Leibniz Legible

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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. 410

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: 0.84.

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The machine reads it as

  1. LLLLLILML LLC A
  2. O
  3. eorema
  4. Teiusmodi fioura AD BB verticem habens Ad infinicum ex basin
  5. DDB determinatam, rationem habeat ad inseripcum Parallelooram-
  6. mum AOBd majorem quam infinitam; eadem ACura AL) BB verti-
  7. cem habens AD intinicum ex balin dB determinatam, rationem habe-
  8. bic ad inscripcum Parallelosrammum Ad BD minorem quam intini-
  9. tam (finitam nempe:) EE contra, si situ illo considerata rationem ha-
  10. beac minorem quam intinitam; sicu hoc habebit rationem majorem
  11. quam infinitam: Si denique in licu uno rationem habeat simpliciter
  12. habebit rationem simplicirer intinitam.
  13. Nam verbi gratia in serie Secundanis reciproca, cum tinE (per PrOP. 33.
  14. rectae DB, DB, In diaCITOruM AD, A D, ratione reciproex duplicata: erunt C
  15. ErOTUM AS, AS, rarione reciproex subduplicata; adeoque ip(x SB, SB, _C. TunE
  16. Series Sublecundanis reciprOCA. EL CONTA. AIque (cum idem etiam in aliis ejus
  17. modi seriebus concingat,) Pater propolicum pex ProP. 102, _ 104
  18. In serie rero primanis reciproca; cum (Per Prop. 88.) reclae DB, DB, Cine dia-
  19. metris AD, AD, reciproce provortionales; erunc eriam rectae sB, SB diametris
  20. luis AS, AS reciproce proporrionales, ipsaeque SB, SB, series icem primanis reci
  21. PrOca. Conctaterso propolicum per PCOp. 203.
  22. 1XI)
  23. PROP. CVI
  24. BCISCC
  25. Theorema.
  26. CT series aliqua reciproca ver seriem aliam lEre reciprocam sive
  27. directam) multiplicetur auc diridatur, rel etiam aliam mulciplicet
  28. aut diridat; eadem leses oblerrandae sunt quae in leriebus directis
  29. PFOP. 23eF 8F,. OHI. Lies si e Sis MMSME
  30. .
  31. Frempli pracia. Si seriee secundanis reciproca (puta zyiy q dc.) eujus inder
  32. 2 relpectire mulciplicetur in seriem Pertianis reciprocam (puca 2, 8, 27, sc.
  33. cujus index el
  34. index
  35. 3; Prodibic series Subquintanis reciproca (F, 327 243, etc.) cujus
  36. Iiem s series Fertianis rectloca (+, 37 27, _C.) cujus index - 3; respective
  37. mulciplicetur per seriem Secundanorum (1, 4 0, dcc.) cujus index 2; prodibic sc
  38. ries 4, 8, 373 ec. hoc elt 232, 3, ecc. Primanis reciproca, cujus index =1=
  39. ttem si series Sublecundanis reciproca (7 +3 Y 33 , ec.) cujus incdex -;
  40. respectire mulciplicetur in feriem Secundano.
  41. rum (1, 4, 9, etc. ) cujus index 2: prodibir sc.
  42. Ties
  43. 3V2
  44. ecc. vel ZV 2, 3 Y 2, 2V 3.
  45. ac. vel TV F, 2V 23 3Y 3, dc. vel VF, V8.
  46. Y 27, _c.) radieum quacrariearum cuborum seu
  47. certianorum, cujus index z =
  48. t:
  49. Porro, li series Secundanis reciproca, cujus in
  50. dex = 2, diridat seriem Primanis reciprocam.
  51. cujus index = 2; Prodibit series Primanorum.
  52. cujus index + = - L Y 2, nempe- Lminus- 2
  53. Icem ( series Primanis reciproca, cujus index
  54. , diridat seriem lecundonis sccipiOeam, cu
  55. Ju5
  56. Z UE patet.

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. 410. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0430?run=74