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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. 441

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: 0.86.

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The machine reads it as

  1. PEOP. CLXVII. TNFENETORUM.
  2. UE TUPra, tam numeratores quam denominatores TraCtIONU SunE AFHHMericC prO.
  3. porcionales.) Lt propterea (juxca progressionis analogiam) Li aumerus primo d
  4. secundo incerponendus dicatur a tiune reliqui concnua mulciplicatione Alimero
  5. TUIM a , SxIOY24 dC
  6. Est aurem a = , A; PrOptes ;)
  7. P ROP. CLXVIL
  8. Theorema.
  9. Deoqueu Si series Mminita Subsecundanorum (puita V an YB, Y C, _c.)
  10. respectire ducatur in sciplam inverlam (puta V: D = a. V: D = b.
  11. s: D = c. _C.) atque eadem etiam in seiplam directe positam: (puta
  12. Teries V an Vb, Yc, ec. in Seriem V a, V b, V C, eC.) erit aggregatum re-
  13. ctansulorum illorum (puta V: a D = a 2: F V: bD = b 2: = V: cD - c:
  14. _C.) ad ageresatum horum (puta V a F Y B2 F V c2 ec. vel a + b. +
  15. C8C.) uc unitas ad numeruum intermedium, numeris diagonialibus L, 27
  16. in Fabella prop. 232 interponendum.
  17. Sequitur ex praecedente. Nam leries Sublecundanorum est seriei s qualium, de
  18. Feriei Primanorum incermedia, (ue patet ex dictis prop. 64.)
  19. Series autem Subsccundanorum in seipsam directe posiram (puca V a, Vb, VC.
  20. _c. in V a VB, YC, _C.) eAt series Primanorum (puca V a 2, V B2, V62, c. vel
  21. au b, 6, eC.) cui convenit ratio = per ProP. 44, vel 6q. EF propierca, I ratio qua
  22. convenic seriei Primanorum in seipsam inverlam duetae (intermedia nempe ratio.
  23. nibus Z, 5,) dicatur 52: Racio rationis hujus ad illam E, puta Z) 30 (B, erit
  24. Per PraCCd.) ea quam habet F ad numerum inter F X 2 incerponendum, in serie
  25. diasonialium F, 2, 6, 20, 70, _cc. tabelIX prOD. X32. Qui numerus icitur in posterum
  26. dicatur D. EAque lemistis numeri inter F et s interponendi in serie 1, 67 30, 240,
  27. 630, _c.
  28. PROP. CLXVILI.
  29. Corollarium.
  30. LPFOPterea Circulus ad Quadratum Diametri, est ut X ad ∞, numerum
  31. nedope inter LB2 interponendum in serie Diaxonialium F, 2, 6, 20, 70
  32. 16. tab . L3L.
  33. Cum enim (per PrOB. 233, 235.) Semicirenlus ad Ouacdratum diametri SiE UE F
  34. ad 2B (numerum intermedium inter F _ 6 in serie F, 6, 30, 240, 630, _c.) crit
  35. circulus (quippe semicirculi duplus) ut L ad B, (numerum intermedium inter F
  36. et 2 in Serie F, 2, 6, 20, 70, etc.) per praced.
  37. Ft quidem eadem racio 5; ea elt, quae incermedia ponenda est inter L e Z, in se-
  38. rie i, 3, 197 165, elc. prop. 218, e 121. u et deinceps etiam uuerius parebic.
  39. SC FOL TV M.
  40. Cum igitur (ue ad ea quae monuimus in Schol. PrOP. 165. tandem redeamus)
  41. res eo redacta sF, ut Si pollimus rationes illas incerpolare (PrOP. ZZB, MCMOTAtAS)
  42. 133, 25, 285, _C. hOC C, quashabet Z adt F, 3, 8, 18, c. (hoc ett, ad 1, 25, 287
  43. 2 40, ecc.) sut cermint conlequentes tiunt ex connua mulciplicatione numerorum
  44. 3.
  45. 30, F40, Sc. Fiune ex comcinua mulciplicatione nuMETOTUM F , S X LOX L4. X 18 _C.
  46. 2 X 3 X 4 ec
  47. Vel denique E illas +, 3, 2, 3, _Ec. nempe quas tabet F ad 2, 2, 6, 20, ec. (nuI-
  48. meros diaxoniales rabellX PrOP. 132.) qui trunc ex concinua mulciplicatione nume
  49. TOTUM EXZX 5 Y3 X 3 ec.
  50. 5X7
  51. Ad 29 4
  52. XOCC
  53. 2X426X8eC

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. 441. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0461?run=74