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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 103r, page id 00068196:0203
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Liners.
 curvis angenlibus positione datis, intre data est  curva concursu tan
gentium fotmata. Sed si endem curva quaeratur ex proprietate suam angentim
non apparet eam haberi. Quin non videtur esse determinata Astimamus exemplum,
sit ce parabola, AB, X, BC, 9. _ A7, +, TE VRBCHabetur, 2aX = yy  t = x
V  rax At + rat, AB = Ly b = :y s g 2B Ergo fet ex aequ. c
pr 2 et 3 fiit 2at= 4bD. Ponamus ergo dari aequationem 4caeteras non
haberi, quia TB producta est tangens fiet by ctX + = FB - x D
t: b = ++X, :y t: D = lx: du ops 5gqu. 4,5, 6 tollantur 4  + et D
fiet (a). B -B. a) L A, iis  2Dy = 2bb + ax
rursus (21. a) = lX idus Eeq 1bD o seu 2Ddu  adx seu D- alx. 2dy Unde
ej eq. 7fc adx  ay lx. dy) = aa (dx dx idydus) t aX p 24y dxdus padax fus d ydlus
seu dxx - 2y7 + 4g = gy v, seu ed  = (gy - ax) +y
- 2d 28B: a =. f: b = 26: a = 286 + aX, : ya _ d 2A: a = dx: ly.
dydu
Ergo _ D = adx: 2dy fiet B quo valore substitato in 2DD +aX,: y Z dx: dus
fiet 2aa dxdx: 4dydy + ax, : y = dx: dy, seu a dxdx + 2Xdydus = 2 dx dy
seu dxdx  - 2y dx
dydu
et fit dx =
ly
+ 4y = - 2X + YZ = yy - 2aX
aa
aa
aa
a dy
y + Ngy - 2ax) quae aequatio feliciter dividi patest in duas
coincidentes yy -24x = 0 e fy a
et et ex posteriore fit adx = ydu et ax =. L yy seu 2aX - qu
sed quia quia talem  consensum invenire, magis fortunae est quam artis
Caterum saem considerandum est aequationem hanc ex = y + iyy - 2 ax)
esse generaliorem, at casum quo datu velatio inter A et F esse specialem certe inter
summand summantes adx = ydus potuissemus facere aX  = L yy + ab
nisi alia jam assumsissemus rgy -2 ax∞0
Certe curvam quaesitam per
puncta desebenda Polygonum appropinquans describendo, etsi
non incidamus in puncta vera, patet curvavi 
a quaesita quantillum vis diferentem posse describi per punctum
semper aequationes hbentur T: b = ++X,:y et t: D = ax: dus
habentur
datum
fis adrentu  si pun t: a ; B: a = 0 vel y: a; X: a; dy: dx = o. Et
quidem exd aeq. 3. accedentibus 1 et 2, semper haberi potest aeq. 9. sed
sed non ex data aeq. 4 potest habem aequatio 3.
sit aequ. 4) du: x  y: a; N: a CeB fiet y: a; X: a = x t: t
ope hujus aequationis et aeq. I. tollatur y, si jam simul posset evanescere X, habereta
desideratum. a yF F pro - 9 (7) sit XX + yy3 : aa ty: dx fiet
XX + yy,: aa = +: B, r jam y - BY + Dx,: t = aa t 
rursus XX B + gy B = aat et gy = actt: 6) = X et y = ((aatB + BBX): b = Dt+ BX, :t
seu aa aatBF BDHXX = b4H + 2B2 tX + D XX tia si lacet
fregere relationem inter si _ evamaset tollendo res fuisset in potestate