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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 513, page id 175905688X:0535
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+
DE HIA ZLMES EF MIINIMIS.
Patet itaque, duas has Speciales Regulas in generali illa Me-
thodo esse tundatas respectu hujus Progrestionis 0, 1, 2, 3, 4, RC.
mulciplicando scilicet rerminum, in quo incogniea quantitas x
non reperitur per o; ubi x unam habet dimentionem per L; et
Sic Porro. Sed in generenotandum, quod, dum operando juxta
generalem Mechodum Prooressionem illam Arichmeticam ad li-
bicum lumere licet, semper is terminus aequationis, quem libue-
rit, colliposse, mulciplicando illum cantum pero. Regueita va.
lor iplius z per unam Progressionem limplicius obtineri poterit,
quam peraliam: uc, si in praecedenei exemplo, ubi multiplicari-
us per 3, 2, 2,0, mulciplicassemus per 0, 2, 2, 3, obcinuisse-
IUS A aX X - F 4 b a a X = 3b a 4 Z ∞0, CCH = X = 4b s ∞ Z
3b
Unde apparet, ipsam quancitatem Z (live maximum vel mi-
nimum), Si x cognita supponatur, inreniri atque exprimi posse
multis diverlismodis, e quibus Faciliores pro Constructione eli-
gerelicebit: AuchZ cognita supponatur, poterir x totidem di-
verlis modis inreniri. Porro considerando Z de x, utincognitas,
pocerimus ad alterueram tollendam aequationem instituere inter
duos ex limplicistimis ralores: ut, in superiori exemplo, incer
2
X
3bX X + 2aa X + 2b A a g 7  X X + + b ∞
3∞ X
3. Si termini Alcebraici. Maximum aut Mlinimum desi
enantes, plures unâ quantitate incoenitâ includunt; suppo-
noiplos ∞Z; de per hanc aequationem e per cxeteras datas, seu
quae ex nacura Problemaris manane, (quae que semper Siiul, (I
omnes Problematis conditiones includune, tor numero exictunt,
quotincognite quantitates, una excepea, habentur, nimirtum lI
unum tantum Maximum auc Minimum incer intinicas maonieu-
dines quaeritur, non aurem incer intinita Maxima;) reduco ae qua-
tiones omnes ad unam, in qua necessario duae quantitates inco-
Ouica continebuntur, de inter eas Z. Cumque tunc (ola Z ad Ma-
Ximi rel Minimi inventionem nota esse debeat, manifectum est in
cum finem duncaxat concipiendum ese, alteram quantitatem In-
coonitam duas aequales radices habere.
Sumamus, exempli gratias tres aequationes, quibus maximam
lacicudinem currae determinari, quales illa pag. 498 Exercica-
cIONuM Cuum MLALhEIMATICARUMI RCPETIUNEuE; exCepEOtancum
Et
quod