On Printing Presses and their Theory. 323 
being fixed, and A being moveable along CA; the power 
applied at B” and acting perpendicularly to CA is to the 
resistance overcome at A, as twice the tangent of BAC is to 
n—I1. 
Suppose in the bah place that the power is applied ae 
by Prop. 1. Cor. 3. it will be to the resistance : : 2 ta 
BAC: i.. But the nature ofthe combination requires thatthe 
rods should in % states be parallel to each other; hence 
velocity of B’=3x vel. B; vel. B’=5x vel. B, &e., and 
power at B’= ‘ ; power at B; so that power at B : resist- 
ance atA::2 x 2 tan BAG : 1 ::2tan BAC: 5. In the 
the same manner it may be shewn, whatever be the num- 
ber of rods combined, that power: résistanee :: 2 tan 
BAC : n—1. 
Prop. VI. (Fig, 5.) Let the two levers of Prop. I. instead 
of being united at B, act on each other by means of cireu- 
lar cheeks BD, B'D, having equal radii BO, B’O, Jess than 
BA : itis required fo determine the power whieh, applied 
to B at right angles to oe shall overcome a given resist- 
ance acting at A in the lin 
To simplify the investigation of the relative velocities of 
and A, let it be sup that 
nitely small cha of panied, Ac hod (habe katalige in 
direc ce Then the centres O, O/, of ihe ais B 
, BD, vill, describe lines perpendicular to AC ; and if 
the motion of B be continued, the point of contact D, the 
tres 0,0’, and the points B, B’ will all fall upon AC to- 
sete. Let ab (Fig. 6.) be ves position which AB assumes 
it has moved an indefinitely small distance : the point 
) ° will be: in the perpendicular OP, and ao will be Pee to A 
O. Drawing the perpendiculars, bg, oh, Ae, and placing f 
at the intersection of AO and a it may be shewn a8 as in the 
demonstration of Prop. If. that he Oh=ea. Hence Ae: 
ho:: tan OAP: cot OAP:: sin® OAP : cos? OAP:: O 
:AP?. By sim. tri. ae: ho ahi But fO may be 
taken as=fo; therefore A f: fO:: OP? : AP*. 0 
sition, fO: AO:: : PA? : AO?; hence, putting A to 
the angle BAP, fO=AO cos? A. — abewid olveAe. <2 <4 
and Ae=Aa. sis to tht ON Bee Bh. fo it Sd 
> 
oh:: Bf: Of: thatis, (by substituting y found,) 
