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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 16
# Folio 8r, page id 00068229:0015
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eo Methodus triplicium aequallatum.
A X + 8Z3 1 1b
ivenire methodum generalem ex uno exemplo.
problema Numericum quod Dsanna judicat
3
ficillimum ex his quae solvit
onc
1lb - X p
fiat 16v - X V Z. + 27c+ co
Ergo Z r lbva- X p
=DC1 +
sit majoq ahuilo
G
et fict: H IbV - X p 4 Bb- 1X
Duplex aequalitas.
X 1
(+ 2t-
F, 1b
42
Ergo 1tq e Joso 145 posa
(2. 2 16721)
ex-
Ergoleue e ut
sed non ideo raliquas licet sumere pro artitrio
vventus valor ipsius7. substituatur in ejus locum
aequatione Z2
1)
2X
jamque purs inveniatur
valor ipsius x. quod eadem arte
ootentis
nabus aequationibus facile obtinem potest
quibus X, facile vobtiieri potest.
ponatur 25 Y Hsi fie b et X S Et tam s. quam
490
2.
perconendi aliquid prodesse methodus
sludesor
quam dicam.
sume duos Numeros si quos habes, saepe autem habemus satis facientes, et
ipsos resolvendeo, eue ex illis methodum deducendi id quod prae stant analyticam
utrique communem; ea methodus forte ducet ad l generalem
quaentuur modus datis num duobus numero invenire quadra duos quadratos, quorum
summa datus; pone 34   7 esse datum, constat duos quadiatos esse 16 et g.
item ponc. 13 esse datum, componitur ex 4 et 9. jam quaere methodim ulrus
communem, emendi propositum: Fac . 34  bc. et 13 p CC + l dati autem
funt quae quadrati sunt et + et d C + E + 2bC + e
Ergo fier e +C bC, et 2e+CE rbel  CC + B
saltem sta miquisitio artes plurimas ostendet, quibus, natura ad exitum utitur