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. 413

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: 0.82.

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

The machine reads it as

  1. PrOD. CIX.
  2. LNELMTTORUM.
  3. Sic verbi pratia terminus aequalium quilibet
  4. _ primanorum maximus R; ejulque pars infinice
  5. parra dicatur a = =; numerus terminorum om-
  6. nium (vel figurx altimdo) A: s cermini
  7. concinuentur in intinitum usque ad . . ..
  8. eric Reliduorum ec Ageresatorum lumma . . . .
  9. Nam omnium AE qualium aBBrEBaEUM exIE A R (UE pateL;) Primatorum aeGre.
  10. pacum ejuldem semissis EA R, (per PTOP. 2.) ErgO AR - ZAR = = AR, e
  11. A R. F 3 A R = Z A R. Nempe seriei Aqualium (AR) illud clt Z, HOCZ: PTOUT
  12. altirmatur. Hoc est, erie illud ad seriem Aqualium ut Z 2d Y, vel uE F ad 2:
  13. hoc aurem, uc Zad cn ret ut F ad 3, vel 3 adt 2.
  14. PRO P. CTX.
  15. Corollarium.
  16. RBO, Si Parallelozrammo auferatur Tri
  17. ansulum (super eadem vel aequali base
  18. aeque altum) Residuum (quod quidem e ipsum
  19. erit Trianculum inversum) erit Parallelorram-
  20. mi semissis: Sin addatur. Triangulum, erit
  21. axoreeatum (nempe Trapezium) sesquialte-
  22. rUM.
  23. Patet ex praecedenri; est enim Parallelopram.
  24. mum series Aqualium; Triangulum, Ceries Pri-
  25. MaHOTUM.
  26. PROP. CZ.
  27. Corollarium.
  28. Tem, Cylindrus Parabolice excavatus, est pleni semissis. (Quod idem
  29. verum est de Prismate analorice excavato.)
  30. Nempe li ex Cylindro (serie nempe Aqualium) eximatur Conoeides Parabo.
  31. licum (super eadem bale aeque altum) quod quidem est series Primanorum (por
  32. PcOP. 4 vel 63.) quod reliquum est eric semiltis Totius Per PFOP. 108.
  33. Arque idem accider s Prismati eximatur Pyramidoeides Parabolicum.
  34. P R OP. CXI.
  35. Theorema.
  36. T Series Aqualium mulctetur serie Secundanorum, Fertianorum,
  37. Oartanorum, etc. Residua erunc torius duo Frientes, tres Oua-
  38. drantes, quatuor Ouintantes, _c. Sin ita avSCaTIE, CrUNE AGOrESALA
  39. ejuldem sesquitercium, sesquiquareum, Sesquiquintum, _tc.
  40. R +0a
  41. R2 FI a
  42. NemDC (i Termini 3 D2 = 4 a
  43. conineneur asgue ad
  44. R2 79 a
  45. Ec.
  46. R = P
  47. R + R
  48. crune summae (per Prop. + H.) AR F5 AR AR F + A R3 AR + Z AR
  49. Hoc cst, Reliduorum summa +-
  50. Axprexacorum summa
  51. c+ 3 =3. +
  52. drat
  53. X 3= 5 CC.
  54. a
  55. ec
  56. 2 = R
  57. AR L Z AR
  58. L R
  59. AR Y : AR
  60. le F Oa = 04
  61. R + Xa3
  62. lq La
  63. H + 0a3
  64. R = 27a
  65. ec
  66. R~ Z BF 4
  67. RA Z R4
  68. IC + 169

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. 413. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0433?run=74