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[Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ, fol. 103

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.

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

The machine reads it as

  1. V B CF.. ZI.
  2. XXVIII. SiE CirCulAS AMB Cujus Radius C A, SC adhane per-
  3. vendicularis recta D BP, Sic item curra A N P calis, ut duet d urcun- l1G. 15P
  4. que recta P M N ad D P parallela (quae circulum secer in M, dictam
  5. CurraM in NY) SIE recta P N aequalis Droui A M; Cir demum axe
  6. AD, base D E deseripea Parabola AO P, heC extra eueram A N P
  7. tora cadet.
  8. C: 5133VE E eSLCASB, AIEACII M
  9. Nam secet recta P HI parabolam in O; Se connectantur TuBCeNSa
  10. AB, AM. estque D F. P N :: AEC A B, aEC. AMC AB. AN
  11. :: D E. P O. quare P N + PO; unde liquet ProposEuM.
  12. XZIX. Exhrinc (e C rulgo roris spatiorum ADB, AI F dimen.
  13. 3C A XDB
  14. sionibus) Facile colligirur haec regula: Z CA ] CD ~ ArC. AB.
  15. POFFO SIPONatE arC. AB =- 30 grad. (IEquC2C A ==-LL3; juXtA
  16. resulam istamm compucando, proveniet tota circumferentia major quam
  17. 355 minus fractione unitatis.
  18. ZXX. Hinc eriam dato areu A B, nominarisque AB = p, C A = r; e
  19. DB =C, ad inveniendum sinum rectum D B adhibebitur hXC Xqua-
  20. io:
  21. 3FY pP
  22. 12rY
  23. Orr -) pp Orr. pp = 0c. vel ponendok =
  24. Bp = 4kC = ec. vel 2 h = V 4RR = Rp = c.
  25. P
  26. exic
  27. C13. 13a
  28. XXXI. Sic A M B Circulus, cujus Radius C A, d huic perpendi. F18. 253.
  29. cularis recta D BF; SIE item CUIrVa AN P pars Cyoloidis ad Circulum
  30. AMB perrinentis; demum ad axem AB, baCin D P Ntacuatur Para
  31. bola AO F: HXCInEr2 Cycloidem tOta CadeF.
  32. Erenim urcunque ducatur recta P M O N ad D F parallela, lineas
  33. expoliras secans, ut cernis; connectanturque sabtensa AB, AM;
  34. eAtque DE. PO:: AB. AM :: CAEV. AF. ANC DF. PN;
  35. deoque P O -= P NI. unde constac Propositum.
  36. XXXII. Extrinc, _ C noris seementorum circularis atque Cgeloida-
  37. 2C AXDB + CDXDB
  38. lisidimensionibus, haec elicitur Regula
  39. E AEC. AB.
  40. A1 - 2C D,.
  41. Porro B Tueric are. AB = 30 grad. e POnaTuT 2 CA = F135 C
  42. regula hac contectatus fore totam circumferentiam minorem quam
  43. 355. plusfractione.
  44. Vides isitur uc c propolitis duabus regulis starim emersit Diametrs
  45. ad Circumferentiam Proportio Metiana.
  46. XXXIII. Duoniam exorbicanci se obviam dedie Crclois hoc adno
  47. cabo Theorema, nelcio an uspiam ab illis, qui de Crcloide cam tuse
  48. scriplerunc, animadversum: Completo Rectansulo ADFC, spatium
  49. AFC

Cite

[Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ, fol. 103. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/797435492:0325?run=74