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# Title: Leibniz-Handschriften zur Mathematik LH 35, 7, 6
# Folio 5v, page id 00068078:0010
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EGZ =GH OIp. H ( + G0. GH, : quG H - qu. CP
Habenius,
 lam duarum AZ, seu insius HZ et ipsius (Z) Concursus
sit  ex E agatur in Ad pormalis AC ∞V
Z0 t ∞, eet ZV sit v, et v=
etfiet sit x et fiet Z.  F O H( + G0. GH, = (qu G H - qu OY) E: V
e
et qua Z eto communes utrique puncto H, et Z, fiet
OpdHW  F KIP+OI = G0dGH f GH dG0 = 5 :V, 2GHdGH = 20 1p do1
G GH =   OGX sit Z, fiet Gdt = rY ZE
GHAGC + GOdGH = _ GHdque + qque dz: GH = GH qu + ZZ, de: G H =  qu. OH: GH
GH = 1 (rr - Z2 dGH = - CZ d Z: Cg H,
GH =y fiat e dGD. GH =  rraZ:y
y = fErR - X5) du - 2F = 2X, dxe = r - X dx Z - 1 X, 17 - . 4
Xdy = rX - XX dy: y 2y ydx.
Xdy + y dX = rX - XX + yy, dx, : y = E YX - 2XX, dx : y
-rdy = - YY + YX, dx: y X Ergo A (yY - ry) - eXx
+29dy = 2r 2X, +X
quia dupla nec trianguli H0Z = GH in 9Z = C 1 in HZ
 (29y -- rr: 
d yZ - y dz - 5 dys
fiet. YY dy :Z
ry +7Z + 27
Ergo 2 d CH)
Est autem
tur
e oiit
Z0 et
eusen
+ 1
V ad C. Ergo O+  est rv: C Et HIp = H(HO. HO . - Bp. 01) = 1
fiet H ep = v fCC - rr). r Caompendo HIp = vt.r
et fiit Ex HV = Frrcc Y S(Cc - vV): C Ergo fiet
Cn(ErX -XY) 9Z =Y rv L (CC- v1) + ar v 1(0Z0Z - rrvn)
vel ccy 0Z 267 rVI +er V H(CC 020Z - rrvv)
Ex punctoqus   concursu ipsarum HZ ordinatim datarum
LXX -
dx =ydus :  r X) = 2y7
agatur in diametium Ad, si opusproductam normals Z
a ico Y, -x +0Z. Se 5uau rus Cum autem et
rridus
et rydz22d
des Eugo 2 d. (12).
b2
yt 2) (d3F au  et aly). ydy +zclys
ol y2) = ayaq + 2dus et dy   = 2ry dy 22 aevra
unde ex aqu. si fiet.
cc yx-cegr +cegisa: c0)=rrtii
= Yv, vlb+ICCez Z+ Ccgy  a - 2CCy Z b - r r vV)
 di = (r. )
do: du
dY(cckEL...) 
fiet co: ∞7  HGH: GZ. seu  co,   y:, 1 - x L OZ r + as: Co) - - Z  co)
et vocentur ZV,  ; et VE vocetur 
sumtis punctis  H et Z H,et (H); item Z et (Z,
 +2
Cr go
d
4y. Vr
agrs
deoip) = d.
Adx +Xdy sd   Xdx.) yydlx ds
hydX = Xrax - XXC(X, - y
lementanter diversis manet punctum , ideaque et etiam inter differentiandum uraer xrux
nobu
y2
) Z dy= ydy. Z yd Z - Z dy = gncus 2
gy +Z
qu(
 Op. 04) e Hinc GH. DZ = oV. Is1 + p  (020Z- 0y. C)
fiet GH. OZ = OV in HW + 0Y in 2Z.
manent V et co, tn et fiit 5 dy:c0 = - dy + d. Oq seu daZ = v dy.  + dx
dip = -, v dv: cV. Et differentiata aequatione N, fiet vec OZ doZ- A, vrrvar ==CC is: c0) dy + cc ydx
seu fuit sC :Co) s + CC  dx + CCCV: Co) ydy N(C. C)d + Yd (Ccjeo c ccodgy +Cc gutr . X) - 2cc (as. c.) y (x a) = 1 VV)
enis doz + CC0Zdy  Ydv t, dv N(cC 3703 - rr vi)
rVB
(CZ
rer. C)aotrd Ccu DZ rrY ErCEVEZ dx + nc.OZ dysov. c) Er er vdo= 2cc a. c) dys tcc yd
10702- rrvi
soad
oiro
ccZr
= Ce gay .c0) cCyBZ + Ceydx Ccy CZ + P’ex ccy OZ ACcyd 2y (a. co) rr YX - ccydx rNVP , V u ro
seus
ilqueiffererhata aequ. B, fiet cerdu (ayy- 1r) + 2 ccydus  = rffir a et 1rcC dv F rdv, A(cC2) +...
v
fiet Ce du (2yy wr) 4 2cc a y  - rr cedr,
in
CeyX -recy + C  yy - rrni,: rb
(cZ
sc
ed
r0
LCccZ2+.. ) = co Scey tcer. pu nuiv. 1
cGy - 2Cc yZ rrum
12cc (ve
iu
Errvdo
e (cez