OF THE PROPERTIES OF CURVES. 53 



parallel to CD, and EB to FG, Z. ABE=CGF=:CHF : but ElB is 

 a right angle, as well as HCF, and EI : IB: '.FC : CH: : AE : CH, 

 since AF is equal to twice the distance of the centres, which bisect 

 AH and FH, and therefore to CE, and FCzzAE, or EI : AE: :JB 

 : CH ; but EI : AE: :ID : AC, therefore IB : CH: :ID ; AC, and 

 the triangles ACH, DIB, are similar, and Z.DBI=:CHAz=DKA, 

 and AD is a parallelogram, consequently KDziABzuCG. 



If the circle CG be supposed to revolve round C, the intersection 

 H will always show the angular distance of the point in which ihe 

 curve crosses the axis ; and the distance of the centres will be equal 

 to the greatest ordinate. If, therefore, the circles are equal, the 

 greatest ordinate will also vary as the chord of an arc increasing 

 equably, or as the ordinate of the harmonic curve. 



