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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. 741

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. Prop. LVI. DCuam Centri Cravitatis
  2. Verum in horum Semisolidis, solidisre impersecta quaris conrertione deserio.
  3. tis; Vnoulisque correlpondentibus: nondum decerminancur ipla Centra; ut qua
  4. L13
  5. 259
  6. non in ipto Arc polica sunc, sed alibi, exrra axem, in planO per atem Iai 160.
  7. Feunte.
  8. Cum tamen in quo per Axem convertionis, seu Aeiem Ungulx, transeunte plano
  9. constiruta Linc, jam constet ex s G prov. T2. hujus; (nempe, in eo per conversio
  10. nis axem plano quod solidorum, conrertione tactorum, arcum convertionis bile.
  11. Cat; eoque per Ingularum aciem plano, quod bisccac ungulae alcicudinem:) AF
  12. que in qua quidem hujus plani recta, jam lic determinatum; nempe in eis quoxum
  13. Axis seu Acies eA A a per Centri graritatis distantiam, a ra, T A, BV, ec
  14. e in eis quorum AXis elt Za, F A, vel BV, per ejus ab Aa distanciam: Id F0-
  15. tum superelt, uc in quo iltius rectae puncto sicum lic, determinemus per ipsius a
  16. convertionis axe distanciam in eis qua convertione describuntur Solidis; ee, in
  17. Ungulis, per discantiam a perpendiculari per Aciem Plano. (Unde iplum grari
  18. cacis Cencrum determinarum ii contat, peT PrOP. 26. CaP. Prxced.) Id ducem
  19. sic axcrectimur.
  20. OE Sectorem Sphaericum incesrum, B CBA, S A, (plani BC. A cicea rectam
  21. Aa incegra conversione deleripri,) sic ejuldem semillem seu Semilectorem Sphae
  22. rieum, aliumre impertectum, (convertione dimidia, aliare impertecta deseriptum, )
  23. incellisamus ex Pyramidulis (similibus e aequalibus) componi, (juxta det. I.
  24. Cap. 4.) Ouarum communis vertex lc Sphaerae centrum, Basesque compleant
  25. Superticiei Sphaericae porrionem Semisectori huic, Sectorire imperfecto, convenien-
  26. rem: nempe Frilineum Spharicum, quod Sectoris Basin appellabimus,
  27. Cunque (per s hujus) Cenrri graviratis in Pyramide, diltancia a vertice pyra-
  28. midis sic 2 corius alcicudinis; Pyramidularum illarum omnia Centra graritatis
  29. (aequalibus ab inricem distanciis remoca) incelsisancur complere Simile Prilincum
  30. Spharicum, ut b a Hig. 265. Cujus radius sE C b = ZC. B = 8 R. Cujus cum Cin-
  31. sula puncta, (urpore aequalium Prramidum Centra gravicaris,) aequaliter onerata
  32. reputentur; idem erit Prilinei hujus, ipliusque expolici semisectoris, Sectoritve
  33. impertecti, Centrum graricaliS; (Per 76 Cap. 4.) adeOquC, capcundem ab A a con-
  34. vectionis axe distabit.
  35. Ouod de limiliter accommodabicur Onpula eidem BC A Sectori Circulari infi-
  36. stenci; Cujus utique (pari ratione) Cenirum gxaricatis idem erie aeque Suverti
  37. ciei Ongula Cylindracea areui b a insistentis aciem habeneis Aa; adeoque tancun-
  38. dem ab A a Pe penMlait plano aalo.
  39. Est autem (per S V, W. BIOB. 23.) Semiguadrancalis Ongula superticialis, ar-
  40. cui B A inlistentis, momencum respectu iplius ao; idem acque Tumima quadrato.
  41. rum linuum rectorum ipsi A B arcui conrenientium; adeoque aequatur facto ex
  42. BV a semisegmento, in R ducto; hoc elt, (prOpter BV A == ZC R f 3 5V, ver
  43. SF. SPrOP. praeced.) ZC R F 35V R: Aique hoc, per Ungulae superticia lis maoni-
  44. cudinem diritum; hoc ell, (per SN. (. prOp. 13.) per v R divitum; exhiber iltius
  45. Ongulae Superticialis B A, diltancium Ceniri gravicaris ab A a. = -
  46. + Z5. Ad
  47. cogue (propiet CB = CB = Z R) areui b a insiltenis Ongulx supertieialo, e
  48. propterea (per jam demonstrata) Ongulae Solidae ipti BC. A insistemis, aciem ta
  49. 8b +35. (De, specia
  50. im, illius quae tori A Da semicirculo intistie, ingula, distancia Ceniri pravicacis
  51. ab Aa, PFOPter 5 ==0, ad eo que = 4 = Z P, _ v = 2 R, exi
  52. Eademque eltet diltancia Cencri graricatis Solidi, impertecta ejuldem BC A cir.
  53. Ca Aa convertione deseripri, ab Aa convertionis axe; dempra CurratTA. oSCc
  54. propter curraturam, minuenda est pro ratione quam habet ad, convertionis aveun
  55. chorda sia; (Der PrOP. L4. hujus) hoc est, in Semiconvertione, ut 2 R ad 3~
  56. seu uc 4 P ad P; (et in aliis convertionibus similicer, mucatis mucandis, in ratione
  57. Chorcae ad Arcum;) Adeoque Semisolidi, ipsius B C. A semiconvertione circa A a
  58. deseripris distantia Ceneri orar lais a convertionis sue Axe Aa, ef( 3 a + 3 sV
  59. et
  60. (L speciacim, quou semiconrertione Semicirculi A. D a dascribicur, Hemisphaerii,
  61. distancia Cencri praricatis ab Aa, elt 3 R.
  62. d’acque
  63. t

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. 741. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0761?run=74