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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 420, page id 175905688X:0442
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+20.
TOT ANHES HIUDDENELEBTSF. L.
R F C V L A.
Duae modum docet reducendi omnem aequationem, quae
produci potest ex mulsiplicatione duarum aliarum, quarum
una liceram aliquam comprehendit, quae in altera not
continetur.
Supponatur aliqua litera D o; inrestisetur que num
aequatio, quae hinc relulear, habeat cum Propolira
communem dirisorem. Si non habeac, supponaeur ite.
rum alia licera ∞0, investigeturque num ilta Resultans
habeat comunem dirisorem: acque sC POrro, doneo
aut communis reperiatur dirilor, aut nulla amplius li
cera supertic, quae non luppolica sic ∞0. Ec li non inve.
niatur communis divilor, sionum erie, sequationem
Propolicam, ex mulciplicacione duarum aliarum, qua-
rum una liceram aliquam comprehendic, qua in altert
non concinetur, producinon poste.
FX. Gracia, si proponatur hac aequatio
X5 X-  + a b ∞ 3 f 30b3 X N. f 34 a b3 X - + 20 a b+ ∞0,
 bb  20abb t 7 a+  20a+ b
a 4
a 4
supponatur que licera a ∞ o, resultabit inde _ 5 X -  b b X 3 -f. 30
bbbxx ∞O, quae cum Propolita communem habet dirisorem,
NEMPCXK - 3b x- L 10bb ∞0. Ouod, si alicer crenisser, aliam
liceram, nimirum b, poluissem ∞0. e li inde Resultans aequatio
etiam non habuisset communem diritorem, conclusistem aequa
tionem Propolitam, quoniam tantum duas iltas a e b diverlas
haber liceras, non reluleare posse ex mulciplicatione duarum alia
XUI, _CC.
Res eodem modo se habet in aequationibus, quae irration
les quaneitates includunE, ita uE non opus sic alia exempla ad.
UINSCIC.