204 
Trans. Acad. Sct. of St. Lows. 
260 INVOLUTION. _ 1 206 
INVOLUTION. 
First power. 206. Three feet in length (7 111) 2 are 
a yard, linear measure; 3 in length and 
width, 3x 3==-9 square feet, are a yar 
Second power. square measure ; 3 in length, 3 in width, and. 
hight, 3 X 3 pT 3—97 solid feet, are 9 
a yard, cubic measure, (113. 
When a number, as 3, is multiplied into’ 
itself, and the product by the original number, and so on, the | 
several numbers produced are called powers, and the process ) 
of producing them is — Involution. 
The first number, represented by a line, is’ 
sak the first power, or root ; the second, rep- 
ted by a square, is called the square, OF 
in, a ae 2 power the third, pe ini by. a cube, 15) 
d the cube, or 3d pov 
he 4th power of 3 i is 3 times the 3d 
power,’3 blocks hke that employed to. 
Steere the 3d power, and may be rep- 
resented by a figure 3 times as large, that 
is, 3 feet wide,3. feet high, and 9 teet long. ' 
The Sth power, by 3 times such 
a figure, or one 3 high, 9 wide, and 
long. 
The 6th power, 3 times this, by. 
a figure 9 rong 9 wide, and 9 
high, or a - 
Third power. 
Fourth power. 
hus may be shown that the 
19th, 15th, 18th, &c., ar 
may be repreSe Sented by cubes ; 
7th, 10th,. Nath, 16th, &c., by fg. 
ures having greater length than 
width and hight; the Sih, eh 
“14th, 17th, &c., by figures havi 
greater length cod width than 
hight. 
=a 
aan 
aT be 
SSS! SS SS 
ae Lt 
Tot 
@ factor as many times as is mnuljented by the required power. 
involve a number, take 
Note. 1—The number denoting the power is called the index, or expe 
nent ; ce 64 denotes that 5 is cained or powived to the 4th power. 
tan 
{ (From Adams’ Arithmetic—See p. 201.) 
