This historic book may have numerous typos and missing text.
Purchasers can download a free scanned copy of the original book
(without typos) from the publisher. Not indexed. Not illustrated.
1906 Excerpt: ...property that when e3 is deleted the remaining
units elt e2 will form the ordinary complex algebra. That is to
say, it has, in part, the multiplication table: It is assumed that
e1 is the unity or modulus for our algebra, i. e., ele3 = e3et=e3.
The multiplication table may, therefore, be written: We assume,
moreover, that this algebra has in common with ordinary algebra the
property that all its numbers are commutative. In particular, then,
e2e3--e3e2 and therefore: It will be shown that the desired algebra
has the multiplication table: 2 Cj e2 e3 e2 e2---x aelJt-iae2+ie3
e3 e3 ael+iac2+ie3 bei + ac--ia2--ib)e2+ce3, a, b, c, being any
quantities in the domain R(i, i); and also that this algebra is
reducible. 2. The Multiplication Table Of The Algebra I. Besides
modifying the multiplication table (1) in accordance with the
commutative law i. e., introducing the equalities (2) account must
be taken of the associative law The associative condition, (3)
e2e2, e3=e2, e2e3 II. As stated at the end of 1 this algebra is
reducible.1 Making the following transformations upon the units:
For the definition of reducibility see Epsteen, Transactions ol
American Mathematical Society, Vol. V, pp. 106-0. THE APPEAL OF
ALEXIUS FOR AID IN 1095 By Edward Tuthill Many historians affirm
that the immediate occasion, if not the cause, of the First Crusade
was an appeal by the Eastern Emperor, Alexius I, to Pope Urban II
for aid against the Turks, who were said to be threatening the city
of Constantinople with destruction. The most convenient and
comprehensive version of this story appears in Gibbon's great work;
and an excerpt is given here because it reflects present tendencies
in our textbooks and reference works. At the Council of Placentia,
which was he...
|Country of origin:
University of Colorado
||246 x 189 x 5mm (L x W x T)
||Paperback - Trade
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