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[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. 718

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: 0.89.

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The machine reads it as

  1. De Calculo Centri Cravitatis.
  2. Cap. V.
  3. FI itaque Sectoris BCB A magnicudo a R, (nempe Z BA BK G A, per proP. T2
  4. Fis. 159, hujus;) ejusque demiltis BC A, La R. Ei, spcciacim, iocius demiciiculis (propter
  5. Trem Frianguli BB C magnitudo : BBx CV (per PrOP. 6 hujus;) hoc est SX:
  6. (Nempe, SR = - 5V, A V HCrIE CuPEa CentruM; vel 5V = 5 R, si intra:) Adco-
  7. que BC.V = 55 ∞: HIOC CA, Z 5 R = Z 5V, S luPrL; vel Z5V = = s R, Ei intra
  8. Adeoque, Si a Sectore BC. B A = a R, Auteratur Friangulum B BC = 5 K
  9. =52; vel Addatur Friangulum BBC =5V -s PP; (prout tuerie V supra in-
  10. Frave Centrum:) urroris calu habetur Segmentum BB A = (a R F 5 N =) a R
  11. =sR + 50 = e R F 5V. Adeoque BV A = = a R F Z 5 N = = a R = 2 5 R + = 5V
  12. ZC R + = 5V
  13. Hoc clE: Si inCeripro (in Circuli Sermento) Friangulo aequialto A B B (= 52)
  14. addatur Friangulum aliud (a R = s R = e R) cujus nempe Balis sic aequalis C ir
  15. culi Radio (= R) e AIcicudo (= 2a = 25 = 2e) equalis excelII AreUS LUI-
  16. pra Tubrentam: Flabetur Segmenti B B A masnicudo; a R 5 R f 5V =- c R + 5V.
  17. Ejusque Semistis, Semilegmentum B V A = = a R - 35 R + 3 5~ = Z C R L 2 5V.
  18. Adeoque, duo timul Scgmenta abscista AB, AB, (qua, cum interipro Frian-
  19. sulo, complem Segmencum BB A, ) aequant a R - s R = e R, e corum utrumris
  20. a R 2S R = ZCR.
  21. Hoc elt; Si (a = 5 = e) excestias Areus B A supra suum sinum rectum B V.
  22. ducatur in (= R) semistem Radii: Elabetur magniudo Scemenri BA; = 2 a R
  23. Si vero Semenros BB A (= e R. F 5v,) adjieiarr Feianeulum BB a (= B 5:)
  24. Hhabetur Sector B a B A (angulum habens B a B in peripheria, et B A B arcum,)
  25. eR + sV F sh: hoc et (propier v + b = 2 R,) e R F 25 R; vel (propier
  26. e= a sy) a R + 5R = fR. Adeoque Ba A = Z a R F 3 5 R = 3 f R
  27. (Idem proreniret, si Sectori BCB A = a R, adderencur duo Friangula B C a,
  28. BCa: quorum communis Balis ett C a R, e urriulris AIcitudo BC =-5: adc0.
  29. que simul urraque sR. HIOc elt, BaB A = a R + SR = fR: EF Ba A = = a R
  30. F25R = 3
  31. R.)
  32. HOc est: Si (a F s=f) aggrexatum ArCUS BA, e Sinus Recti BV; ducat
  33. in Semiltem Raci (= = :) Hlabecur Sector Ba A = 3 a R F Z 5 R = 3 f. R.
  34. Similiter de Centro Craricatis procedendum.
  35. Nempe, (per jam demonstrata ad hanc propositionem S A,) Sectoris BCBA
  36. (sire Semicireulo major sic, live minor, sire ipli aequalis) Cenirum graricatis clt
  37. in CA recta, supra Cenrum C, quancum elt = = R. Nempe ea raione ad 3 R,
  38. quae est Chorda BB = 2s, ad arcum B A B = 2a; sive ut s ad a:) Adeoque il.
  39. lius, a puncto e seu ra tangence, distancia est R. f 2= X = 3a F 25 R. Ad.
  40. eoque d P A (cangente verricis) R - = X = 3a= 25 R. Fademque est, ab
  41. cildem ram T A, diltantia Ceneri pravitatis semisectoris BC A; Propier dimidias
  42. B V ec hruic parallelas semisectorem complencibus, toris B B et huic parallelis com-
  43. plentibus Sectorem inceorum, proporrionales, ee in eisdem cum illis distanciis sire
  44. d ray sire a Y A. (Quod ee similicer incellixendum crir de Semi conis, Semi-
  45. sexmentis, sc. quorum Centra pravitaris sive a Balis plano, sive à Plano verricis
  46. bali parallelo, cancundem distant, quantum inde distant C’entra graritatis integro-
  47. rum luorum sire Conorum, sire Sesmencorum, ec. Ouod semet monitum csto
  48. ne opus sic idem Caepius repetere.) Li speciarim, Semicirculi ADa, Ceniri pra.
  49. vitatis (urpore in DC jacemis) distancia Ere d ran sire dTA, est R = C. a
  50. C A.
  51. Adeoque (proprex magnicudinem Scctoris BCB A = a R, _ BC A = ; a R,)
  52. Momencum (respectu rectae ra uc axis Libra) Sectoris B C. B A, est 3 a + 2 3 p
  53. Cmenivdine seilicet ia distantinme ducta; ) et Semiletoria BC a, 3 a + 25 .

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. 718. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0738?run=74