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. 725

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. i
  2. Centi
  3. vitatis
  4. nati CO diridatur; ducancurque ordinarim.
  5. applicaca V B, OcCurrenEES ipB DO in MI, ipI-
  6. que CO in N: Maniteltum eA, Ouadratum
  7. ordinacim applicatae B V, aquaFI GUIadratO C B
  8. minus quadrato CV (per 47 cl. F. Fuclidis:
  9. FIOC ell, OVactraTO V AL MInUIS quadtato VH
  10. sime enim V HI =C B, e Y N ==C. V: ee lic
  11. ubigue e
  12. Adeoque, Omnia quadrata B V complencium
  13. ADC quadrantem; aequaneur omnibus qua.
  14. dracis V MI complencium AOD C quadratum,
  15. minus omnibus quadearis NV complentium
  16. ACO Priangulum. Ec cingula lingulis re-
  17. spectire TumBCIS.
  18. Adeoque li ex Parallelepipedo ODCa (quod
  19. compleant omnia ML V g;) eximi incellisacur Pyramis OC A (quam compleant
  20. omnia NYV 9:) quod reliquum est, aequabitur omnibus BV g.
  21. Auc etiam (propeer Circulos Guadracis Radiorum proporrionales) Cylincrus
  22. ODDO, exempio Cono OCO; aequabinue Tremisphaerio, D A L
  23. Sed e (propier singula BV q lingulis M Y q = NV q aequalia,) etiam par-
  24. res parcibris lerpcecre mpils dequantur.
  25. Nempe; Paratlelexipedum OM V A dempro Exramidis LTunEO ONV A (SIV
  26. Sic Supra Centrum) vel dempra Pyramide aucta OCN V A (si intra Cenerum;
  27. hoc est, dempro OC A FNCV: A quatur quadracis ordiracim applicatarum in
  28. ABV, Tegmento. Et lic ubique.
  29. FEbmilluer: CstinaruS OMMO, deMPTO ONNOvel OCANO (hoc ett
  30. dempro Cono OCO, mulctato vel aucto simiti COnO NC N, PrOuE lupra in-
  31. trave cencrum tueric punctum V) aquacur Scxmenco Spharico ABB. Et sic
  32. Ubigue.
  33. tis potutis: crie ( propter M1 V q = R, et A Y = v,) Pacallelexipedtum
  34. OMVA = v R2.
  35. TrM; (prOPter O A g = AC g = R2, et AC = R,) est Pyracis OCA = 3 R3.
  36. Trem (propier NV9 = VCq = v, _ VC =~; ) PyramiS NCV
  37. vi
  38. Fsergo, Summa Ouadratorum omnium Ordinarim applicatarum (puta omnia
  39. 02) complencium ipsum ABY lemiscemencum; OMt Y A =OCA FNCV
  40. =DR2L
  41. Fst aurem, supra Centrum, N = R = V; IIa CCMM, N = = R F V: Adeo.
  42. que illic NS= R 3 au 3 V R Z F 3V2R = 23; hic verc
  43. 202R f V3. Ergo (cum illo calu habeatur L = ∞ 3; hoc vero
  44. x3) exie
  45. VR2 = = L5 ~3 = v2 R = 5 V3 (utroque catu) summa omnum o2; Teu Ou2.
  46. dratorum ordinatim applicatarum complentium A B V semisesmencum
  47. Veleriam (propter v2 = 6 2 = 52 = 2V R = 5; adeoque v2 R = ZVR - sR
  48. 2R = 3 52D = 3V
  49. Lutrima 22 R = 3 03 = 3~ A2
  50. pt
  51. R-
  52. 52
  53. 552V;) cric eadem Omnium a
  54. Sed et manitectum porro cst; cujusque rectae ut B V, ( acque de huic parallelis
  55. Semileomentum BV A. complencibus simile eris judicium,) momentum respecti
  56. rectae Ra, aequari semiquadraco ejuldem, (propier Recta Cencrum gravitatis in
  57. iptius medio; adeoque YBx = V B = = V Bg.) Fx Similiter quae lemiquacranca
  58. lem Ongulam (aciem habentem A a) complenc plana, iplis B V inCiltencia, aquart
  59. gjusdem BV semiquadraco; (nam, propier angulum in V semirectum; alcicudo
  60. 3V2R-
  61. vA
  62. Hure vero Semilegmenei BV A morento (respectu recta Aa) Se invento; St
  63. addantur Friangulorum BV C, b ra (respectu ejusdem A a) MomenIZ; (SR, 3
  64. reverta:) Prodibune Momened (respectu ejuldem Aa) Sectorum BC A, B a A:
  65. Cxceraque de Solidis conversione cisea A a lactis, C’encrisque gravicacis planorum
  66. PrOP. XV. De Calculo Centri Cr.
  67. In B, aqualiS CFIEIPLI BV bali; ipluneue Priangulum Rcctangulum IPosceles
  68. eric Ouadrati dimidium.) Pr consequenter, cum Semilesmenti BV A momencun
  69. respecta iptius Aa; cum semiguacrancalis Ongula cidem BV A in siltens, acien
  70. tavetto Aa; aeguabitur corundeo semilumma; Hoc elt,
  71. 852 R + 352V =5v= R f 5 528. Idem quod supra (5 R.) repercum erat.

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. 725. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0745?run=74