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# Title: LBr. 437 · Huygens
# Folio 106r, page id DE-611-HS-3595205:0217
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-3595205&page=217
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Ad
Epistolam Hugenus. 23Fcbp. 169)
 sit, jam
C
1
 yyaa-XX: aX
Ex 1 et 2. Ce fiet dx: dy = y Vaa -XX: ax
ec
jam a 0=
C
C
ydx:  dy
quaeritur curva
O, d0 sit C= 1: 2 fiet dC) = = 1: 2 C
Ergo fiet Cexe anm
Ergo tanem ex 4 et c fit. a d vaa - xx = dy y.
c
rentialus aequatio est vdus
P.2
dC
ergu
uras
lonap
ex 1.7
uod si faciamus b=a fiet
a
s
s
otsen bbarna- xX = Ryy. 2
a aaxX cujus diffe-
14
y u. (a)- aagu +y: 4 = (as- aaxY ubi
15
.24a quam og. conferendo cum aeq. 3. fiel
at
1e)
est aeq. 1 14, adesque haec salis facit. Gmeraliter 4(+
vat bb = 2aaL et
qua
3a-
aa
fiet 164
es
aagu +y =
Gld7Z +4 y =  aelp
ag
aca Xx + axx = a
Si jam sit
Vaa = XX  2aa - gy. Ergo (4a 4aaxx = (qad4 aagu + i
qu
c
ax
AaX, quam
aquationem jungendo ipsi aeq. 3. fiet araa - XX = = Dyg: 2 unde redit aeq. 9.
3)
a
quaerendo differentialem prodibit 13do - 2409du  - 2aaxdx. H un
sit
X dx: Yaa-XX
quo
9.4
a
= 2aa Xdx, et Ax: du C- pa
12
L= a d Vaa -XX = ax dx: laa -XX
seu bb - (9y. = a Vaa = XX. Si faciamus b= 0 fiet 
araa- XX dvaa. X)
et dxax: Taa - XX = dy y
2
A aa = XX) fiet d Yaa - Xx (= 1: 2: Vaa - XX . = 2x dx
en
et d0 = = 2X dx s
et
e
t
a
4aaXX.
a aaXX
seri
ficC