Leibniz Legible

Machine transcription of the Leibniz Nachlass

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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. 509

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: 0.83.

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The machine reads it as

  1. E C FCLO4
  2. C. =D = a respectire ducta, danc Relidua a D = a omnia rectangula FC Y
  3. hoc est omnia Ouadrata LL, qua ad bocidem D. Cunt ut F ad 6; Residuorum
  4. vero Ouadrata, hoc est rectarum YZ Biguadrata, ad coridem D, uc X ad 30
  5. Reliduorum cubi, hoc est rectarum LZ Porestates sextae, ad toridem Z, ut 1 ad
  6. F40,_C. Unde colligitur series F, 6, 30, 240, 630, c. (Arich. Infin. pr. 133.)
  7. Dua non alia cAt quam Series 1, 2, 13, 158, 387, ecc. in seriem Geomerrice provor-
  8. tionalium 1, 4, 76, 64, 256, ecc. respectiro ducta: Adeoque series illa (ibid.
  9. PrOp. 189.) interpolata 2, B, 3, ZF, 3, ZB, ec. in hanc item interpolatam +, 2
  10. 49 8, 26, 32 ec. respectire dueta, exhibebit illam prunam interpolatam 1521, 6)
  11. =E 30, 251 140, ecc. Et propierea, lieur T ad 6, 30, 240; ecc. exhibent racio-
  12. nes quas habent rectarum omnium YZ porestares sccunda, quarcas Texta, etc. 20
  13. tocidem DE, D, D5, _c. Sic L ad 2B, 331, 23D EC. exhibebune ratiONCS quaS
  14. habent carundem rectarum XZ Poreltates primas cerria, quinta, eec. ad coridem
  15. D, V, Z, Scc. Fc Speciarim (quod nostra jam interest) omnes eubi rectarum X2y
  16. ad cocidehi D sive cubos FC, rationem habebunc F ad 33B, Livo uc 3 ad 32F.
  17. Duod lulcepimus probandum. ls.
  18. 6T. POrrO, quum calentus ad 5 5F, 52, 53,54 Cubi agieur de cenro graricatis centrum
  19. Colidorum ex conrertione Semiereloidis circa rectam C F.) omistus Hc, caleulieravita
  20. tancum fundamenta remoriora extribica: libet hie calculum illum aliquarenus ex. tis semi-
  21. hibere, juxta methodum quam 555 intinuari. FL primo quidem Dervendemus solidi cir
  22. convertionem Friansulio P P, deinde Frapexii Vier P Rectam autem in PPIanL
  23. dulo p, adeoque et Br in Frapezio, dicemus B; ejusque aliquoram partem intinre
  24. exionam b; ad eoque V P erit B F B, vel 2 B. Item Z L, dicemus Y; ejusque partem
  25. intinue exisuam, y. Ec rectam FX, hoc est altitudinem, rel etiam diltantiam ab AF
  26. dicemus A; ejulque parrem intinite exiguam, a. Rectam denique Z Z, dicemus 2.
  27. 62. TTis politis; supponimus in Triangulo . Lp intinitas rectas parallelas Arich-
  28. merice proporcionales, a vertice F ad DAHIT CuC vP COntinUataS, O, +b, 2 b, 3b.
  29. vlque ad Bearum maximam, quae est ip(avP. Hae aurem recta, dum circa rectam
  30. C convertuntur, deleribunt coridem annulos planos (falcem hujulmodi annulo-
  31. rum partes similes) aequales toridem rectangutis parallelosrammis a rectis ip(is qua
  32. Convercuneur, ec peripheriis quae catu punctis mediis deleribuntur, contentis:
  33. quas peripherias, live incesras sive dimidias, cum tnc radus proporcionales, per
  34. rum momenta Lelpectu cc ea aoM dutantias pro-
  35. portionalia; Cincque distantix, (UI O, a, 2 a, 3a, ec. usque ad A; CruHL Cd HIOIHICHCZ
  36. 27abY, _c. ulque ad ABV. FTocelt, omnia momenta, lune leries J’eprin
  37. Dux Percianorum leries, ad toridem maximo xqualia hoc all. ad maximum n alei-
  38. tudinem ductum, hoc elt ad Cylindrum vel Prilma ejuldem vel aequalis batis aequet
  39. bZ +7 B, By
  40. CF.
  41. norum, Eive Aritimetice proporcionalium, quorum maximum eAt D: quae in
  42. ID (OS TacOS CCL CaIo, LCLDCC, L, 2503 _C. ulque ad , hoc est Z Y radio.
  43. rum illorum maximum. Frunc isitur plana illa, i 0, LR2)3 2DX27, 3bX 2)
  44. Ec. hol CA 00, Lby, 4b7, 937, c. ulque ad Br. Deinde, cum horunt plano
  45. u OhyXOa, EbYXEa, 4by X2a, Oby x 3 a, etC. hoc est 000, Taby, 8 ab7
  46. alcum, ex puncto Y suspentum, est ut X ad 4. Quod dicamus igitur : A ABF.
  47. B = B, live 2 B, hoc elt VP in dunc B + 0, B. F B. + L0, . 3b, cecsalgue
  48. ad 6 =B. _Radii veto peripheriarum d mediis rectarum punetis delcriprarum.
  49. Tun L. F0, Z= p, Z. = 27, Z = 3y, dc. usque ad L F P. Lp GuIB IeICBIS
  50. Enricem respectire ductis tu series magnicudinum, sL. F OL + 0B + 00, BZ 1
  51. 5Z = 2bZ F. 2y B + 4 by
  52. BL+ 3b2 f 3y B + 9by, dc
  53. ulque ad BZ F BZ F Y B. F. BY. Oux li ducancur in respectirao suas abi A F
  54. distancias 0, a 2. a, 3 an ec. usque ad Ag tier Series Momentorum ib
  55. 0B7 1000Z]0d B f000
  56. Z + abZ + a y B + ab.
  57. C 4erB = 8 ab7
  58. C+ Oay B + 27
  59. c. usque ad
  60. it
  61. Cujus summa est Z A AI L. F; DC. +5 2AB + = A1B)
  62. tive
  63. 351811
  64. ilicc. D. MEMIK SBOE
  65. 63. Fgdem modo; Lutinita rectae Praperii, a minima B, hoc elt. Bi, ad nisque
  66. BH
  67. 1B + A
  68. 3A uta

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. 509. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0529?run=74