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If a fquare APCO be circumfcribed about a quadrant ACO, P>^«.« ^'T- 

 and the radius AO be divided into any number of equal parts 

 whatfoever, and on thefe parts redanglcs as moBD de erected, 

 and infcribed in the quadrant, and through the extremities of the 

 ordinates nm, BD, right lines tp. rB be drawn parallel to 

 the radius AO, and thus as many correfponding redangles, as 

 rBtp, be infcribed in the exterior fpace : then the breadth of 

 thefe redangles being diminifhed indefinitely, each reflangle in 

 the quadrant will be to its correfponding redangle in the ex- 

 terior fpace as DR to DO, that is, as the fum of the radius 

 AO and the fegment DO between the centre and ordinate to 

 that fegment. 



Let the abfciffe AD=X ; the ordinate BD^Yj the dia- 

 meter AR=a. 



Y*=aX-X\ from the nature of the circle. 



Therefore 2Yy=ax-2Yx (Lem. 2. B. 2. Prin.), y=-^ 



2aX~X''2 ' 



but- moBD is to Brpt as Yx to Xy. 



aXx-2X'x; 



that is, as Yx to 

 that is, as Y to 



aaX^x^i 



aX-2X^ 



aaXTx^i 



that is, as fkX-X^w to -7^" 



2''aX-X1^ 



that is, as aaX-zX* to aX_2X* 



or, as a-X to ia-X, or as DR to DO. 



In 



