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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 93v, page id 00067993:0186
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Idem plone
in circulo alibi
In oini figna constat ex alibi a ut demonstratis
productam dare differentiam applicutarum
applantam dvisam, per
Est applicata y. producta p. critse diteletia applicalte Datarra proxine majore
In Htyperbola, cum applicata y sit  sax, + X) erit Y= ax+ x. et ut habeatur producta
Sax+X  a + 2X, vel
fiet: 27 = ap + 2X p, vel,  2aX ut 2X = , et ep = 2AXA2X
a + 2X. a+ 2X
Tax IX
sarte
a +
Ergo figurae hujus, iiqua aequalio est. a + 2xa = y. quadrtum
haberi potest. Quam ut per partes examinem pate
=Y, dare 
TaxIX
ax+x2
inde fit: a+ = axY + X5 vel  aX + X,, vel a2 + a = aX +X + a, vel
Sa + a= a + X. sumta jam aequatione hac.
vel posilo at =x
Ya + a = X. Comisso a, quia istante) potest rursus aci.
= Fx a
+ unde y =
aX sive
vel    vel y --. 1. , vel y = a
o v0
r a
 vvel X y - Y a = a. vel X = a + a vel
idea in Ercul facaedu
X = _ S +a. Ego in tanc landem figuram superior aequatio redicitur.
-y. Jam altera: fra
Taxty=
 =Y. dabit Xa  y Side X. = y.
rar+X
aXEX
est trgua segnituted
ac pronide Xa = ya + Xy. Ergo X = Y) XC = X = ya, ver X = ya d eet
fier potests inde Y= X. vel ay = Xa = Xy, vel1 ob 
auyr
a = a v
tam a =X in falle alibi ex ostensum ex Z pudatura Abpribolae pendere.
pu vel Y aex - Yx = a vel aX. a yx vel a - 9 = y. vel 1- 2 = y; vel
y - 1 -= sae-. Ut productam huus figurae habeamus, fiet:
aX =X = 27 X  ac pinde a p - y p = 2y x, vel p = 27
sulstituto aequivalente, fiet: 
a2 tn
ut P ad y, seu ut prad 2x X ad (a) a, ita p- X ad 7.
fietque a- a
 et pro is
a= 1a- ax- 2X -_X. Jam fiat
a - a + a
2X -+X
2XLX
F vel 1X = 2X ad Z
sa= a -
2X - X
vel a a- ata. . Atue hiorum summa
ida a  -id q a
1X - a
aequalis segmento duplicato summae omnium sae. Ergo dimidiata
Bad u
allorum summa aequalis segmento hujus ergo differentia inter summa
differentiarum inter suntmam Ya a, et ra-a- a ta-a
semper ect Triangulo post absectum segiaentum residuo
2X -a
aequalis
vel
1a- a - sa- a + aa a quatrabiles, g 1 1x+
Ergosi 
Aa
2X- a
Sa a + aa a=, erit umma
2X - a
omnium y quadra
Alterntia ergo horum quadrata etiam altra quadrati erit? Inquoramus
fantum in a  a - a = y. fiet à  a- 8 - y, vel ax - a= aXy + axy- aXay
4X + a- aXa consiveem pine. 
sed haec nimsplis
vaey
aa a
4 =y
ide intirculo
Ergo in circ, X Maja est
inor, in Hyp. hoc loco
major quam a.