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. 733

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: 0.91.

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

The machine reads it as

  1. PrOD. XVI. D Cm Sentri Cravitatis.
  2. FNTcellIZatuIE B C B Sector SphaerieuS; (inect-
  3. lise Piguram Solidam in Sphaera, quae con-
  4. vertione Sectoris Circularis BC. A, ICu BC a
  5. Circa AC a deseribitue:) Fx intiniris nume
  6. ro Prramiculis limilibus ee aequalibus (juxta
  7. det. T. Cap. 4.) componi: Ouarum commu-
  8. nis vertex sic Sphaera Centrum C; Balesque
  9. componant Sphaerica Luperticiei sesmentum Se-
  10. etori sphaerico conveniens. Frit saque, Pum
  11. Timul omnium Magnicudo, aequalis Frienri
  12. Radii (communis Alcicudinis omnium) in
  13. Sphaericam superticiem B AB, vel B a B, lecto
  14. si convenieniem, (upore Balium Agpreea
  15. cum) ducto: (Onod ex = vel 6 hujus pro.
  16. Babitur; Propter Parallela Pyramidum Plata similia, atit etiam parallelas Sectorum
  17. sphaericorum curras superticies similes, in ratione Secundanorum:) Tum Centra
  18. craricaris omnium, in Simili Supertiere Sphaerica, deseripea, Ractio Cb- CB =3X
  19. proprer Cencra graritaris Pyramidum, in Axe Tuo polita, eres quadrances ejus-
  20. dem ad verricem abscindentia; per shujus.) Cujus quidem superticiei D ab, ra-
  21. dio Cb deleriptae, cum lingula puncta incellisantur aeque onusta, (UE qua aqua-
  22. lium Pyramidum Cencra gravitaris Cultineant;) idem erir hujus Centrum gravi-
  23. cacis, acque expoliu Sectoris Sphaerici. Puta (in sectore BCB A) in C, medio
  24. puncto recta a v (Cinus versi arcus ba) per FZ hujus. F auTeM, (PTOPTCK
  25. CD =ZC B = 3R:) recta a v = 3AV = 30: Adeoque 2C == Z 2 V = 3V, _ CO
  26. V = 8h, (DTOPtErE R = V = B.) ECB
  27. milicer oltendetur, in oppotio Scctore BC Ba, a V =d a V = 3B; e 2C = 3 a
  28. 8B; CC == C. a-
  29. 8V, (propier 2 R = B = v.) Hoc est.
  30. Dutancia Ceniri graricatis Sectoris Sphaeriei (in Sectoris AXC DOlit) d̀ Centro
  31. Sphaera, aequalis Pribus Muadrancibus Radii minus Fribus Oetancibus alcicudinis
  32. Tuperticiei Curra lectori convenientis; aut etiam (quod eodem recidic) aequalis
  33. Fribus Octantibus alticudinis religuae superticiei sphaerica. Ouod crat propoluum.
  34. Hoc cl, speciatim in Hlemisphaerio, (PrOpter V = B = R, ) 3 R-
  35. Corollarium constat, ex prop. 3. Cap. praced. ITam Scctori BCB A, dempio
  36. BBC Cono, habetur Sesmentuim B B A; e Sectori BCBa addico eodem BBC
  37. Cono habetur Segmentum BB a. Cum icaque cum sectoris lphaerici (per jam
  38. oltenta;) cum dempri addicire Coni (per 6 hujus;) magnicudines et Ccurra
  39. sraricatis altignantur; habebicur et Relidui, vel Aggregaci, Segmenti Sphaerici
  40. cum Magnicudo, rum et Cenirum gravicaris. Ec similucer, (muraris murandis,) in
  41. aliis Sphxrae porrionibus.
  42. Exempli pratia. Ceniri pravicatis Sectoris inceeri BC B A (convertione se-
  43. B
  44. misectoris Circularis BCi A, circa C A, desexipei) diltantia a C, (per modo de. Pip
  45. monstrata) est Z C. A - 8 AV = 8A a = 3AV =3V a, in ipIO AXC AC
  46. Hoc elt (policis ur in demonstratione propolicionis pracedencis, Radio C A = 160.
  47. CD = Ca = R; inceera Peripheria = P; ArCU BA = a; Chorda B A = c; Finu
  48. recto BV = 5; ee verso AV = v; vertique reliduo ad Diametrum V a = 2 R -
  49. e = B; d Centro Dictancia Y C. = ~ = R = v vel V = R; Tiem a - 5 == e; a 7
  50. =f; _cc.) 2R - 3V:
  51. Adeoque ejuldem Cencri cravicaris ab a vel ra, lincellise; a plano in a
  52. Sphaeram Fangente,) R = 8b = Z R - 30. AIque d F A, R
  53. is
  54. Eademque est ab nildem ra, vel TA, planis; distantia Ceneri pravicacis semi-
  55. sectoris, (puta, qui plano per Aa transeunce, incesrum bilecante, decerminacur;)
  56. aur Sectoris Ouadrantalis; aliulre impertecta quaris conrertione deseripii, (adeo.
  57. que duobus ejusmodi planis, quorum communis sectio AIC A a, interjecti;) prOpTOK
  58. omnia plana, Sectorem incegrum complencia, iplorum partibus, Sectores partiales
  59. complencibus, proporrionalia, acque in iildem d ra, T A, planis Tansencibus
  60. distanciis. Ouod de lemi conis, vel semilermentis Sphaerieis aliis, atiisve Solidis
  61. impertecta convertione deseriptis, es correlpondencibus Ongulis, dec. Similiter ob-
  62. tinet. Ouod semel monco, ne lapius Lic Opus idem repetere.
  63. bZ. Z. Z

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. 733. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0753?run=74