COMPOSITION OF PRESSURES. 



247 



AB and AC, which are equal, must be represented in direc- 

 tion by AD ; and therefore by the same in quantity also. The 

 equivalent of AE and AC being the same with that of BE and 

 AD, which are equal, will be represented in direction, and 

 therefore in quantity by AF, (vid. Lemma). Thus may the 

 proposition be proved of any rectangle whose diagonal makes 

 with one of the sides any angle found by the continued bisec- 

 tion of a right angle. 



2. Let (a) be any angle in the series above mentioned ; the 

 proposition shall be true in relation to any rectangle whose 

 diagonal forms with one of the sides an angle that is any mul- 

 tiple of {a). 



Let AB and BC be two sides fig. "5 



of a rectangle whose diagonal 

 AC makes with AB an angle d 1 

 in relation to which the propo- 

 sition has been already pro- 

 ved ; and let CAG be equal to 

 (a) ; the proposition shall be 

 true in relation to the angle 

 BAG ; for let GED be parallel 

 to AC, and draw the perpendiculars AD, EF, GH. It is al- 

 ready proved, that two forces represented by AD and AF are 

 equivalent to the single force represented by AE ; for 

 < DAE — < BAC. AE may therefore be resolved into AD 

 and AF ; that is, the forces AE and AC are equivalent to the 

 forces AD and AH, or to the single force AG. Since, then, 

 AB and BC are equivalent to AC ; and AC and CG equiva- 

 lent to AG j AB andBG must be equivalent to AG. 



3. Let 



