The London, Edinburgh and Dublin philosophical magazine and journal of science . either V or Q the smallest additionalforce, the direction at least of the resultant will be changed,being brought from the previous direction nearer to that of theincreased force, as it must be the resultant of the previous re-sultant and the added force. Corollary. If the two forces be equal, their resultant must inthis case manifestly have a direction which bisects the anglecontained by their directions; and any other pair of equal forcesacting in the same directions, but greater or less than those, willhave a r
The London, Edinburgh and Dublin philosophical magazine and journal of science . either V or Q the smallest additionalforce, the direction at least of the resultant will be changed,being brought from the previous direction nearer to that of theincreased force, as it must be the resultant of the previous re-sultant and the added force. Corollary. If the two forces be equal, their resultant must inthis case manifestly have a direction which bisects the anglecontained by their directions; and any other pair of equal forcesacting in the same directions, but greater or less than those, willhave a resultant whose direction will still be that of the line bi-secting the angle, and greater or less than the former in thesame ratio as the equal componentsare increased or diminished. III. If two forces P and Q which acttogether on a material particle are re-presented in direction and magnitudeby AB and A C respectively, which con-tain a right angle B A C, their result-ant, whatever be its direction in theangle B A C, must be such that itssquare shall be equal to the sum of S2. 248 Dr. Stevelly on the Composition of Forces. the squares of P andQ, or R2=P2 + Q2; and therefore its magni-tude must he represented by the length of B C, the line joiningthe extremities of the lines representing the two component if, to fix our ideas, we suppose A R to be the direction ofthe resultant of P and Q represented by A B and A C, and at Aerect xAx both ways perpendicularly to AR,then, because B ACis by hypothesis a right angle, <2?AB= RAC, and #AC = the direction of P divides the right angle x A R into thesame angles that A R divides the right angle CAB, and the di-rection of Q divides the right angle a?AR into angles equal tothose into which A R divides the angle B A C. Hence, if wesuppose P to be replaced by its two equivalent components inthe directions A R and A x, and Q by its two equivalent com-ponents in the directions A R and A xr} and call these respectivelyV,
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