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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 187v, page id 00068196:0370
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Omnes Curvae simplices sunt quadrabiles. t) vel absolute vel
Omnes curvae rationales sunt quadrabiles
per Ccirculum et. fulsum fore
sit: Ita aequ b +X  aqu. 0. sit y aequd Z + B+ fco
5. aequ, aZ2 + 2de ZV + 2 df Z Co + ee vn + refrco + ff coco
ay aequ a
d’aequ Ya
Hyplibola
adque + aev+ at c
Za a aequ x sit V + Z aqu. y. fieta
fiet y - 22y +Z2 aequ x a. et quia q aequ x+ a. fiet:
fet yy = 2xy + 2 ay + X +Dra + ad aequ (Xa). seu yy + ray + XX + Xa +aa aequ 2Xy
quae est ad parabilam.
v+ Z aequ. y.
substituatur fiei:
9 aequ L + ad
X aequ x’y + ay
X eqo XV + XZ + a v F avZ + aZ.. Divitatur aequalio haec in duas:
X’ aqu. X V + a v et
Zaequ. x 1m 8. Fyaqu. S0 + tZ. fist: y aequ.+ Sbx+ SC
_ vaequbxti
v y  +X y + X aequi X + X. Ergo y aequa Y X + a
qa
quaeretur ergo tantum
4a
40
X + y aequ a. Ergo  XAX a d s dy aequ. 0
 x quaritur. sit : X y+byR F Ci+ dE+ e
+p+m
ax aeq y aequ Tax X anqu. Z. Ergo y dx aequ R
y aequ abta X+X sit X aequ
ia
Z ago X YX + X2 posito y aequ Z - 
a
Y aequ  a- x Y x rgo X. 
e fii
Yago S+ 87+ 
b
+cZ+ 4 6
a
182
bgobaez AZ
excestZ
ut vero quadatis (V + 5D + O fiat extrahibilis,  considerandum est eam habere arbi-
trarias : b. c. d. e. f. et comparandam esse cum quadrato ipsius g 4 hxet KXX+ lae ubi
rursus arbitrariae quatuor; summa novem, la quibus si auferas duas velut utrobique superflune
rostabunt arbitrariae septem, quae  sufficient profiduabus formulis septem terminorum
haud dubie comparandis. Nec dubium est rem in altioribus, eodem modo sed quid si
plures cirationales simul rationates reddi debeant, ut si sit yago itXx+ +
+s bxx +x +X. sic agi poterit primum fiat Xe aequ b+ CZ+  +diZ, ut quemud
e+ 2esZ+ f2Z
modum dictum est, fiat 96+O25 O exhahibilis. Jam rursus _fiat Z aequ. l+ in v+ nvi pp
q +r v+s v4tv
idque subsistulitur in valore ipsius X loco ipsius Z. ut ope harum novarum arbitarum fiat
etiam quantitas. Na +bXX + Cx+ extrahibilis. abispatet etsi necessarium fuerit
niminatorem valoris ipsius x esse quadrutum, tamen non necesse est nominaiorem
valoris ipsius Z esse quadratum adeoque plares. Et puto sufficere: Z aequ l+ mv
imo vndeo non sufficere, ett allioem ut Z aequ Camo + nod ad huc imna
gtretsor
g+rn
x p ....
aego Xx+Cxaeq
e + retZ+ s) 2Z seu Xajo 
et curva ABC erit pa