192 



HINTS RELATIVE TO 



therefore, prove that the common method is really a 

 confequence of what that gentleman himfelf allows, and 

 that his objeQions are not well founded. In the firlt 

 place, he allows the force AB to be equivalent to the 

 forces AV and AD or VB; now (excluding friction) if 

 that part of the arch which touches Pb was removed, it 

 is evident QbbP would immediately begin to defcend 

 along Qb with a force reprefented by VB or AD ; but 

 this defcent is prevented by that part of the arch which 

 touches Pb ; and therefore the force of that arch, in the 

 direction HA, muft be fuch as to be equivalent to DA 

 in the direction DA or B V : but no force greater or lefs 

 than HA will be equivalent to DA in the direction DA, 

 and therefore HA is the real preffure or force againft 

 Pb. Again, HD is the preffure in a perpendicular di- 

 rection to Qb arifing from this force; and as A V is the 

 preffure againft Qb arifing from the force AB, therefore 

 AV, together with HD, is the whole preffure againft Ob 

 in the direction AV ; but becaufe the body is in equili- 

 brio, and confequently the aclion or force in the direction 

 AV equal to the re-action in a contrary direction ; 

 therefore AV+HD or AN (becaufe NV is equal to 

 HD by the property of the parallelogram) reprefents 

 the preffure againft Qb, and AH the preffure againft 

 Pb ; which is contrary to what P. Frifi afferts, and 

 agreeable to the ufual method, 



The fame learned author has made another very ma- 

 terial miftake, from a fimilar caufe, at page 67 of the 

 aforcfaid Treatile, relative to the teniion of ropes; 

 which cannot be attributed to hafte or inadvertency, as 

 he exprefsly afferts the holders of the common opinion 

 to be miftaken, in confequence of their ufing the theory 

 of coirpoiition of forces without fufficient precaution: 

 I fhall, therefore, after giving his own words, take the 

 liberty of {hewing where I apprehend he is miftaken. 



" Parleremo 



