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( 444 J 
fho. Godfrey therefore confidering this, applied 
himfelf to find out fome Contrivance by which the 
Neceflity of bringing the Rays from the Sun, and 
thofe from the Horizon to coincide (which is the 
imoft difficult part of the Work) on one particular 
Point or Line from the Centre, might be removed. 
In order to which he confideFd, that by the xi. 3* 
Elem. of Euch all Angles at the Periphery of a Circle, 
fubtended by the fame Segment within it are equal, 
on whatever part of the Circumference the angular 
Point falls $ and therefore, if inftead of a Quadrant, a 
Semicircle were graduated into 90 Degrees only, ac- 
counting every two Degrees but one ; this would effe- 
ctually anfwer: For then, if an Arch of the fame 
Circle were placed at the End of the Diameter of the 
Inftrument, every Part of that oppofite Arch would 
equally ferve for taking the Coincidence of the Rays 
above-mentioned. But fuch an ’Inftrument would ma- 
nifeftly be attended with great Inconveniencies ; for it 
would in great Altitudes be much more unmanageable* 
and the Vanes could not be framed to Hand, as they 
always ought, perpendicular to the Rays. He there- 
fore further refolved to try whether a Curve could 
not be found to be placed at the Centre of a Qua- 
drant, which would, at leaft for a Length fufficient 
. to catch the Coincidence of the Rays, with Eafe ful- 
ly anfwer the Intention. 
A Curve that in all the Parts of it would in geo- 
metrical ftriffnefs effeft this, cannot be in Nature, 
any more than that one and the fame Point can be - 
found for a Centre to different Circles, which are 
not concentric. It is certain that every Arch on 
the Limb may have a -Circle that will pafs through 
the 
