aio 
i ee 
_AC makes with AB an angle: 
COMPOSITION OF PRESSURES- Q4AT 
AB and AC, which are equal, must be represented in direc- 
tion by AD; and therefore by the same in quantity also. The 
equivalent Bo 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 (@) be any angle in the series above mentioned ; a 
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.3 
of a rectangle whose diagonal: 
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:. Ie 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 AK 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 ; AB and BG must be equivalent to AG. 
3. Let. 
