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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 411, page id 175905688X:0433
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lorc
equ
DE HLEDHCTEOHE AEBHATIONUM. 4XL
Exempla, ubi aequatio Resultans pauciores quam Pro-
posita dimensiones habet.
=. Dihabeatur x + L = C∞3 = = CC X X = + bbCX L b = ∞0, dC
d a
et
bba
TUDBONAEUES∞ F, b∞ F, d ∞ T, relultabie inde aequatio numerica
∞3 - 4X ∞ F FX = 4 ∞0. Juia vero haec aequatio trium dimen
Cionum non existit reducibilis, etiam aequatio Propolita ad pau-
ciores dimentiones quam ad tres reducinon poterit.
2. SIPFOPONAEUIEN3- abV XX. = aa bb L 3aXX L ; abx- a ab
=bbV 3aa F bb
_ supPONAtuTAA= bb ∞ 0, seu a ∞ b, resulCabIEX3- L 3 axx F L a 3∞0.
quxe etiam non poterit reduci, ideo que indicabic Propolitam x
quationem ad pauciores quam ad eres dimensiones reduci non
Ponse.
Diconon ad pauciores dimensiones illam redicibilem fore, quippe
aliquando contingere potest, uc Propolita ae quatio ad cundem di-
mensionum numerum sic reducibilis. Ouod etiam in 1ma Regula
locum habuit, ibique explicacum est. Sed si roges, quoc exo di-
mentiones 2d0 huic exemplo adscribam: respondeo, metotdi-
mensiones cuilibet aequationi adscribere, quoc ejus incoonita
quantitas ad Cummum dimensiones habet, dempeo omni ligno
radicali, quod illam incognitam quancitatem includit: ideoque
illud 2dum exemplum habiturum s dimentiones, postquam signu
radicale ante quantitatem incognitam, nempe V X X- L a a -- bb,
ablatum fuerit.
NOT X duae in hanc L es II Reculam.
T. Nocandum est, utram que hanc R egULAI NON FANEIIIM I a-
num habereulum in inquirendo, utrum ae quatio aliqua liceralis
reducibilis sic, verum etiam eodem modo inguiri polle:
mo. Num aequatio illa vel etiam quantitas quaeris compolica,
per aliam aequationem vel auantitatem, qua racionalis lic, dividi
DOIHIE.
d0. Num admictat radicem quadratam, cubicam, vel aliam.
FF2
eic