( 445 ) 
tTie Center, and be a Locus or geometrical Place for 
the Angle made by that Arch to fall on : but then 
every Arch has a different one from all others ; as 
in the Figure. Let ABC be the Quadrant:, and 
A B, E F, G H be taken as Arches of it : Circles 
drawn through each two of thefe refpe&ively, and 
through the Center C as a third Point, will manifeft- 
ly be fuch Loci or Places: For every Pair of thefe 
Points Hand in a Segment of their own Circle, as 
well as on a Segment of the Quadrant ; and therefore 
by the cited ai. 3 *-Elem. the Angles Handing on thefe 
•firft Segments will every where be equal at ‘the 
Periphery of their refpedive Circles, and their Radius 
will always be equal to half the Secant of half the 
Arch on the Quadrant. For in the Circle CED F 
(for Infiance) the Angle CED is right, becaufe ’tis 
in a Semicircle, CE is the Radius of the Qitadranr, 
c 
A 
ED 
