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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 19r, page id 00068198:0037
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vita
sed hinc patet ihil nos luga lucrari nam hic res Ardem cedit ad
quadratum.
In quiramus in, talia problemata lungentim
inversa, nubi datae sunt lineae concurrentes verb. gi
Circuli ut si ex datis AP, detur (C, linvenire lineam
Ein ciculi secantes sunt positione dati
dyox  y: BB. BP- Ap.   A sit  AP, p. e
su
BP px Ergo dus epx dus. dx = y. p X Ergo fit dypodyx = ydx
y.  po x3  gosit 4qugu = pp + XX - 2pX. Ergo ex 1 et 2. fier
dy: dx - g. 199- gy p a +
sit AB, X; BCy AP( p. PC, q. fiet
(2).
dy: dx = y: 149- yy et yy + pp -2pX + XX = 99
diferentinle determina derique q) Nem exemplo tentemus sit  et fiet
sit p= 4 + _h fiet yy (+ 44)+ 2gh +hh - 2g4 - 2hX + XX = 99)
et h= x X et qua xx ht au et q = yy + hh + Xx - 2hx, :, 2X. 2h
dy: dx = yg:, p - x = y: , 4th- x = y 29 gy +hh + XX - 2hX + 2hik 4 2XX - a hX: 27 . 1
seu dy: dx = 2Xy - 2hy, :, yy + 3hh + 39y  -6hX
dy : dx = y:  pu X
yy + pp- 2px + XX = 99
siiie 
p qun siet ujus (+ 4 + 2gh a hih = 2 X - 2h X +X X  (99)
non a
Ergo 9= y9+xx + fh - 2hX,:, 2X - 2h
1a
et p. X = yy (+∞ X +hh) - 2hX + r2 Xh - (2 ih LM-x + 2Xh:, exo
Ergo dy: dx = ek 2g. x -h: yy x sit X- h = Z
fiet dy: dq = 29Z:, yy - 2Z quae solvi po. proinde.
rata indinavia si esset   qq a, 49 = pp + pa. Ex 2 fieret.
 aun
yf (p  pX + X x = (x p) + (p b seu p. = XX ∞ : b - 2
ne
et p - x = gu (XX) - le X + DXX,: b - 2X Ergo
to per 1 fit dy: dx = b = 2X y,:, qu + 3XX _ - bX
lem ex aeq.7 vel calculi prioris, vel ex aeg. b. hujus
cognosci posse quod queat solvi, seu et quod non nisi unica
 A, = y + e β HB: X = dy: dx seu HB = xdu: ax
Satis faciat Ap, An
se
(1
yg + A_ = Egy + 29Xdyily + Xxdtu .dx = t
elatio inter het p
e
(6)
a
Ap. p. PH PN
rgo
F3.
Cys
p. X4:y = X:, H - y
AN = y + Xdx: dy = N seu dy A F du: dy Z n - y, : X seu pa - py Xy =y
Sindetur quaecunque relatio inter x + ydyi dx et inter ytdx. du
Salui potest problema pir extensionem cumalum
 a via Z a = tr do:du Hiac ex 5 et 7 addilis
seu ytx p. pr
fiet X + y + ydy: dx + x dX: dy = p + e seu cydy: dx + Xdx: dy = p Arc + PB: p + X
Hinc si aequatio differentialis proposita reduceretur ad homoceptotam
et i in ipsa homoeoptota a omnia reduci possent ad  X+y = co
et ad ytus: x +Xdx: du = W haberetur ejus constructio a per curvarm
exsensionem in rectam a= XFy = X + y + 2Xy. W = X ax. di + y dus: x + xy
102- Co = - + ∞g +  X ex idu + y di dx
Zu untrrcus
min man nuloratus
siormre, dtt dus problemm
tutu. Zn osnns in
evemalus
X = y dx dus
P pay -pdys =ydx
P= yax+ xdy, idy
=9= y  ay+ x: dus
Ergo si aluo relatio
inter p et q solvi
p problem peradinano
et est determinatur
non latis
ista videntur
cohaerere.
qu
Ex quo non l t oumin
alicubi habeat
ationem quae
equitur u
id
ibet curva
tum
noum au unu
cumae
unctum poss
po arbitrio. Assamto punc
d .
alu gia tipu tij d imegbet pionus . B
curre
 acis
B3P. G ay. dx
si X+y et ydyi dy + xde: dys
dentur ex se invicem solvi A. procera
per rectificates.