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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folio 9r, page id 00068124:0017
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proposult du. Consiliardus
700
Vata disserentia duorum Numerorum
Quadratorum, data summa numerorum inter
latera interceptorum indenire Nunieos
Vata summa numerorum (integros semper intemu
e
intelligo) inter duos extremos interceptorum,
dataque differentia quadratorum ab extremis,
invenire extremos. sint numeri dety
extremi:
x
X minor,
V major. quaorata
esit hEunctas et a, Sb sint numeri dati
quadrati xtremorum sunt XX, et sy,, quorum datur
differentia yy-xxLan summa omnium
ab 1 ad X est XX+ Xh. Et simi
liter summa omnium ab pad  e
ab
A
go ab 1 ad y-h
du, quarum duarum
yu- yn
e
summarum differentia es erit
Vy - yh
Seu (3+10)
2
XX+ Xh
2
quae _ = bh
yy -Xx + xh- yh
e
= bh unde
per 1 fit (4to) ah + xh - yh = bt seu
-X.
seu (5to) = x+y = 2b+ a. sed per 1 erat y in X+y
mop
6to) = ah. ergo per Sfit  X + y=ah
Ergo per 5 et 7 fit 2- 04a
e
=2b1a
2b+a
20 = aM, +  a = 2b Et (gno) 2X = = ah C (a. 26)
q-2b
1(10mo)
compendio sit a - 2b C fiet
a- 26
 (1mo) 2y = ah +C et (12mo) 2X = aM +C
itaque
nueruna summa iatere C
vertie
chani