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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 296, page id 175905688X:0318
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296
F R A N CESCE d SCHOOTEN
tionis ZZ = - aZ -- b b ∞0, guae per Z F vel - b ∞0 diridine.
quic, per surdas quancicates exprimi portine: Suppono primum Z
esse aqualis simplici alicui quanticari lurda, uEputa, V X, de fe
Z = V x ∞0. Juam, ut ad aequationem quadratam ejuldem tor-
ma perducam, in qua secundus terminus est rationalis, mulcipsi-
care debeoper 2. L Y. L V x ∞ 0. Sed quonium (ic non producitur
aequatio, in qua etiam tertius cerminus rationalis est, concludo
radices aequationis propoliex hoc modo non porse denocarilive
exprimi. Idem fit supponendo 2 ∞ -- V X.
Ouocirca Catuendo nunc Z∞ y . L V ∞ Peu 2 - y - V X ∞0,
oporcet iplam, ut ad aequationem quadratam ascendat, in qua rur-
sus secundus terminus sic rationalis, mulciplicare per Z - p L V X
∞0, de ticZ2 = 2 yZ F y y ∞0. aequacio ejuldem forma cum al-
lata, a in quaitem cerrius terminus rationalis est. Ilinc compa-
rando secundum terminum unius cum secundo alcerius invenio
=27 ∞ - a hoc eA, y ∞ =a. Tertius autem terminus cum tertio
comparatus dat yy = x ∞ -- bb. In qua li in locum yy subroge
tur = aa, habebo = a a + b b ∞ X. Ac proinde cum pro quaesiris
radicibus suppoluerimus Z ∞0 y. L V X, X Z ∞ y - V x, eruncipla
2 ∞ = 4 + V = aa = bb, e 2 ∞ : a - V = a a + bb.
Eodem modo si inrestigare relimus, quo pactoradices aequa
tionis indirilibilis py L a p -- b b ∞0 per quantitates Curdas ex-
primi queane, Cacuatur (neglect â suppolitione iplius y ∞ 8 V ∞)
p∞ - 2 Y V X (Cu Y. L Z - V X DO, Caque, ut ad aequationem
quadracam altursac, in qua rursus se cundus terminus lic rarionalis,
mulciplicetur per y + 2 f V ∞ ∞ O, _ tt y y L 22 7. + ZZ ∞O.
X
aequatio ejusdem Formae cum allata, ee in qua etiam tertiuscermi.
nus est racionalis. Unde comparando secundum terminum hujus
cum secundo illius inrenitur Z ∞ 3 a. Perrius autem terminus
cum tertio comparatus dat x ∞ = a a -L bb. Atque adeo, cum pro
quaeliris radicibus suxpoluerimus y ∞ = 2 F V X, eC y ∞ = 2
=V X, erunc ip (X : y ∞ = 2 a + V : a a F bb, _c y ∞ - : a -
+aa L bb.
Similiter, inveltixando num radices xequationis Z 2 - 4 Z f bb
∞0, quam per 2. F rel - b ∞o diridere non licet, per lurdas
Quan.