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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 130v, page id 00068198:0260
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W=
NZ db
ZVdZ =
SSEao a + (svaq der
ipsi 
Sit  et sint Z et v ratices quadaticae,  potentia commensurabitres
erit zax rationalis. Et proinde (ZudZue faciliter quadratio quam szudr
aut
dt = 1Z0 = a F Z0 = coco _ Zdo + vdzue - 2c0d. seu
deo =  (2 do + L dque sit v = a + sx et Z = x
fiil co = Vax+ xx  = L ssat sx p +: (satX) dx quaeambohiber
ZXX
possunt quadrabura rationali. Ergo haberi potest et dx Fax+xx
quae resolutio notenda 
Repetamus. C0 - +Z ergo c0 = sq S Ergo deo =, (2 do + L  de
Sit eL (ex sit v = a tZ et do = = dZ: 1Z.
Ergo, ce
aZ +
+Z = (L (10 s +  saqe s =) , is 2  posu sato
a Sunma Schi valyta
ee
Hinchabetur sa
Hinc haeetur sdz
sel si quia  Y∞ + 2) dque vaz +qs sesd t E  + SdZ sdz 
7 = x erit sdz t= as ax Sa + Xx. H Hini patet X d... et  s...
pendere ex se invice
(tZ 2stZedque = sa sdu SZ + sa saque s
(  (17 1Z
et fit E( ZB = datirta,
bt sgra, szra
si esset sq + a = v0 + al i fit Z- v + 2ac WV +ac - a
b+qa pendet ex sdq S,Z
s
si = sded
(b+ t2ta
fiet 77 = 2b
U W0o Z
--
104
+
Si v = b+ 1Z+ a
fit du = 2dZ:, tEta
saque  serota
 btrzra, rita 
 + 4b610+ 4b101o + 1 ((bb) 1t (+ 4bb10) +4blold F)
418
e
4106
Ergo pendet ex curvae conicae dimensione
sit Z+a =  cp 1 sit Z - Y4 - a. Ergo feod - 21  sb + . Ergo et hoc pertes
ipapa
ex Corica
Vra, Xb, XtC = 2(d x xb, XC: nta esx  Xra.  es, nrb + x L XTB, Xtb, :, XrC
2
Ergo Vixta, X+b, XtC = x Inta, xib)  + (X+ a, X+C) + (XFb, XtC). sxta, Xtb, xtC
xta, x+ b, x+c.
seu lxna Bxib, nic = (dir Cna, nib) Aera, nrC) + (ur b, 21C)
. VyX+a, X+ b, X+ c
3XX + 2a X + ab
seu tyXra, neb xac = (dx 
2 V, X+a, Xtb, XtC
V. X X + tabe = 3 Sax XY
(X+ abC
ergo Cgxrrca, hxnato = (dx
6C
sit jam atbic =0 et ab tac+ b =0
et in vtx x + qu aberunt
termini intermedii fietzue
Quod est magni momenti theorema
Corin+
peraa = Suidr, Ex ib omia hubi rnimbi a
ua agx sure
tB
hx (hrri ) + gX (grx la
gnxtar, hxx + b
Sax
hXxta, gXX + b
hhx3 + hbx
dd
ga.
FgXXta, tXXHb
x9 = fxdus + X syx = S (Ax sydx + sxydx ita habemns regulam de
summa summatum Hinc Mxra, suqua = (hax psperb  C sea vacio
Et pari pire Thxxta Sxdx sexxib 
ia
Schxta  Exta Soxi
exta = hxdX Ndx 1
hxxra
Idx (hera ptgrrb
ixta)
X+X +. X +X