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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 7v

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: 0.92.

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

One image of two folio pages side by side, registered by the library under both labels (also fol. 8r); this page is its left half.

The machine reads it as

  1. EE, FF
  2. invenire duas curvas coevolutione generantes curvan
  3. EE et FF CC. Manifestum est Ellipsia centro
  4. fo umbilicis E. F. descriptam ibi langere curvam
  5. Fingamus dari cur punctum C, et punctum F
  6. quaerique punctum E. Hoc ita invenietur, datur
  7. ex puncto C educatur ep ad curvam normalis
  8. axi occurrens in p. datur CB aequ y. B Raequ p
  9. jungatur FC Ex Ex F ducatur FG hormalis ad Cp.
  10. et centro C radio CF arcus secabit FG in G. jungatur
  11. CG patet angu ex natura tangentr Ellipsin, angulos
  12. Gep, et FCp fore aequales. Eodem modo inveniatur
  13. 2G intersectio rectarm 1C 1G et 2C2G dabit punctum E.
  14. quod jam calculo quaeratuo
  15. Idem brevius: si tangens e curvae Fx incidens in curvan
  16. CC reflectatur inde ad curvam EE debet eam etiam
  17. tangere, unde angulas quem recta PC ad curvam
  18. perpendicularis angulum FCE ca bisecabit. Data
  19. curva CC quaeruntur curvae FF, EE, et ex
  20. his duabus alterutra sumi potest pro arbitrio. Sed
  21. curvam Cc intelligo dari, dif proprietate tan
  22. gentium, seu ratione CB ad Bp expressa per
  23. AB et BC sit AB, X. BC, y. 4
  24. AGZ, FG, v. AH, h. HE, C +G+.
  25. ex F et E in CP perpendi culares FK. Et. producantur
  26. et in eas ex punctis , N _K dem Hantur
  27. normales, TM, NZ. Habetur FF aequo t+ v
  28. ob triangata similia FKC et per F ducatur axi
  29. parallela FW, ipsi cp occurrens in W erit.
  30. FW: TP:: CF: C7 Et rursus habetur FW.
  31. et Fursus FK: FW:: CB: CP Habetur FK.
  32. en FK T aeqo TP. CF. CB. Et eodem modo
  33. cT. CP
  34. aequ Np. CE. CB
  35. b angulum FCK
  36. CN. Cp
  37. et ECL eundem erunt triangula
  38. CLH CKF, etX et E similia, eritque
  39. Fh: Et: CF: CE. Ergo fiet:
  40. P. CF. NP. CE:: CF: CE
  41. CN
  42. TP. CHA CT Ergo TP: CT:: NP: CN vel PT: PN:: CT: CN
  43. quod sine calculo praescire poluissem ex noto thcoremate
  44. constat quod bisecto angulo segmenta lateris angulo oppositi, sint
  45. lateribus adjacentibus proportionalia. Est autem angulus
  46. TCN, bisectus recta CP ergo erit pY: pN:: CT: eN. Est autem
  47. PF Denaequ. AP- AF seu X+ p - Z + +, et PN ego A A seu h+A- X -p
  48. quaeratur BP, p. FG + N A n. Ar . FIatM. . . ...
  49. +F TG: GF :: TB: BC, seu t: v:: x- Z+ t: y.
  50. NH : HE:: NB: BC, seu n: C:: n + h - x: y
  51. opus doneoccurrant alei in R et S
  52. est EL
  53. C7
  54. seu et est detap, et EN ost 9. p pepto esse a t apo f. A Epu eps ad id quad jam cum constat tempe dh. dv.. Z. L. v.
  55. e

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 7v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0014?run=74