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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 462, page id 175905688X:0484
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462 IOE A N NZS LIUDDEMIE EPTST. I.
Mlodum inveniendi omnes rationales Divisores ultimi
Termini surdis es Fractionibus carentis.
Cleimus Terminus aeguationis PFODO(IEX AUE CX unO
aut ex pluribus Membris leu quanticatibus, per + e-
junctis constabit. Si unius tantum Mlembri liC, notum est
qua ratione iplius dirilores invenianeur. Ouod ( au-
cem ex pluribus Membris constiterie, lapenumero diffi-
cile est eos omnes repcrire. Ilinc ad eos inveniendos,
considero scortim ultimum Perminum xquationis Pio-
Polica, supponendo iplum ∞ 0, acque pro lubitu eligo
aliquam exliceris, quam pro incoonita quantitace hu-
jus ficta aequationis habeo, cujus respectu Actam Xqua-
tionem illam in ordinem redigo.
Exempligratia, ex ultimo Termino hujus aequationis,
X = 4a ∞3  266 X X  4aCC X  C4
7 aa -- 4 a aC = 4 a +
246 6a3 + 843C
L 2 aC3
∞O
L 3a466
lumendo literam  pro incognita quantitare, invenio xguatio
nem hanc c+  2 ac3  3 a acc +- 8a 3C - 4 a 7 ∞ 0.
Deinde inquiro per antecedentes vel sequentes Re.
oulas utrum haec licta per aliam racionalem dividi
Possic; Si enim hoc heri negueat, manifectum estulti.
mum Terminum aequationis Propolux nullos quoque
dirilores rationales admierere (nili unitarem acque
ipsum ulcimum Terminum inccorum inter dirilores
numerare relimus; sedhi in aequationibus liceralibus,
ubi omnes quanticates cundem dimentionum nume
rum habene, nullius usUS (UME); Ouod E vero diridi
Possie, oportet rurlus codem modo quaerere dirilores
hujus dirisoris se quotientis, acque ita cridens erie,
quo pacto omnesrationales aequationes, qua lianc Li
etam