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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 314, page id 175905688X:0336
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=336
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314
F R A B OFS CF a SOH OOFFN
Temper sic duei polsune, ur daris rectis sine aequales, nec ost Pro.
blema eo calu determinationi obnoxium. J et
Innumeris, eAto B D ∞ a ∞ 7, F. F ∞ C∞ 24, Tiecque aequario
quae lIta X + - 24 X 3 - - 178 X N -- 686 N - f 2. 4. 0 1 ∞ O. OUX
cum diridi nequeat per x L rel - aliquo numero, ultimum ter-
minum diridence, tollo secundum ejus terminIm, de HE aequatio
7
yn
74XL 55L2 L 4375L 6305 1620. Oux ad eres di-
mentiones reducta dabst aquationeim yo = 2203y+ + 32937577
= 19140625 300. Hlac autem cum diridi pollic per yy L 625
∞0, arguieur y elle 25, qua mediance diridetur ae quatio 7+ X
= 552 : Z2 = 4375 Z = 6305 2530 in duas aequationes,
LL
252 = 50220, et Z2, f 25 Z + 2244∞O: FenE
que radices prioris Z∞ 12 E V, 207, de Z3 12 3= V 207;
ac posterioris Z ∞  125 = V 32, d Z ∞ , 1,2 Z V 32.
Verum quoniam, ad collendum secundum cerminum prima x-
quationis, supposita tuit x ∞ Z a: hinc radices ejus crunt
X ∞ 16 - F V 207, d x 3 26 =, V 207, UE e ∞ ∞ - 9- L. V 32.
NCC HON X ∞ --9 - N 32. Ec liquer D F FOrC16 = V 207.
DI26 F Y 207, DK 9 = V 32, dc denique DM 9. F V 32.
Fodem modo, EP D Fuerit 3, ex FF 4, inrevietur aequatio
∞t - 6 ∞3 + 2 X x - 5 4 ∞- 1 81 ∞0, quae similiter per x L vel.
aliquo numero ulcimum terminum 8r diridentce diridi nequit:
unde lublato lecundo ejus termino, tec aequatio Z +X  11 1 77
i 75Z= 105∞ ∞. Qua ad eres dimentiones reducca, dabit
_GUATIONCM y0= 23 7+ + 775, 97- 5625 D O. LleC, CuI
Per yy = 25 00 diridi poltur, sequitur y Fore 5. UInde dirisa
aequatione praecedente in duas aequationes 77 -
y = = 200,
X ZZ = 5Z F 14 + ∞ 0, inveniemus Z ∞ V 7 -[ 2 =, vel
∞V7 = 2. Oux bina cantum radices ex utraque aequatione
erui possune, cum posterior ae quatio ZZ  5Z -  24 1∞ O l
impossibilis, per ca, qua p. 265 expoluimus, adeo que nullas ad
mictat radices nec reras nec Fallas, sed tancum imaginarias. Oui-
bus radicibus si addatur F = (quoniam ad collendum secundum
terminum primae requacionis poluimus X ∞ Z L 7 =I habebitue
∞∞ V 7 -+ 4, vel ∞ ∞ V 7 = 2. Id quod monstrac lineam D s
Sumendam esse aequalem V 7 = F, de lineam D TI ∞ V 7 L . EX
quibus constat, quod, poltquam aequatio inVeNEA X + - 6v
L 2 N X = 5 4 X = 81 ∞0 nullam agnO(CaE radicem Fallam,
(quan