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# Title: LBr. 437 · Huygens
# Folio 97v, page id DE-611-HS-3595205:0200
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-3595205&page=200
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e
Nolanonet
captea.
signom
Tractoria
sit filum AK, cui annexum ponduslk. sit AK affixum regulae
AT. et applicanda ei manu, cum pars fili AT applicata erit ad
regulam, reliqua TC erit tangens curvae cC applica tractionenter
F= ydx: dys et
applicandum descriptae, quaenitur curva cc
X BC, y AH seu AT+ TC =a 
AT = X + ydx: du TC = _ sax +ay: du. ergo fiet =B.
sit X - a = Z C et dx = de
AB
+ ydx: dy + y saxtd: du = a
7 +ydz. dy +y dx +y . dy. fiet: ZZ + 2Zyz. dyf yy z: dyt
gy +Z: dy) + yyale fiet ay. 4 = dz: dy = - , Z:  + L y. Z
2
V
quy + (3 = = 1s
es
il
jam
l
2Zdy + 2ZY dZ = yydy seu L
Si y=o occurret curva axi in BV. et firt y =0 ergo b = 0 itaque
d
7yd =  y s seu 32 = = 377 = 9y Ergu y = Z73 sed hoc est
seu
idetur enor oriri a signis. Nam quia crescentibus
impossibele, ut linea CC sit recta
ost 2dp
uel x decrescunt y; videndum an non scribendum sit ideo non licet facere
s
yyu = 1y dus + 22yd7. sit enim ZZy Clee
gyy +  (
(y) =
nam
77+ 23dZ + 43, y - dy = L
r21
7Z y) + 28y d7 - 22 dy (- ZZy)
Hoc ergo exemplum
A
Alterum oportebat, vel initio pro
l
Ls
qu
du scribere- dy. vel si voluimus et considerare, ut quantitatem
summe notandum.
osolatam)oportuit ejus quantitatem considerare in differentiant
Redesimus ad aeq. dZ: du = FBY - 2. sit y.qa ora setu
b: y = v: a fiet dz: dy = a : 2V - b:3a Ergo dy: Y = duta
e
dv: a: afEx. - v: 2a = v: a (nam sit, Z: y = V sit Y du: y + Zdy: yy = d0
Et
seu dZ: dy) + v_: y = dv: dy seu _1: 2 = v: 2 Fv: y = av: dy.
1
  duidus Ergo dy: y = dv: 4: 20 +v.2a: a
 s du. y = seu dy: as = 2 + AV: aa + vo. itaque haec curva
ergo
paveniri ex suppossita hyperbolae quadratura
P.
AB, (X BC, y AE, a  EC b san constans AFZ; EFV
ZZ+ vV =aa
BF seu CG =  X- Z EG=   x + 27 - 2XZ + v0 + yy - 20y = aa bb
13
u seu IXX +gu = 2XZ - 2∞y + ad = bb, si a = b fiet XX+ yy = 2XZ- 2V9 =0
a
sit porro. dy: dx :: - V:X - Z fit dyx - dyZ = vdx = ydx fiet
 = Ed X = vdxidu +ydxidus = EN X. f y9. 2X. - vy: X. Ergo
et
it
lat
d
 y: 2 - yy. 2X +ydx. dus. dx: due - g. . Ergo At
pqu Xdx: 2dy _ f. 2D (+ydx: 2 hyy3. 2∞-yfy.9
dx : dy = H. X 
ne
RXy seu Z = KX dx = gy dx - 2Xydy3 :, 2Xdy - Z y dy un
3 29
dx ( yydX: X Ey
v = XXdy -yydy +2Xydx 1: ,2∞ dx= 2ydy. Restat Z+ e= aa
ita habetur li aea, sed panto protigur. Nempe
Ammnuneue
31
e
+-
2
e
1 2 X.
e
E
+
1b
2
et
ee sit
XH
tu tit
egayau
rxerius