Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 40r
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: 0.83.
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The machine reads it as
- 4 seu 22 =
- grbb
- sit conicae centricae centrum C vertex A, curda AV. Focus vortici
- proximus F, ordinata ad ab F ad quem FGer Erit FG semilatus
- rectum et AC semilatus transversum. sit AX, X; et CX, Z;
- et XY y et FG a et AC b. fiet 2ax + (a : b) XX - u
- unde ubi tantum observatur, quod b in Hyper
- bola est quantitas effirmativa sed in Ellipsi quantitas negativa
- A X = Z - b, et fiet 2aZ - 2ab + a 2Z - 2 a Z + ab = yy
- seu fit (a: b) 22 - ab = gy . Unde (a: b) ZdZ = ydy seu fiet
- dy: dz = (7. y) (a: b) Et dydys. AZ (22, 9y) (aa : bb) Et dy dy + d2dzue, : dz dz = Z2 (ac. bb) + By,: yy
- Curve
- Eodem
- modo dz: dy = (y: Z) (b: a). Et dedz . dydys = (yy: 27) ab: 4) et dz dze + dydys,: dydus =
- gy (bb: 4d) +22,: 22. 1 r dy du) = d ((b gy +bb seu fiet
- (dydus + d2dZ) = dy (((6b. (+ eb. 1) yy + bb, :, 1b: a) gy +bb)
- secundum priorem fibdq (ZZ BC) - b2C, atb), :, b, ) b., at b)22 - Bato
- Seu de (22 = bb bi arb), ZZ bb): (L2- bb, veb:, at b))
- s
- Et rementum
- Tautum Ergo opus est ut dz 1 (Z2- bbib: arb), 27- bb) seu dq sele
- seu d
- a
- nales simpliciores. pro a, et b substituamus Y et 9, quia a et b aliter
- bb
- mox usurpamus et fiet summandum
- Eudem modo mocetanus cum
- d
- aequatione valore 6.
- 4 (3t - 24 992Z + 9(9. p 4)
- IC riq
- 22- 96, 1(9:, r+4)
- Nempe sit ad (yy +abbi a+b),: (a:, atbdyy tab (, a +b))
- seu du (yy + ab (a:, atb), yy + ab): yy + ab, s(a: at b)
- e et denique mutata a in Y, et b in q, fiet
- G. (3 + .V + pp G (p: Y.1))
- sendemque de
- (dydyt d2 1)=
- ides
- pi
- P yy +, Ver:. r+4)
- in Hyperbola aequilatera se primaria, compendiotor
- posito Y esse latus rectur
- 9 trans versum, et
- D Z y, esse
- coordinatas ad duos
- axes primarios transe
- untes per cenbrum
- Sin Hyperbola autem q esse affirma
- in fillor prodest prodit valbr ad Asymplitum
- xy= a ff 3 = ff ax et dy- de xx tivam, in Ellipsi nogativam
- a suae molis
- et
- et dydy = f+ dxdx: X et
- dydy + dxdx = 5 4 (5+ + X olXdx, : X
- sed sit p ubi oblique CY. E, Y = CY. s Eis Y agatur normalis YX ad Cy
- Sidydus + dedx) = dx (f+, X) eXX
- et sit XV: XE = f. phet fiet X et ZY_. y = f: (V+pp) seu : CC - yfs.
- sed C∞ = _CX + XE = X + yff:f. Et fiat ff:, Xot yp. f = yp. l.. seu dem
- fiet EAp5F+= PX + yt, yp et fit X = fB. _ B 1H rpp - fyy): py
- B
- seu fiet f (x 1 yp, f _fYCG) - fX+py Jy se
- ff (f+ pP) = FXy + pyY, ubi posita p = 0 reditur ad As Xy. sed
- hoc loco fit X = ff YB +pp) - pyy,: Fy, et fit hinc
- ab dx= fxdu +fydx = = 2pyd X seu dX - frdys : (5t 2p) y compindii lausa
- f+ Ep vocetur m, et fpp) rocetur n, erit X = fn- py. fy et erit
- seu dx = - fn +H pyy, dy: 4m7 y
- et
- a
- dx = - afx dy : ny.
- et dxdx =g fmm 2 (pim Gs + (sp. na) y: t
- unct2 2(payY + (pptmM, ina) y,: y
- app.
- et dx Ax tdydys a anpttyy + porin
- :m yy. Vestam)
- ubi pro irrationali compendiose scribendo (y + ab yu + aC), et
- ppenm
- seu xAx + dy dy) 289 (V
- in summando evitabuntur ircationales imaginariae, si sit qac- bb affirma
- tiba 4dc = 4 fh: ppX et aabb = a nn pps:, p + mupp +m, et
- +ac bb erit at pet asann 4nnpest qu Errinu). Ergo debet esse
- petyn maje auc bb erit (esa napp) + 4f4, ( 4 mpp f:, qu Cpp tinn)
- Ss1 PP + S3 tqu
- seu (tac - bb) efsum: ppron + 2ff fstpp.:, f5 + 2 pp
- ateunun (t 4f nupp - 4 nupp s,: qu (pp + MM) adeoque
- VAaC aabb) = +2H ran:, mn + pp serB: (s Astrp) 1sreod.
- 2Hs + Spp F 4Ps
- et 4 ac= aabb erit
- et
Cite
Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 40r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0079?run=74