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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 321v, page id 00067993:0644
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Resectarum. Aperbolae ex diainetro Congugatas
Inveninus aequationem alsissarum esse hanc: posita Resecta , . absista Hyperbolae X. latere
recto b, Resecta autem posita mo:
Xb + X x= f- b. Ergo f 11
vera d haec sedmntunt locuu 
6+1Z m = ab 2
A x) xteexb = bf - b
siet vi +s M2b = 4p6- 26... 
Xb 4b) fiet: mb + 4m Z = 4b
et habebimus: m  = 4b2 + 4bX vel m
in vel m  A-
Et ponendo 2y+ b = W,
ax  a abx
A eritque m 4b2
ets mnb
ab- 4m
et si tam omnium M Quam omnium Z
centrum gravitatis haberi potes, habebitur cantrm
 x prudieundidit. sed detts ncoper intart quadiatu alscister atio quaidinco aucta
aequaton si  sit Xa, Sa = _y X + Y a X.
cop Pa -yX  = ax. Ergo  = aX. Ergo Z
jam Z a 2 = 1- 
Ergusx xb
gravitalis figurae momentum ejque figurae ab
si ex a ax + x pb. cador a - 7 - 2 facias ax, fient non applicata
et cuis ductis imnibus in n, fiet a d= y.
Ergo ad summam omnium s habendam ops est cylindio, hypebotae
par a
applicale hyperbola vel siltem Vaapplicata hyperbolae
est  Ergo aromentam figurae Aet
ex quadentua prypebolaer
AECd, ex axe AB pendet
At ductis omnibus  . habetur mdimetum
omnium X.  ex eodem axe +AD, seu momentum figurae AECB. ex axe AD. er coplementi
adea figurae AECd. ergo Tumma rectansulorum Xx. etiam ex quadratura hyperbolae
a b  alu  
et a x =, 6Z + yX dilrX
fiet : Vy X = 2byX+7X - a
sive b + 2Y X -267X  a.
ax   a ax. s a x. f.
td s  = a5 5
as jam yx ya - ax fie yr- ya -
rra. Ergo si qua sit
on Jam cum sit X= Za aerit XY = 3
5+al X7+ xya Ergo si
asigum, cujusaequatio ay-
+a v2.
qua sit figura hujus aequationis.
un a snfier: Ya -y7 - af
Earo. p
Far = X, vel Y = YX + a.X
en pendet ex quadraturm Hyperbolae cum hoc nostia initro positao
isa y
de a+y.
a +2 pendedt ex quadtratum circuli.
Y A- X. sed ut ad promam aequationem X’a = 7x + ax redeamus
his ita positis ducto y in a - x, fiet _ - yX - A Et quia y= sax
hoc ducto in a- X, vel ami s a + X - 2ax fiet   = s aX , a - X, a - x
Sive ay- yx = sa x = ax mtum quorim sumqa erit mo-
mentum signrae AECd. ex basi C D. cuis sumtum ende pendetus ex
muma Mamum f. ut mox dic interim figura huic summ
 rectangulocum progressioni homogenea, est 1ax - dX = H. sive eju
aequatio: sax - ax = Ya et aX - ax = y a hom sive aX - X = y
unde putet ipsum circulum esse figuram homogeneam momento hujus figurae ex basi-
 AECd, ex basi CD.
ud Sed ut ad primam aequationem y a = Yx + aX initro propositam, redeamus
ameisa ndacum hoc modo sit sa = X. erit 3 a.
tartuae
= X. quae proinde quadratem
ab X. summa a momento fignia AE cd. ex cytindio si Rectantuli AC
ablata relinquit momentum fegura AECd, ex busi, sum o summae sinuum homoge
emus. Calerum ut his X- figuram quaeramus hoprogeneam ponendum est:
arara
= X. (= 1 - at + 2G
taetyat) hta= xtat Ex aY _
AmX + m. b + 4mXb
+ ub X
no 
er i ex imndo   12
M ni
si ba = 1 x =  bexbi ergu  nX erit Xbb f no xb. + +7.
n +4Z,
Sip
habesstur.
unde reperta jam alia gelhodo
exhibendi fignem rationalem
homogeneo cinulo
pnotem per resectas
perius puspate nemdenam