204 



Trans. Acad. Sci. of St. Louis. 



260 



INVOLUTION. 



H206 



INVOLUTION. 



First power. 1F 306. Three feet in length (IT 111) are 



a yard, linear measure; 3 in length and 3 in 



width, 3x3 = 9 square feet, are a yard, 

 Second power, square measure; 3 in length, 3 in width, and 

 3 in hight, 3 X 3 X 3 = 27 solid feet, are a J 

 yard, cubic measure, (IT! 13.) 



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 poioers, and the process j 

 of producing them is called Involution. 



The first number, represented by a line, is 

 called the first power, or root ; the second, rep- 

 resented by a square, is called the square, or 

 2d power ; the third, represented by a cube, u 

 called the cube, or 3d power. 



TMrd power. 



Fourth power . 



Fifth power. 



The 4th power of 3 is 3 times the 3d 

 power, '3 blocks like that employed to 

 represent 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 5th power, by 3 times such 

 a figure, or one 3 high, 9 wide, and 

 9 long. 



The 6th power, 3 times this, by 

 a figure 9 long, 9 wide, and 9 

 high, or a cube. 



Thus it may be shown that the 

 9th, 12th, 15th, 18tn, &c., powers, 

 may be represented by cubes ; the 

 7th, 10th,. 13th, 16th, &c., by fig- 

 ures having greater length than 

 width and hight; the 8th, 11th 

 14th, 17th, &c., by figures having 

 greater length and width than 

 hight. 



To involve a number ', take it aa 

 a factor as many times as is indicated by the required power. 



Note. 1 — The number denoting the power is called the index> or expo 

 neni ; thus, 6* <lenotes that C is mised or involved to the 4th po\ver. 



Sixth power. 



(From Adams' Arithmetic — See p. 201.) 



