is proo. Nempe uc Ouadeata retiduorum teriei AEqualium muletaie lerre Sublecuncallo
  10. rum, ad eoridem maximo aequalium. Cum enim in Semiparabolae complemento
  11. AOT, rectae ipsius diametro AT Parallelae, sinc relidua LeGuasum demptis Sub-
  12. secundanis (ordinatim- applicatis in lemi- pacabola AOD;) si volvendo comple-
  13. mencum illua AOF cirea iplam O P uc axem (vel etiam alias, ut alibi dictum
  14. est,) tormetur Conoeides, (aut etiam Pyramidocides analosum,) cujus vextex O;
  15. circuli sic rolrendo deseripri (vel similia plana similiter polica) crunt in recta-
  16. rum illarum (ipsi A F parallelarum) ratione duplicata. Hoc elt, ut quadrata
  17. Reliduorum seriei A. qualium sublacis Sccundanis; ideoque ut L 2d 6 per praccd.
  18. SCHOL ZV M
  19. Ft pariter judieandum eric de Copocidibus, e Pyramidocidibus complementi Se-
  20. miparabolocidis cujulvis cirea iptius ordinatim applicatam apcatis, juxta propos.
  21. tiones lequentes: Nempe, muraris mucandis, prour Semiparabolocidis gradus po-
  22. Stularerit. Puta in semiparaholocide Cuticali, ut +ad FO; in Biquadraricali, ut
  23. 2 ad 25; in Supersolidalis + ad 2F. esc. juxra cabellam PrOP. 13L.
  24. PROP. CXXX
  25. Theorema.
  26. TerDONACAL LLICo SEqUaNuM mulCtata SeNIC SHIBLEFEIAnOTHHH, KCH
  27. duorum Ouadrata, Cubi, Biquadrata, etc. ad seriem totidem eorum
  28. maximo aequalium, rationem habebuntcognitam. Nempe
  29. V3H-
  30. BF
  31. _c. ac
  32. ~3R-
  33. AVR ZAVR
  34. Ouadrata.
  35. 2V3 aR + V
  36. LVDa FV
  37. 2V6R
  38. aC. ac
  39. QV3KL L VR
  40. Cubi.
  41. V3R SV aL SY a R = 13 d
  42. BR
  43. 3V DR2 = 313b2L
  44. MSK A 3VC2R= 13C
  45. ell ulque a
  46. VK = AVL F3AVRZ AR = Z A R F 3AR = Z AR
  47. Scriei
  48. ENE
  49. 4
  50. Et sic deinceps; continue addendo numeros trian gulares seu aBBreSATA numero-
  51. rum Arictmerice proportionalium, uc hrabeacur, con lsquiens racionis cyjus ancecestens
  52. olL. 2.
  53. 131
  54. Si
  55. 5
  56. L120+10 = 20
  57. 1O. A LL.
  58. Theorema.
  59. DAr modo, Si exponatur etleS sGualum selata lerie Subquarta-
  60. norum, Subquintanorum, ec. Residuorum Ouadrata, Cubi, Biqua-
  61. drata, etc. ad seriem tocidem eorum maximo aequalium, rationem habe-
  62. BUNLCOBHIEAM. lE) cOOgO SiiSM L. NWEENe
  63. LSICLI SuSIIEO L dB C. site
  64. Nem ut in Subductione seriei Sublecundanorum, consequentes rationum tune
  65. continua addirione numerorum Arichmenice proportionalium, 1 L 2 =
  66. T f 2 + 3 = 3 +3 = 6. 5+ 2 +3 + 4 - 6 + 4 = 10. F + 2 7
  67. t. + 5 =
  68. 10 +5 = 15. F + 2 f 3 7 4 f 5 f 6- 15 f 6 = 2T. ec. Ita in Subductione
  69. Subiertianorum consequentes rationum tiunt concinua addirione numerorum illo.
  70. PUMt

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. 422. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0442?run=74