190 HINTS RELATIVE TO 



wedge, in thofe directions, compound a force equivalent 

 to the diagonal CA in the direction CA, and therefore 

 a force reprefented by AC in that direction, mult be 

 applied to the head of the wedge at a to overcome thefe 

 forces. Let gr be the n part of Ag, and let the lines Ar 

 be drawn, and alfo GK and FZ perpendicular to AG 

 and AF, meeting the lines Ar in K and Z; then will GK 

 and FZ reprefent the friclion againft the fides BP and 

 BO, being each the n part of AG and AF, the preffure 

 againft each fide refpectively ; wherefore if Be be taken 

 in PB,andBn in BQ, equal to GK and FZ refpectively, 

 the forces Be and Bn in thofe directions, muft compound 

 a force to which the force BC in the direction BC muft 

 be equivalent; and confequently if Bm be the force 

 compoundedof Be and Bn, and Cm be joined, Cm muft 

 be perpendicular tomB; fince Be or GK is the force of 

 friction arifing from the preffure againft BP, which tends 

 to prevent the wedge from moving either in the direc- 

 tion BP or PB; and Bn or FZ has a fimilar effect with 

 refpecl to the direction in the line BO 3 and by hypo- 

 thecs, BC i^juft fufficient to balance thefe forces. It is 

 alfo evident from what was faid concerning the inclined 

 plane, that Be and Bn muft be taken in the directions 

 PB and OB for the moving force, but in the directions 

 BP and BQ for the fufpending force. 



The method of calculation is evident; forasaB, AG, 

 and AF, are perpendicular to OP, BP, and EO, the tri- 

 angles QPB and LAG arc fimilar, and the parallelogram 

 Bnme fimilar to FAGC ; whence by fuppofing certain 

 parts given, the reft may be found, &c. 



Corollary. When the wedge is ifofceles, the point m 

 falls on C, and Be is equal to Bn, and therefore Be or 

 GKiscqual to (AB-t-BCJPB) : (n.QP)jbut PB:Ba:: 

 2 Be: BC, and theiefore BC=2 Ba (AB-f-BC : (n.QP) 



or 



