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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 29r, page id 00068195:0057
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Invenire quatuor quantitates Geometrice proportionales
a quibus
X X. y. yy. yquonum quadratorum summa sit data a
et cuborum summa etiam sit data b.
Evit XX+ gy + y + y aequ a. et X + y + y +Z
XX
3)
XX
XX
p
modo ex aequ 2. fiet: B + 3 + y aequ b -
X3
compendii causa a -1, vocemus f et b - vocemus y
9 C2)
aequ b.
Ex aequ 1. fiet: 3Z + _ + 96 aequa  1. et eodem
(7) Xx sit c
(e0
et 37 vocemus 7 et y volemus v. fi
(10)
fiet: ex 3 et f Z3 + ZZ + Z aequ f et v + vB + vaq. g.
1)
erit  et praeterea ex 7 et 8 erit Z aequ vv.
Ergo ex aequ. 8 et 11. fiet: vv +. ZZ + Zaequ. f. seu ve22122 aqu. f 
4
15)
vD
ex aequir est ZZaequ. f - vv - Z. et ex aequ 13 est 2Zaqu. fZ - vV -voz
(1
aequando valores 14 et 15 fiet f- Z aequ fZ - vv Z.
Ergo fier Z4 qu. F
6E
ergo
Rursus ex aequ 11. ZZ aequ BD ae
f+1 - yV
(21X
aequ
FZ. vB.1
ergo fiet vn aego fZZ - vvZ - vvZZ seu Z2 aequ v0 + vrZ.
VV
ungatur cum aequ. 14. fiet: f- 2 fvV + v CZ + on Zgo 
son 7 aego f2- 2f vV + V2 = vV (3)
ex aequ’y et
1
ex aequio. it et II fit
16
f.
aequ
fit: _ vr + ZZ + Z aqu f
Crsli
v3+ Z3 + v aequ. 9
Nota quia ∞yZ aego 24 per 11. hinc ex aequibfier
+
r
si
t
f - Z aequ fZ- 74 sed hoc nullius
usus fit enim ex aequ. 9. multiplicata per Z-1
V4 VV+ Vaequq Z
aequ S. aequ d vv. seu
f+ 1 - vV
+ Z2+ Z aqu. f
63
B
jam f +1 aequ. d
et vnaego  ergo Sonaequ s7 v
Ergo fiet
Xx
XX
aequ. 77
Xx