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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 159, page id 175905688X:0181
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Equa
nodo
ajore
reume
Toblem
nC, d0
m Aqua
Can
D
ee dittet
1
octerie
at
COMMEN TARLL TN LEBRAM I.
259
In qua si uerinque extrahatur radix quadrata, habebitur 2y ∞ 3
_ EC y ∞ 1.
Cxterum inrento utroque numero incognitox e y, quonian
promajori qualitorum polueramus x- L y d pro minorix - y:
exit major v 7, et minor ∞ 4. EcColucum eric Problema.
Aique ita reducendo illas, efficere oporiet, ut rantum una re- I
maneat, aequalis alteri cognitae, aut cujus quadratum, si ve cu-
bus, sive quadrato. quadrarum; sive surdesolidum. sive qua
drato-cubus exc. aqualis sit ei, quod provenit ex additione vel
subtractione duarum plurium ve aliarum quantitatum, quarum
una quidem cognita sit, reliquae autem composita ex quibusdar
mediis proportionalibus inter unitatem es dictum quadratum,
sive cubum, sive quadrato quadratum, esc. multiplicatis per
alias cognitas. Quod hoc pacto desieno
Z ∞ b, aut
e
Z∞- aZ.+ bb, aut
3∞ F a Z
F bbZ =c3, aut
(+∞ a Z3 +- bb ZZ63Z. + a+, gc.
Hoc est, Z quam pro quancirare incoonitasumo, est aequalis
quancitari cognitx b. Auc quadratum linex Z clt xquale ci, quod
prorenit suberahendo a Z ex bb: quarum quidem bb coenita est;
sed a Z compolita ex Z media proporcionali incer unitatem et
quadratum ZZ, ut supra explicarimus, et ex quantitate cognita a..
Aur cubuslinea Z xequalis est ei, quod provenit ex additione de
Subtractione erium quancicatum a ZZ, bbZ, ec c3; quarum qui-
dem s3 cognita est; at b bZ compolita ex Z, prima duarum me-
diarum proporcionalium inter unitatemm ex cubum Z3, ec Cx quan-
citate cognica bb; ac denique a ZZ compolita ex 2Z, sccunda
dictarum mediarum, _ ex quantitate cognita a. AEque (iC de
CXtErIS.
Eibi notandum est, per quantitares cognicas, intellisendas esse
Cas, quae in qualtione rel datae lune, vel per certas operationes
dacarum quanciratum, jam traditas _ notas, Sic Praeparatxe lunc;
uc pro cognitis sire datis sine habenda, acque guxlitis sire inco-
nicis aequiparandie.
Sic cum ponitur Z ∞ b, indicatur lineam incognitam, gux
Der