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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 425r

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: 0.77.

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. 426v); this page is its right half.

The machine reads it as

  1. CA usum
  2. anta
  3. FA qu= f. L qu. jam l Lqu
  4. CX, x. XTy CB - db y = bb: X
  5. dy = -bb dx: XX Y(d Xdx + dylus) = dx SCx + b+): XX
  6. Datur summ SXdx Y(X +b) seu cur AY momentum
  7. ex Hsymplota CE, posito enim exX = BZ fiet 2X dx-
  8. seu Xdx = LbdZ et SXdx SCx L64 = B sdZ ((22+66). b
  9. quae summatio pendet ex quadratura Hyperbolae
  10. Eodem modo datur momentum arcus AY ex asum
  11. ptota CB Est enim D X = bb: y et dx = ubbayu: y
  12. et ( ydy + dxdx) = dy Cyt +64) :yy sit gy = bv
  13. seu ydy - de et t curvae momentum ex CB, seu syduy ( ( + 62) dabit
  14. LbSd) S(ov +bb): V quae misus pendet exquadiatura Hyperbilae
  15. itaque inventa ratione ipsius (aZ S( + bb) ad abs L (OB +bb 3.v ex supposit
  16. hyperbolae quadratura, habetur rc positione recta Csi quae
  17. Ducatur jam Hyplibolae Axis CAW, inquem ex. Y agatur dormalis
  18. sen et qu - 24 t 2 oa ot compleatur rectingulum C Ctr Et CW0 vocetur W, et c8
  19. mursi FL 4u + Ctqua CB qu BE qu
  20. saocetur D. ipsa 8Y secet ex in H. C8 = GH XY = HX CH (9Y2
  21. et su eA + CD4KBtq
  22. 3B qli , BF quam 2BA. bt etsit
  23. et sed hoc hoco BA= CB
  24. etsia Cqu + DCt 2BA. BE.
  25. aaquet pt Aeotm oAv
  26. qunesiqu AeAt quBqu
  27. HY = XYI2 CX = C912 + XY
  28. X Y : CG CX XY 2
  29. en D CW C:, CX XY seu fret
  30. :C8 - CW -C8, CfZ XF = XYF2 = (W = CG. seu
  31. Au. BF. q
  32. AV. Cx - C1- ():, i2 Ergo CX = (72 + C. W (1. 12) - C9 (1. 12) jam est
  33. est antem CxBA = CA. (2
  34. seu H = W - G, in 2 et X = c + CW. 8 + Wd, : 12
  35. et esigu i BCtEgo x bb (= X9) = _ W1 = 89. : 2. seu A 2bb +.
  36. siet CA+ ABs CL
  37. otiract
  38. ct CAa B CA BF
  39. r sit 2bb = aa = quadrato BE et fiet _∞ L aa = WoW. jam fd = dn
  40. aqu. F2CBBF(2 + + BEqu. + Gfiet d = - W dW: P et des dc + do du = W diodu, Wd t 8G,:,
  41. iodu _; doW + o 54,: 9 du dwo, WoWd aa WoWo
  42. + qFCqu ( 4BCqu+ 1BF)
  43. et fitt
  44. codd, 1 + son:99) duare, Aa
  45. it ergo seudi - - dys g.: d (d W dW = dGd es = dedes, 1 + (89: 110) = de dis 1010 + 9.: cas
  46. CA. B( Y2+ 2BFqu
  47. IE: L
  48. seu denique e d9 d d∞, 288+ aa :, P + aa, vel (dode + duo d 10)=
  49. seu n = CAXBFs2
  50. CAt BFA
  51. momente
  52. H de Y(aa t 289,: aa +95). Et etenrentum curvae AY ex
  53. xe AW, erit ( de + (aa =+ 288, : aa +8). sit 88 = a V)
  54. n Bet = 3. BC+ O: et cd = L a diV et saet Elementum curvas AY momenta ex Axe AW
  55. est autem BC - CB. ∞ :C
  56. averia
  57. ecBC C
  58. BFs = D. CA: 0. ciri erit L a f dip VCa a + 2a, :, aa + a2) quod ex quadraturo senica
  59. sed BCs2 = CA. ergo fit
  60. Rursus al quia 52en haberi potest. Quaeratur rursus, momentum curvae AY ex ax e
  61. denique n - O-
  62. ne A verticem curvae ducatur ngt Conjugato CH
  63. retento de tolatur d relento tollatur G, et ex de dis + duvato
  64. fiet et du du c. + (Wol:8) du du, 88 ui: 8 seu fiert
  65. ce diodus, ac +290 eut dudu, 1 + ols 4 (ion: 98) X
  66. (C ) = dudio, 8G + WW, : 4 = duodi, Wt- ia t WW,: Wwu-na, seu denique
  67. Elementi curvae est duo, s(2c1 = da i oW = aa) et momentum Carvae A)
  68. 50+5) = 9(0 D)) ex une Conjugnto a, ent sudWo t(ruto -aaq:, vn - aa) sit Wo1 =aa
  69. esse quantitates fiet Wdi = =a dβ et habemus Momentum curvae AY ex ae conjugato CE,
  70. AP hyperbolae aequilatera
  71. ipla atta producta transit per Gcentrum gravitatis curvae AY
  72. tucta .L
  73. =2Cst qu + a BF qui
  74. seu FL = C1
  75. FL: et
  76. eo in Hyperbutia
  77. n putosu ducatur et per lentrum C, apis conjugatas, C angulo ad CE semirecto
  78. equale Za ( aβ 1 (23- a, i, B- a) quod pendet ex quad aura Hyplitio (onica
  79. Dacatu AF tangens Hyperbolan in vertice A, ert monentum curvae AY ex
  80. C, tagente verticis = La (d β+ (2β- a3: , B- a)
  81. Ad Cora AY suct. rectam (A duct.
  82. eid (CB. BF CBi sideque ((bba ZI): Z), in S(dv ACbbave) V) EtG f i ste
  83. sdide at trari parate),
  84. ao AY - 5: Q sit cno
  85. Stpi 6. q Dubi, 917 o i neidiem tris p mi 426
  86. psumbus
  87. hoc loco, quid
  88. rattimo eva
  89. rectus cuvani si ponit,
  90. Ct_ CA+BFVZ,:
  91. FL = CA -BFSC,: 2
  92. CQ eet M
  93. FL2CF = l. eZ
  94. BA A i 2a )50
  95. BF C
  96. Rat saaes
  97. tic
  98. CF = 1Bq +BFqu
  99. L= teAqu
  100. Sxdxtuxne et QA = n B: 5 et GA - M-
  101. seu m - a. siet M= a F. n
  102. ergo denique fiet
  103. = 82, a8+nE
  104. vel nS. O+D = nO-
  105. sd
  106. ia fine huius pa
  107. sa
  108. su cu
  109. situs
  110. a explicatus
  111. Arexax t
  112. pts ivedam per
  113. 5eCO
  114. uo cion et b2. 4
  115. D Xt Sid s ma

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 425r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0845?run=74