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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 19
# Folio 6r, page id 00068268:0011
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repenetur in integris
e
4
a +6ab = 3ab,
4
y = b +6 ab5 - 34b
et latera
E
L
n- 49) -4
B8 et per consequem
cate pro rectis
Et pro ipsit P, 4,r, habebimus tres formulas pagina praecedente
signatas 5.
Alia via sit ly - lx = aa BZ- ly = bb
lco -lZ = d
numeri erunt (X, lx.aa, Ex = aa - bb (∞ - aa - bb = de, et fieta (X - 3 aa = 2bb - dd = le
unde pro  seu lx = = lc + 32a + 2bb +d0. quo valore substituto habentur et ly, 1Zeco
punc Jam residuae differentiae, 2da, otia quinta differentiae erunt
aa + bb, aa + bb + dd, aa + dd qui ut aequentur Quadhatis Formetur ex
recstarus
et reusproce de pF et 1.
pq et rs triangum 2p9rS, ppgq- rrssi pp9q+r
trianus. rectanus. 2pgr(, Gp rr -4qs), pp rr +94 et sumaturaltitum
Communis 2 p4Y pro b,, et duo latera pp, 49 rrB, pprr. 4uss pro duabus
alus literis d, b, tunc duae differentiae aa + bb, et aatdd erunt quadratie
sa
ex natur Mranguer rectanguli. itaque restat tantum differentia aequandi
 pro culus latere ponendo
quadato aa +bb + dd seu p44 4q. +4 q
pp44+ ress invenietur S= pr: g, quod cum non sit aptum, sumemus
es
e
9 + 1
444
S+ p Y 4 4
y+ priqu et integris eut potentia aequanda quadrato P4 + 204Y +pY+
44 44 4
(,34 p  1(gr’y. + 6ppgqr y +6ppabrryu + 4 pqr1 + +p Br y +4y + qr y
s
lui latus si sumas ppa+ ppr + 2p qy + ggrrsy + 2Frryd
et y+ H seu 5=
ul
a
6p9 + 3pgor- or
64r+39rd - 9)
quaturati quadratorum quorum sutama
604
atu aju
14
10110
6qr + 34r = qr
6bE, 2ab292a b +4a b +64862
10510.
141
fiet y =2pbp- 1Y ∞Y
692113910 - 
et pro quatuor lateribus P9, Y5, p5, 45, (quatumr
641,6+ 34b1r - L10
695Y + 34r9 - qur
a rab L6a b0a b +21 aD 4620
10 1614
10(10 etI2
qu
44 44 44 44
( Hic simul invenire quatuorquadrato
s quabratos, quorum sum maquadratus
1ts2 120
a +164b4 21 a b 6463-32 a b - 6 a +21ab Hb a b +b
20
4
sacert differentiam aa +bb +dd, seu pq eY5+ p5 + 4S
in integris habebuntur haec: 6gr + 3991-
quatuor numeriquaesit
a
p1
10
nempe sit ph= f +s= g prxt qu. K
fiat p- f: q se g. r A = R: Y
L K:q
ergo g: r = K: 4 sea Y = 9quK. et
p = tik: 99 = f:g. Ergo sit fa = HK
unde palet horum quatuor quadrato
quadralorum latera hic habere aliquam
dependentiam inter e. Et problema
sic fieri potuisse invenire quatuor
qu ub biquodratos quorum duo
sint c inter se, ut alio duo reliqui
sunt intur se, hinc et strictius aatem
possumus invenire quatior biquadrato qui
sint en continua propessione geome
trica
si d