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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 142r

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: 0.87.

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. 143v); this page is its right half.

The machine reads it as

  1. in circulo sitAR AH a, ABX, BC, y et 2aX - XX -gy
  2. AH sit y, et
  3. in circulo sit AH radius a ordinata nommalis mum seu deametrum _, absussa
  4. abscissa AB sit X, erit vap XX = gy, hoc est re jam rectangulum ABH = quadrato
  5. CBE, et fit ron ra aX - XX = y
  6. sit alias sabe sitli recta in circulontrinque termeta FG, ad quam a perpendiculariter
  7. ducta CE, secans ipsam in L. constat esse c rectamtum FLG aequale rectangulo CLE
  8. sit x
  9. vet LB sit b Dimidia FG sit f
  10. sit FG, B et BL, b et FL Z, et CL, V
  11. FM sit m, pG sit g t Ad FG sit normalis FM, ccur us colculo in M, diamcetro in d.. ja
  12. ADH = FDM = sd et AD- AH - FG, 2 et DH = FG4 AII FBytL AH+ FG, : 2 erigo
  13. ADH = AH aFG: = pD = YM. 4. Ergo A AN. F = FB, on bien FM F FG = AH, quod
  14. et ex figuaa per se patebat dimidia pC sit jam FG214 + PDa
  15. sit FM hormalis ad FG occurrens diametro in D, et circulo in M, cum ergo GM sit
  16. d -y
  17. diameter, patet fore FM + FG = aa sit CL in CL Fd Ct B
  18. A vg FD Z0X AD, et fic L
  19. += y = v+ Fd X = Z+ AD et fiat aZ + a. Ad - ZZ- Z AD. ZAV = v0 + 2Fd. ∞+ Fd
  20. Y+D et sit v et FL sit Z
  21. sed 2FD est FM et a - 2Ad est FG et fiet v ZZ + vV + FM B = FGZ = a Ad - FD = AD
  22. sed Ab A FG,. 2 et Ad si sid a Ad F D ABC sid A a Ad - AD = FD = 0. ergo
  23. fiet ZZ + vV + FM. D - FG.Z = 0 ubi FM FG= AB2
  24. Veniamus ad ordinatas i obliquas ducatur recta crculum secans Nque ai occ in
  25. diametio decurrens in O, et ex N ad diamelium sit noom alis rp. darique ponamus AO, et AP,
  26. quibus mnia determinatur NG. jum NRAsit pt sit T et CR sit cd
  27. jam NRsit H, et CR sit co NF Nq sit n fit N. n - H = co. Cs - W
  28. (s = CR 2N + D2AB RB: Np = H ONFN,: ON sed NP: ex datur et sit Y
  29. fietus RB = ON+F, P et Cs = 2 + v (OXFN) 2p et nA -X N = 2Co + 25ON es t EsEN
  30. seu Hn+ coco + 2∞COH + 25. ON. co = 0
  31. n HI
  32. sed prestat generalius rem definire etsi recta oR sit extralitutum
  33. applicare ad sectionem Conicam in genere
  34. sit sectio conica AC, cujus Axii AB, cui occurrat in H recta
  35. indefinita e, cui angulo dato _AN, occurrat d CR ordina
  36. ta ad ipsam EA ex sectione Conica sit AB, x BC, y.
  37. et semi latus rectum a fit 2ax + ax = gy
  38. qu
  39. ER sit Z et CR sit v
  40. norinalis TA
  41. cupenstati
  42. jam
  43. AEsit C. Ex N ad AE agatum
  44. occurrat ipsi ER in F, et
  45. per agatur paraliosa AE, occurpem ipsi AN in G.
  46. et AB, f et et BC producatur dum
  47. occurrat ipsi CR in A. EB est etx et BH_ = etX, f: C LCCA +y
  48. sit AE, e
  49. CR: CH se CH = C + R, f. C y
  50. C CRa =CH, An: f, adeoque siet
  51. CR - etX H etX. B: C - xy:f CH: e = RH EH seu (C +X) 5. e y
  52. sec et xfe(e X, f. 1) - y i (etX, frC) = EH ER; CH seu y: (ern s. B) = E
  53. BC BH = ER. EH seu (C+X, f. 1. 9 - Z. C
  54. Z: ((C+X) H(sfreC): C
  55. EH (: EB = EF, A seu EH = etQ CFX, se C+ s): C. jam ER. EH = BC: BH
  56. et fit ER seu Z = (e +X, Rec + S): e), y : (et X, f. C) seu _
  57. BH = CH + y sit CH = (etX, f: C) - y et CR = (et X, f: C) =y, n: C = v
  58. Rursus RH = V, NF: f s
  59. sit Et EH = EB. EF; EA= etX, 1 et H): C eritque EK
  60. ER = EH = RH = (e+ X) ABCtH): e = VNF: F = Z
  61. NF = 9 ee+ H):C
  62. NG sit q AGsit g et fiet
  63. GK et EG = C-g et GN = eg, f: e et A N seu An = 99 + e g: C
  64. seu nn= egee +ec ff + ggf 2eg9ff; ee
  65. et x - v9: f, Hec + s): e = Z. Ergo C+ X = ZC: lee+ ) + vg. f = yn: f + ve: f
  66. et A Zef. Aece+ B) - yn, i e-g et y = ZCf. X(cet B) + v (9- C),: n
  67. Geroraliter sit curva quaecunque cC cujus axis ABB sit AB, X BC et recta quocunque ER
  68. et X = ZC: ((ec +H) + vg: f - e
  69. occurrens axi AB in E, ad qu siet ad ondinalae ad axem normales CB, y. ABX ordinatae ad ipsam
  70. AEsut e, AF sit f
  71. titque ER Z et CR, ~
  72. ER obliquae CR

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 142r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0283?run=74