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. 898

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. De Calculo Centri Crravitatis.
  2. Cup. V
  3. Fis. 200, TLm MF FigurX ConrOlrenda tig. 202. aequalem CurrX FiguIEX Convolut
  4. N L L~ 13. 200. Ouippe Demonstratio prius achibita in comparatis invicem
  5. polloniona Parabola, e spirali Lrchimedea; in aliis non minus obrinet. Nempe.
  6. in parcibus sntinite exSIuIS, Habenda esse vrrobique T Y P crilinea, pro Friangulis
  7. rectangulis, e quidem (propter aequales urrobique angulos ad E) invicem Cimili-
  8. bus; adeoque, propter aequales utrobique Z F, aequales item erunt F I; acque
  9. hoc Temper. Aqualis itaque cota MF curra Hg. 202. LOt MI Y Y F HB. 200.
  10. Et propterea; ex cognira vel figurae Spiralis magnicudine, vel Curva Spiralis
  11. longitudine; similiter cognolcitus vel Magnicudo tigura cujus convolutione tu,
  12. vel Longicudo livex. Pc vice verla.
  13. Et aurem, ex conroluta Parabola, tic Spiralis Archimedea; Fic, ex Paraboloci-
  14. dibus conroluris, tiunt Spirales alixe; quarum radii M P crescunt in rarione angu-
  15. Jorum ANC T duplicata, criplicara, aliatre mulciplicata; vel subduplicata, suberi
  16. plicata, alialre Tubmulciplicata; aur eriam ex his urcunque compolita.
  17. Ouod eodem modo oltendi porest quo in Parabola id octentum est; Tumpris
  18. Parabolocidibus idoneis, in quibus roctae M B, MIH, SiC diridanEuE UE MI B, V. P,
  19. Ec. hoc eAt Z Y, Z Y, _C. snE ipSIS MP, MP, _c. proportionales, (quo sectOreS
  20. Z. NI T. H3. 200. ex rectangulis Z uV. Y fis. 202. convoluris tacti, similes Cnt,)
  21. Paraboloerdisque curra per ip(as Z Y, Z Y, rectas cranscar. (Quod aliis aliisque
  22. modis, pro variis Parabolocidium generibus, taciendum exit.) HToc enim tacto.
  23. ostendetur, ut prius in Parabola, lingula Rectangula, in respectiros Scctores,
  24. iplorum dimidios, conrolucum iri: reliquaque qua hinc lequuLIE.
  25. Cum vero alius occurrat modus expedicior, aliunde sumpris principiis, ideu
  26. praeltandi; (neque loctori, credo, displicebir varietas;) rem sic asgrediemur; ca
  27. methodo qua ad Trithm. Insin. prop. 36. ecc. utus Cum.
  28. L18. 199. In Spirali Archimedea, MTTF, lig. 199. Tumpris Sectoribus Cimilibus; 2d.
  29. eoque cum raciis M F, M P, _c. HOC eA MP, MP, Scc. cum angulis P NIY
  30. PMT; dec. arichmerice proporcionalibus; ut 2, 2, 3, 4, dec. Frunt arcus PY,
  31. PY, Cmpore in ratione qux ex radiorum MP, et angulorum M P P, rarionibus
  32. COMPONITUE,) UE F, 43 5, 16, ecc. leries Sccundanorum; (nempe uno gradu al-
  33. tior quam elt Ceries Radiorum MP, propter ansulos M PY, in racione leriei Pri-
  34. manorum, seu arichmerice proportionalium:) adeoque, si in rectas expandi intet-
  35. ligantur, crunt ut tocidem ordinarim applicatae in complemenio Parabolae, (axem
  36. habente MIP; alcicudinem, ip( P F, non ut prius hujus dimidio, aequalem,) ut
  37. pote in ratione duplicata axium MIP, MP: (quales Tune PT, P P, complenes
  38. Semiparabolx complementum MIT F II Ag. 202. Sumpris BF, FHI, Fg. 202. Xqua-
  39. libus iptIS MF, FOP, fie. 299.) _ propterea, limul omnes, (hoc est U FP
  40. spiralis complementum ad conterminum sectorem,) aeguancur Prienti Rectansule
  41. Parabola circum Ccripri; Hoc Cst, SM PXPF, SCu ZMHXMF, (per L. vel 6. hu
  42. jus.) F Aque Concerminus Sector M P PM, (nepore ex arcubus arithmetice. pro
  43. POrTIONalIBS ContlatUS,) = ZBI LX P F, (per T. hujus.) Frso, figura Spiralis
  44. (mepere secloris reliduum) == 6M PXP F, (PTODtEF Z = 3 = 5;) hoc est, (PrOPICK
  45. 218. 2993. Requis aurem taetivet cur parabola MF B tig. 202. alcicudinem, jam Donam
  46. eo LBL. ipliuS arcus contermini P F H8. F99. longicudini aqualem; quam prius teceranr
  47. arcus P F Fg. 200. dimidiam: racio in prompeu est. Cum enim recinencibus Tuam
  48. Tingulis lonsicudinem rectis Z Y, uur in axem curratis; dum, in rectis MB, con-
  49. trahuntur ee in unioum in punctum; adeoque Parabolae magnicudo decresear:
  50. necesse ct u, in HF, rectae E0 (ipsis Z L aequales) prorratianeur puta in ZY
  51. quibus respondeane, in Sectore Spirali concermino, areus OO;) adeoque Com
  52. plementi magniendo creleat. Fr propierea, dum complementum contideramus.
  53. (juxta hanc hyporhetin,) Tacienda erit H F (complementi Semiparabolae seu Se
  54. miparabolocidis balis) iph PO F semper aequalis, (quicunque fuerit Parabolae seu
  55. Parabolocidis gradus,) crpote quae ex omnibus =Y, (hoc M, omnibus OO,
  56. componitur. Dum vero Parabolam vel Parabolocidem liguram M F B (juxra
  57. priorem hypothelin) consideramus; facienda cst. M B Parabolae seu parabolocidis
  58. alticudo, (non quidem omnibus OO, hoc est ipsi P O F,) Sed omnibus Z T simul
  59. sumpris aequalis: hoc M in Spirali Archimedea, (ProDuer iplas M X, adcoque
  60. 2
  61. 202.
  62. 5. 3:: x. 3,) ad Sectorem conterminum, ut 1, ad 3

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. 898. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0918?run=74