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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 54r

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.

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. 53v); this page is its right half.

The machine reads it as

  1. in curocilliptica, habemus perpendicalarem aream momentm tam exaxe conpagato
  2. primarum AC, quam ex axc conjugato tCB, ita positione datur recta per C et G
  3. posito C esse centrum grav curvae, sed patet ham nunquam posse langere curram
  4. centiorum
  5. Esto Hyperbolae centrum C, versex V, axis CVL, ordinata, normalis LM
  6. vn
  7. Assumatur diam eter ali CN P per V dacatur parlela ipsi LM, diametro
  8. occurrens in N et cum dala sit Cr assumtu re determinabit diametrum.
  9. jam producaturL M dum diametro occurrat in P, et ex M
  10. agatur My normalis ad CN. ob triangula CVN, et CL
  11. similia sit LP: et = YN. CV, et LP = et. VN. CV, rugus
  12. obtritnguls cD et map similia, fit Mp: G MG = mp. CV. CN
  13. mo-+ (Am La MQ ALF(Y) LM, CV: CN = et ( FCL. vN)Im. 1 C
  14. a et P = ON C+ CL. CN: CY et yP
  15. et QP = Mp. C: VN et fit t jam CQ = X p - ZB, fiet CZ = EL VN. CN - Mp. CN. PV
  16. CV. VN
  17. crar po
  18. LV. ter e
  19. tet Cq = CLx a. CN. Vi AB) YN. C1. ex () LM. CY, CH,: ev
  20. similia nt triangula CYN, et B, MQP., quaeruntur CZ et qM ex CL et M
  21. Sit Hyperbola V. L, vertice Y, centroC, axis rectus CHitrnus versus CM per V, trans-
  22. versus CN, pu coordinatae ad hosaxes LM, LN Ducantur alia binae diametri
  23. quaeritur
  24. inter se normales Cp et CQ occurrentes tangenti verticis V, in tGG et F
  25. LP 1 LQ, ex LM, LN F ipsa cor et ad has coordiratae hormales LP, LZ
  26. quaeruntur hae ex LM LN. priores coodinatae secent novos axes, nempe LM
  27. ipsam c in Z, et CF in si et LN ipsam in T, B CF, et CF in W
  28. iem d tot= HF jam loq -Wot CV. C AL CM et et N CH Eit simolite
  29. Wg.g L = CV. Y Wg = ZL. CV: VF. aD = ML. CF: FV
  30. TB PL FY 2HC RA RP = PL. CV: VF CR = NL. CF: FV
  31. jam CW + Wq = PL = 3L. CY + ML CF et CR - PR = NL. cF = PL. CY 1 2L
  32. ML et NL, nam foet
  33. ope harum duarum aequationum
  34. PL = ML + AL C PL. C
  35. M. Cr. (V + NL. CKFL, : (t V eY
  36. et 2FV haberi potest PL et QL, pe
  37. Ct. seu et=M
  38. Ht. Fs EV
  39. (FV FVFCV. CV =) FC. FC, : FLLFV
  40. et _g - at PL = ML. CF + HL. CF. CV = PL. CV. CY. crgo B = ML CF. FV+ N1. CF Cv v
  41. seu PL = ML FV, AI CY B B = 17 + Nu N ( Ego (FV. FY + CV. CH) PL M. cerN
  42. CE RREYEY
  43. FV. FV
  44. seu E. CF (CD = ML (CF EV + NL (CD CV. seu PL =
  45. Et 2L = NL. 1 = 2t 2 ML
  46. D + M2. Cx - np a ve
  47. Ergo (EV. FV + CY CY) GL = NE (CD) FV- M L (D CY
  48. et Fit 9L = NL. F = ML . CV = Lβ - Nd
  49. perbordinatas LM, LN
  50. sit punctum L, relatum ad Condirectrices normales CM, CN,
  51. et rursus relatum ad Condalias condirectrices normales eque pri eodem
  52. vesdinatas
  53. NF0
  54. C p,C9
  55. Generaliter
  56. is conddirerium per N agatur parallela ipsi CQ. ipsis CP, LZ, productis si opuis, occurrenso
  57. quo priones puncto concurren
  58. in punctis R et S. ita habebimus Lp et LQ per LM et LN.. Nam est
  59. it data in CM datar
  60. = SNERA NNF NS+NR et Lq = LS = CR. Cumque trianus ila L5N, NRC sut somilia
  61. Tlangulo FVC
  62. id est LP = LN. EY + LM. EV et Lg = H LN. EY - CM C
  63. Si XL et XM. rad
  64. normalem
  65. porro ut CN est extra, con intra alterns condiretrices; ita Cp est extra, Cq intra. Et ut duximus VF uni directri-
  66. GreotasL
  67. peminia
  68. Cium lateriorum CM, oecurrentem alteri cq; ita possumus diaere CG normalem uni ipsicq occurrentem ipsi CM,
  69. et LM = Lp. FY - LG ci
  70. ut per i dox imus paratelam ipsi _B, interceptam inter ep et tq ictaper ducamus patalletam ipsi C M, inde
  71. et fiet
  72. LN = LP. CV + Lg FV
  73. ita per P ducamus parallelam ipsi cm, interceptam nter NN et LM
  74. et LM = L -
  75. fietque LN = WP. _ + CP
  76. Sit jam L punctum curve Conicae cujuscentrum axis directus seu per verticem, M, conjugatus CN, si esset VM, X. olats rectum ,
  77. transversum 9, foret, gy = 2rX + YxX = 4, XX + 2gx +99 - 4q = F 7 -99 = FqZ - rq = gy, et fiet
  78. ydu = XZdque. et dydy = Zd7 3, XZ2- 1 = v d 7dZ ZZ-4qB et a bementum Curvae conicae seu
  79. +Caxdx + dydy) erit L (a ZaZ 22 49 + 722: , ZZ 49) seu dz (6+2) 23-99: 72 94), huius
  80. ut ex alio ffim
  81. eoctum Eementum napu
  82. nilio
  83. Ducatur faxdx + dydys) in L
  84. teducitur ad quadraturas ratiorales
  85. seu in L-VM, sed utrsue modo res rede
  86. Qm +yH. Aliud et P
  87. si quae ramus momentum curva conicae ex axe ep, seu elementum ejus
  88. ta po curva Hperbolica, sed certo tantum nigarcu
  89. itatis
  90. et caut iatra cepujus
  91. Eagretitunum aete s au posia i ut aieo sepius
  92. enic

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 54r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0107?run=74