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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folio 123r, page id 00068124:0247
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068124&page=247
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quoq quoyqe
imitiles ne douvent pas estre moins
estimées par cequ’elles sont des aaccest des exeples de l’ait d’inventerj donnent quelque
les inventions
belle et ingeniense,
heplematu
Ouadraturae peooreminai tetragonstita
nonnelle veule pour pousser plus’avant cet art. a
gocto
er
teneratia ex tatigentibus
A centrum Hyperbolae AC. abscissae ex Asymploto CBordinata
BD langens occunens alteri Asyriptolo in D. AD sit BCE recta
ita ut CE HAD. idque ubixis factum intelligatur. Curva FGH
transire intelligetur, per illa puncta quae etro,  cui etio
DA et AC protuctor Asimmplosiciunt) Sputium e respondens
Eit exempli gratia spatium mixhilineum ECLGE, aequale
trilined AABH BAHB. ut exatibi Creoremate meo generali
gstat. Jam quaeramus calculo AD vel CE. ducta DBM, erio AC M
aa
AD,2CB. sit ACGX. erit CB+ = et EC
X
Hinc demonstratuur illud sant pulcherrimum quod sector Hyperbolicus ABH, equetur duplicatus
aequetur ipsi ECLGE, id est duplo BAHB, id est quod sector Hyperbolicus aequetur portioni respon
denti adi ymptoloque. Ducatur Axis APg. vertex g. axis transversus ARS. sit DR.
adem nonnalis, ob angulum RAD semirectom erit AB
AR HRB
A.
1 S7
qurbolae
2a
X
PL
4a
2
 AM 2X
AR + ROV
 et RD AR, et AR +412 Eode modo ST, plrgendicularis
AD + DT. ergo SY (2a + DT. jam 5+
∞ ad a. ergo 5+
et
quadrilinem
dupla AC F sive AC CM. ex natura Hyperbolia aquilaterae
ergo
2
et Asp n
a
ad A
)
se 24X+2 quae etiam pendet.
AI.
24)
X2 - qu
X -AX
ideo ex quadratum
quod tamen et atunde demonstrai potest, quia si addatur, Hyperbola commensurabilis,
st 2atira, fier 2ax 12 + 2a Si
no video erorem merm, non X seu
Y
ADH 2a H = seu in duplicata ratione
a
DTH 2a + DT. Ergo _ X3DT - a XDT (, 2at. et DTp
2atX.
+ais
2
quae
et dicidendo per Xta, fier; 2ac, ad Hyperbolam
sede AC. sed Ay. sumenda est
X  a
o a. pu pd11)