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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 509, page id 175905688X:0531
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l.l
M, Teu
est pec
DE NI A Z TN IS E F HIEN LMTS.
509.
Nlam quoniam haec producta x5 - 2 7 ∞ + - F y y X 3, _ X X -
2X X F x x in x3 eadem exiltune, erit etiaI x 5 -- 2 7 x = L y y ∞3 mul-
ciplicatum per a, a 8 b, a 8 2b xquale c; sic de, quoniam. L P X +
2 Py X3 + Py y x x idem est quodx X = 2 X N L X X IM P N N, CFIE
quoque p∞t - 2py ∞3 + pyy xx mulciplicatum per a 8 b, a 8 2b,
a E 3b (liquidem, ut ex pracedencibus liquet, primus terminus
Proorecsionis ad libitum Cumi potest) aequale o; atque sic dein-
ceps. Cnde tic, ut etiam Productum corius x quationis per hanc
Teriem proportionalium sic ∞ O, nec non utunus valor iplius
X ∞Y, qua una duarum radicum aequalium est, necellario inclu-
datur. Ec cum hic rurtus nulla habeatur ratio mulcicudinis quE
Paucitatis aut etiam qualicatis mulciplicatorum: erit Propolitum
Pheorema univerlaliter demonstrarum de quibuscunque aequa-
tionibus, duas radices aequales habentibus..
Flinc emanat
Si in aeguatione aliqua 3 sint radices requales, ec ipla
mulciplicetur per Arichmeticam Progreltionem, quam
libuerie, eo modo quo jam dictum elt, remancbunc in
Producto duxe adhuc aequales radices ictarum erium;
ac proinde Pioductum hoc denuo per Arichmericam
Progressionem mulciplicari poreric. Ouod si autem in
Propolita aequatione guatuor radices aequales fuerint,
acque ipsa mulciplicetur per Arichmericam Proorel-
sionem, relinquentur in hoc Producto adhuc 3 xequa-
Les radices iltarum 4, ex (ICPOTFO, guotcunque aqua-
les radices aequatio habuerie, semper per lingulas ejus
modi mulciplicationes una tancum iltarum aequalium
radicum colleTuF.
TToc itaque demonstrato, transeo ad meam Nethodum de
Naximis se Minimis, quae sic se habet.
Poltis quoreunque quancitatibus AlgebraicIS, ME-
ximum aut minimum delignantibus, ponantur ip(x DZ;
X Ordinata aequatione multiplicetur ea per Progressio-
nem Arichmeticam, eo modo, quo dictum est: e PtO
555
ductum.