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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 165, page id 175905688X:0187
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WIM I2.
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COMEMLE A E ARTE EN LTBRUM I.
265
vic, cum nempe in ea Ctacuitur minor quantiras a quari alicui ma-
jori, vel cum jubemur ad cam re lolvendam aliquid praestare, quod
tierinullo modoporest, uc, quanticatem aliquam majorem a mi-
nore subducere. Ouemadmodum in xequatione Z7∞ aZ -- b b.
quoniam ad inveniendam radicem Z, bb ex = a a Tubirahi debet;
OpOTFeE ut bb non lic majus quâm = a a, sire ue b non sit majus
quam L a. Aliasenim radix ejus lic explicari non poset, de Xqua-
tioimpossibilis foret. Ouod e ex ejuldem constitutione licet
aenolcere, liin ea dua lint radices vera. Si eniI PONAMUS Z ∞C,
(Cu Z -5∞0, icemque Z ∞ d, Peu Z - d ∞0, acque deinde muI-
cipliceuS Z - c ~ O per Z =d ∞O, ex TUrSCE X quariO
C
 - + 2. FCd ∞ 0, (Cu Z
D
LC
t (= 6d. In qua (1 - (- c -  d InEeI
pretemur per a, _ =cd Per =bb, hrabebimus aequationem
propolitam ZZ∞ a Z - bb. Adeo ut conster aquationem hanC
duas veras radices admietere, seu quae majores lunt quamr o, qua-
rum quidem summa est a, _ productum ex earum mulciplica-
tione bb.
Sed uc duas lemper verasradices recipiat, requiritur, ut bb
non sicmajus quam : aa, seu, b non majus quam  a: quoniam
maximum productum quod tc ex parcibus ipliusa, est, cum a in
duas parces aequales diriditur. Ubi notandum, quod ubi bb ∞ L a a-
a elle Z, qua quaeritur, atque aequationem eo calu unaM Can
tum Corciriradicem, aut duas quidem, sed aequales. AC vero b b
exiltente majore quam: a a aequationem esse impossibilem, nec
ullam admietere radicem. Id quod similiter de aequatione
(∞ - aZ= bb estincelligendum, quae de duabus Falsis radici
bus est explicabilis. TIc patet ex ejus consticutione. Etenim po
nendoZ ∞ = 6 Peu Z - F 6∞O, HCCNON Z ∞ - d (Cu Z, F d ∞0,
de mulciplicando Z Fc∞0 per Z = d ∞ o: proveniet Equatio
yyL c
L+ a E +6d ∞0, leu 22
a
= cd
In qua (I InTerPreteMUT - C- d Per  a, _  cd DeF - bb, c.
tnerg er aquatio proPOsita ZZ ∞ = a Z -- b b. Cujus porro radices
Ceometrice inreniuntur perinde atque Aquationis praeceden-
tis. Quae denique siC exprimUNEuT Z ∞ = = a   V = a A - bb,
Et
3 . a mun V a a A bb.
Exterium quod ad duas reliquas aequationes attinet, primam
X. 3
vide-