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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 159r, page id 00068195:0317
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sto tigna ABCDA, cujus complementum ad rectangulum. AC, sit AECDA. et aliqua rectangili apomplement.
applicata FD, abscissa AF. posita AF =  Y. et FD = X. esto x natura figniae, ut sit ya- y Xt aX.
fra: at y= a x. Summa omnium X. seu area figurae pendet ex quadia
Tura Circuli et summa omnium Y, semu vel GD, seu momentum figurae ABCDA ex AB
a -X
duplicatum aequtur pendet ex quadratura Hyperbolae ut alili ostendi
ordinatae
at Aque ita omnes HD,  si appellentur
Sidem X = a - a3,, vel a = X = a3
nunc Y, ut, et CH - Z nunc Z. et BH. maneant y, erit Z = 
a7y
summa omnium X pendet ex quadratura circuli ut alibi ostendi
posita B infinitisima a. X + aC - axF aY fiet AX + ae (3 - a x - a (3x - a2X + ax
Subtrahantur a se invicem
duo y progima
a - Xa - Ba - xa + X + XB
a - X
fiet a  = 2C. posita e. intervallo tangentis Ergo a = = 2 ea =  W 2
a + X -2Xa,
=G
2xa
a = X - β
Ergo W0 - a. Eg Ergo Wd. applicata Hyperblae est a v. v  
est
a’ +X- 2xa
qui quadrati potest,
aY2a7 aequatur appellatur quadratis applicata Ordinatarum Hyperbolae ad Rsumptotani di
a + Y~
a = X
r a yet 2a7 4+ a divitatur Y per e, fiet a uX.
7+ b, - Y +b+ 2yb
2aX + 2aX - + a X = GL.
siet
a- aex
a - 2a+ 2p- 4Xa
sed quia GL non ad X sive AG, sed ad Y. sive AF. applicanda est ideo pro X substituatur,
6139 a427a 4 a5
x
ejus valor fit et quia + = ya
a+
GL=
cujus figurae summa pendet ex circuli quadratura
a x.)
44
uaeta
at +2a
seu ex quadraturm frgurae propositae ABCdB
Nunc figurem propsositam ponamus esse Resectarum Hyperbolae, erit aequatio ejus
4Ya 4X Y + a2- 4aY = 0. ut alibi ostendimus ergo Xa
4X ta2
a- 4a y = 4Xy. Ergo y = a
et 4Xy = 4a7 = a. Ey
4 +  7
4aY + 4+ siel. 242 7, vel
+V
16y
4 
quaeralisunt X= X Luorum X. poximorum fiet 4ay +4ab +6 aby- a
intercalentanti sine ayt lall i  4y at iha ytab aeu B aeb + ay a 1 86 a 18y bat) 7
fiet 
s 3
a
4y + 4b + 8yb
A16y+ 16b, + Ayb
quos ingreditur b aut  ya a16 hcujus figurae quadratura rursus ex quadratura tam Hyperbola quam
2y4
hyper bolvcidtis a pendet hoc lono vero aova ratione habetur,
eatqnita duplicem habemus typertola  Altrago in smum;
1= yea
s atata
dmilti possunt termino
quos non ingreditur b.
ilem quos et plenique
altior potestas.
uno iutia ut exdaslis
sequentibus tatet ingredi seu 
ad altrur b. potestos.
sunceristatiu ab imitio
intret: Mabijiriend esunt potistales
en mum qua prrtertirs