22 MATHEMATICS. 



is yet of all curves or straight lines that can be drawn, 

 the one the body will move through in the shortest 

 time. Birds that build in high rocky precipices, drop 

 from height to height in cycloids. 



The Parabola. 



When you drop a stone, or any other substance, it 

 goes in a straight line ; when you throw it forward it 

 goes in a curve line until it reaches the ground, as 

 may be seen when water is ejected from the pipe of 

 a fire engine. The line it moves in is called a para- 

 bola ; every point of which bears a certain fixed 

 relation to a certain point within it, as the circle does 

 to its centre. 



Algebra. 



Algebra is the expressing of quantity or the ope- 

 rations of quantity by conventional symbols, a, 6, 

 c, d, are the signs or characters that denote given 

 quantities : z, y, x, &c. are the signs of unknown 

 quantities. Equal quantities are denoted by the 

 same character, m, n, r, s, t, are the characters of 

 indeterminate exponents. 



+ The sign of addition. 



- of subtraction. 



= - of equality. 



" - - of arithmetical proportion disjunct. 



: : - - of identity of ratio. 

 X of multiplication. 

 -i- of division. 



- - of involution. 



* - - of similitude. 



A/ - of radicality. 



In all the applications of algebra it is not the mag- 

 nitudes concerned that we consider, but merely their 

 proportions. The letters of the alphabet, or any 

 other symbol used in algebra, are not therefore, 



