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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 412, page id 175905688X:0434
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+22
IOM AN N ES TINDDENEF CBTSF. L
2cio. Num duae vel plures aequationes, rel quanticates dicta,
adnittane communem aliquem dirisorem.
Nam, si non admirtant divisorem rationalem, vel radicem aliquant,
velcommunem divisorem, illud plerumque, monstratum jam ineun.
doriam, reluno intuitu, rel lalcem admodum facile, innocelcer;
praelertim in aequationibus rel quantitacibus ralde compoluis,
acque exmultis dirersisliceris constantibus, quod lapenumere
incundo aliam riam ralde dissicile inventu esset, magnumque e
laborem de industriam requireret. Hlac enim Mechodus tantum
exigit, ut ae quationes, rel quantitates dicte, decerminentur (sup.
ponendo unam rel plures licerasnihilo, vel unicati, vel numero,
vel quancitati, ad libicum lumendis, aequales,) ad alias, quas
aliunde scimus non admierere reductionem, vel rarionalem diri-
Lorem, vel radicem aliquam, vel communem dirilorem. Quod
omne, exemplis explicare, Cuxerracuum crit, quemadmodum
eriam omnem ejus methodi ulum enumerare, quem latis insis-
nem essejam patuit; ac rel eonomine, quo d ipla nec tractiones,
nec irrationales quantitates moretur, non raro magnum adfere
compendium.
Denique, si aequationes, vel quantitates compositae, admittant redi.
ctionem, vel divisorem rationalem, vel aliquam radicem, vel communem
divisorem, poltunt etiam illa omnia in muleis casibus hac Metho.
dolatis compendiose inreniri. Le d hac non lunt hujusloci, polt.
hac Corcaltis aliquid de iis indicabo.
II. Ouid relim per aequationem ex Proposita Resultantem, necella-
rium videtur, uc paulo clarius exponam: maxime quia id etiam
in sequentibus Regulis, ubi litera aliqua ∞ 0 supponitur, ulum
Cuum habebic. Ouindo enim una plurelre lirerae vel quantita
tes ∞0 lumuntur, liquet, omnes quantitates, ex multiplicacione
harum per alias productas, etiam aequales nihilo tieri; ideoquein
Propolica aequatione necessario cranelcere. Quemadmodum in
allacis exemplis quoque est videre. Adeo ut in x quarionibus, quae
liceralestractiones non includune, pateat, quid per aequationem
Relultantem incellisam. Sed si licerales tractiones dantur, tune
quidem Eacile, nili quis probeanimum adrereat, error committi
pollet. Fcenim Eractionis numeratore vo existente, tollenda est
ilta Fractio ex Propolica aequatione; at denominatore voexisten
cC, Oporcet terminos omnes aeguationis primum per ejusmodi
der