PRO 

 Here y ;30, x = 1-20, v? = 1GO g, .'. 



a 



1 = 4 tan. 



2 (cos.) 2 



.*. (tan.) 2 - tan. , -77-, 



o o 



and tan. a = 1 or ~r, and . = 45. 



Ex. 4. A body projected from the top of a tower at an / of 45o above 

 the horizontal direction, fell in 5" at a distance from the bottom equal to 

 its altitude ; required the altitude. 



Let a = height, then a = 45, t = 5, and y = a t 

 .;a = a tan. 45 -J. 25, 

 /. a = 200. 



PROJECTILES, resistance of air to. See Gunnery. 

 PROJECTION, principles of.( Vince.) 

 I. Orthographic Projection. 



1. The figure of a straight line is a straight line in the projection. 



2. The figure of 'the projection of a circle is an ellipse, of which the 

 minor axis is the cosine of inclination of the circle to the plane of pro- 

 jection. Hence if the circle be parallel to the plane of projection, the 

 projection will be a circle equal to it. If the circle be perpendicular to 

 the plane of projection, the circle is projected into its diameter ; any arc, 

 reckoned from its intersection with the plane, into its versed sine ; and 

 the remainder of the quadrant into the sine of that remainder, or into 

 the cosine of the first mentioned arc. 



3. In this projection the area of the circle I the area of the ellipse into 

 which it is projected II radius : cosine of inclination of the plane of the 

 body to the plane of projection ; hence the area of the circle will be di- 

 minished in the ratio of radius I the cos. of this inclination. And this is 

 true whatever be the form of the projected body. Also the projection 

 is not similar to the body. Hence equal parts upon the surface of a 

 sphere will not be projected into parts cither equal or similar. 



This projection is not convenient for maps, but is used in the con- 

 struction of solar eclipse*. 



