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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 479, page id 175905688X:0501
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qui lolitu
29
D0
DE REDRCTEORE A OUATLONUIN. 479
Similiter examinaturi hanc aequationem
X 6  6X 5-  25X + 36X 3f. 3 X X  16X 28 ∞O,
in qua p Cst ∞ - 6, 9∞ 25, r∞ = 36, (∞3, FD 16, V∞ -- 28,
ec b∞ F 2vel T, auc L 2 Vel - 2, auF- L 4 velur 4, (negle-
etis scilicet religuis diriloribus, radicem quadratam ultimi termi-
mi excedentibus:) inreniemus, Faciendo, ut ante, periculum cum
unoquoque ralore iptius h, Si pro halsumitur - 2, aequationem
hanC Y3- L5 yy + 1657 + 35∞0, in qua y admictit tantum-
modo unum ralorem rationalem, qui integer numerus estnem-
pe = 3. Per hunc aurem quaero ralorem iplius Z. Sed cum hic
2y (ic ∞P, ec y3- pyy + 4y + = = B = Y ∞ O, nOn pONTUMI euN-
dem per hanc aequationem Z ∞
=pyy + 97. +
renire, quo circa illum quaro per hanc Z ∞
invenio Z∞3, e
2y -
L B - Y
F hyy = 9B
1II-
atque
∞ 3. = yX X F Z~ -  B ∞ X 3 =  3X X f- 3 ~ -- 2 ∞0.
Per quam ipitur examinando an Propolita diridi queac, compe-
rietur divisionem tieri posse, orieturque pro quotiente x3 =3 ~ X
f F3∞ + 14∞0. Si rero in hoc ulcimo exemplo, ubi 2y est ∞P,
non tuissety3- pyy + 9y + 7 L B - r ∞O, OpOrruisCE EraNLILE
ad alium ralorem ipsius b.
Ubinotandum per has Regulas pro aequationibus 4, 5, _ 6 di-
mensionum non solum sciri posse, an Propolita aliqua aequatio per
aliam rationalem, in qua omnes Termini excane, divilibilis TIE;
Sed etiam uerum ipla dirisibilis sic per rationalem, in qua aliquis
Terminus deficiar. Verum cum idem Facilius coonolci queat per
XI Regulam, hanc iis duncaxat aequationibus, in quibus nulli
cermini deticiume, applicare rolui.
2. Ouoniam aurem ulus harum Regularum vel comajor est,
quo pauciores dirilores ultimus Terminus Propolieae aequationis
admitcit, haud inconsultum tueric hic adjungere modum, quo
plerum que leri nesorio Propolicam aequationem in aliam eran-
mutare licet, in qua ultimus Terminus pauciores habeat dimen-
siones, quae que indirisibilis sic (i Propolica sic indirisibilis, ac di-
viss