A treatise of algebra, in three parts. Containing

121쪽

3, A, S, , , , , Me ---UM rabies an quantities that are to ne another in the proportion o lac numbers, must alis have thei squam minis cube mota incommensurabie. Dio9. The oot of sue number heingincomnnensurabie, re expresse theresere bis placing the prope radica sigiover them thus, s 3 7 M 3, 3 io, o . expressnumbere incommensurable it uniti Thesenumbers, though the are incontamensurabia them selves,ith unit, are commensurabis ij οwermissicit, hecause thei poWem re integere, statis, multiples of uniti They afalso be com

mon measine, ac et is the commoni assire os

122쪽

os both, then thei ratio is reduce to an expression in the least rems, a thaco commensurabie quantities, is dividingobem by the

greatest common meadure This common molare is seundos in commensaraiae quantities, oesy the oot of the common measure is obe made thei common divisor. --- ως 3, and

sci Ix As surds may be considered a pomeramissi ractiona exponenta, he are reduee D

123쪽

. . . .

124쪽

. . . ' .

cube

125쪽

tient unde the sign, and thus the sues .illae reduce to a more simple expressimi Thus 3 316. When surd by the ast artici are reducesto thei lea expressions is the have

127쪽

osci; is positive when cis ac d bumber Diis. When an binomia surd is proposed,

128쪽

integer.

The signis D is positive ni vilien is an odd number, an in binomia proposed is

129쪽

whos , numbers have dicthrent indices, Iettheselei and I, and tahe mequat to the least integer number stat is molare is, and by I;