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.
1875 edition. Excerpt: ...the second; the seventh, the same as the
third; the eighth, the same as the fourth; the ninth, again, the
same as the first; and so on indefinitely, as shown in the table, n
being any whole number. To show the use of this table, let it be
required to find the continued product of V--4, V--3, V--2, V--7,
and V--8. Reducing these expressions to the proper form, and
indicating the multiplication, we have, 2V-1 x VsV-T x A/2VT x
A/7v1 x 2a/2a/t. Changing the order of the factors, (2 x V3 x A/2 x
A/7 x 2a/2) (V1)5. Hence, the product is equal to, 8a/21 X
V--1=8V--21. EXAMPLES. Perform the multiplications indicated below:
1. A/1 x A/2.. Ans. a x (Vl)2 =--ab. From what precedes, it follows
that the only radical parts of any power of an expression of the
form, a bV--1, will be of the form cV--1. Properties of Imaginary
Quantities. 138. 1. A quantity of the form, aV--1, cannot be equal
to the sum of a rational quantity and a quantity of the form, b
V--1 For, if so, let us have the equality, aV--1 = x + bV--1;
squaring both members, we have, --a2 = x2 + %bxf1--b2; transposing,
and dividing by 2bx, --=-b2--a2--x2 VX = Ux' an equation which is
manifestly absurd, for the first member is imaginary, and the
second real, and no imaginary quantity can be equal to a real
quantity; hence, the hypothesis isabsurd; and, consequently, the
principle enunciated is true. In the same way, it may be shown that
no radical of the second degree can be equal to an entire quantity
plus a radical of the second degree. 2. If, a + b V--1 = x + yV--1,
then a = x, and b = y For, by transposition, we have, b V--1 =
(x--a) + yV--1; but from the preceding principle, this equation can
only be true when x--a = 0, -or x = a; making this supposition, and
dividing both members of the...
Is the information for this product incomplete, wrong or inappropriate?
Let us know about it.
Does this product have an incorrect or missing image?
Send us a new image.
Is this product missing categories?
Add more categories.
Review This Product
No reviews yet - be the first to create one!