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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. 389

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: 0.91.

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The machine reads it as

  1. D. LiL.
  2. INFLNLTORUM
  3. L LOP. L
  4. Lemma.
  5. Uxta eandem regulam (prop. 46, 47.) Si exponatur series quancitatum
  6. quarumlibet, juxta quamlibet Pabellae seriem; de illarum radici-
  7. bus quacraticis, cubicis, c. aut quibutris intermediis potettatibus, pa-
  8. riter inguirendum exit.
  9. Fxempli pracia; si exponantur infinita numero Onactrara (vel quaelibet plana simi-
  10. Lia) jurca seriem Duartanorum; (cui altignatur, in Labella, ratio L ad 5:) Peries la-
  11. rerum (vel rectarum in illis Cimiliter politarum) rationem habebie (ad seriem X
  12. qualium) Fad 3: quia F, 3, 5, Sine Arichmetice proportionalia: vel eriam, quia
  13. ubi plana Tunc series Duartanorum, eorum latera crunt series secundanorum, qui-
  14. bus altienatur in Tabella ratio F ad 3.
  15. Sic, li exponantur cubinumero infiniri (vel quaelibet similia Colida) juxta seriem
  16. Textanorum, quibus in Pabella conoruit ratio F ad 7; eorum lateribus cubicis (vel
  17. rectis in his similiter posiris) conveniet ratio F ad 3; ee horum larerum quadraris
  18. (vel planis in cubis illis similiter posicis) ratio F ad 5; quia duarum mediarum
  19. Arichmetcarum incer Z et 7, minor elt 3, major 5, (sunc enim 2, 3, 5, 7 Arich.
  20. metice proporcionalia: duas autem medias ArichmCtCAS INFETPONO IMICF TCE 7;
  21. quia coridem lupponimus medias Geoniecrieas inter unitatem et cubum, nempe L. a-
  22. tus ec Ouadratum; sunc enim Unitas, Facus, Ouadratum, Cubus, Geomerrice
  23. proporcionalia. Fc quidem (i Cubi line series sexranorum, Latera crunt series se-
  24. cunclanorum; et lacerum Ouadrata, series quarcanorum; quibus in Tabella conve.
  25. niune rationes E ad 3, Fad5
  26. Sivero quantitates expolica in eadem serie leranorum, Elent Ouactrata (vel
  27. plana quaeliber limilia,) eorum laceribus conreniret ratio Lad 4. Ouia incer L e
  28. media Arichmerica est 4; Pieut inter Unicacem e Ouadracum media Ceometrica
  29. cst Radix vel Lacus. Ec quidem Si Ouadrata Lint series sextanorum, eorum Latera
  30. crunc series certianorum; quibus in Pabella conrenit ratio + ad 4.
  31. PROP. LTI.
  32. Corollarium.
  33. T PEOPtCrCa; Ex cognitis rationibus quas habent Conveidea C Pyrami-
  34. docidea, prop. 48, 49, 50. memorata, ad Cylindrum vel Prisman (suver
  35. aequali base aeque altum;) coenoscentur rationes quas habent plana illa unde
  36. construuntur, ad Paralleloerammum circum seriptum. Nempe complementum
  37. Semiparabolae ut L ad 3: complementa Semiparaboloeidis Cubicalis, Biqua-
  38. draticalis, Supersolidabis, 36. ut X ad 4,. + adt 5, F ad 6, c.
  39. Si enim Conocidea vel Dyramidoeidea illa cornolcantur ellè series Onartano.
  40. rum, Sexranorum, Octaranorum, Decimanorum; dc. cilque convenire rationes
  41. 2ad5, Fad 7, Fad 9, L ad XI, dc. Porum laceribus (qude proprerea. lune series
  42. Sccundanorum, Ferrianorum, Ouartanorum, Duincanorum, etc.. ) convenient ra
  43. tiones + 2dZ, Y ad 4, Y ad 5, F ad 6, _c. Ouid 2, 3, 5, IteM L, 4, 7, ItCM L, 5, 9,
  44. icem L, 6, LF, ec. Sunc Arichmerice proporconales.
  45. PRO P. LTTI
  46. Lemma.
  47. I intellectis; patet adicus ad inrestigationem rationum quas
  48. (ad seriem marimae aequaluu) Hlabere ceantur ejulmodi letLs
  49. rorum sire quancicatum slerice proporcionalium, a puncto velo
  50. C 3
  51. Racicum Ouadraticarum; Cua BddTaLICaTUM, AC. HIIHC.
  52. cBala

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. 389. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0409?run=74