the minor directrices D Q in wiB'^oints a, (3. y, 8^ the seg- 

 »i^)t§(k9i(|8^^lMrM£)ik^@&4S£>Cil^d«intl-e, u4m;h(tfm(l(^k^f 



nf ^te tHe. section become^ a cii-^le.^h^ 

 recede to an infinite distance, hence tne lines Ua, Op, Oy, 

 P 8 are parallel respectively to the sides a, b, c, d of the qua- 

 (InfateMf ^cf iMefe^re the an^l^ bfet\^eehi<i'iind «?i's'ti^tiai'ty 

 the anglea O Sj and the angle between c and b e<\ua.) to th§ 

 angle y O jS ; hence we infer, i/iai the opjiositc angles of a qiia-f 

 drilateral inscribed in a circle are togethff^ij^^Qi^J(^ two right 

 angles. ^-^^ 'm\\'\oi^ h6\ ^^i^ti ^'^-i'vt'ovv\V, uoiusv 



V II. When two of the sides of the quadrilateral a and d^ 

 supjxise, are fixed, the point of intersection of b and c upon 

 the curve being variable, the angle /3 O y is constant; or if two 

 fixed points be assumed on a conic section and a third var 

 riable, the cords which pass through the latter and the tw«^ 

 former intercept on one of the minor directrices a segment 

 which subtends at the centre a constant angle; hence we may 

 infer, as in the last proposition, that the angle in a given seg- 



odw 7ru5 oj an (bsaas'iqqua iigad surA gnoiJBiJanoniab adJ ^wsn 

 ni Jas'iami nn aifij odw hnR J^i\&aR ni baa'iav ^(bJB-oborn s'ju 

 Jl .tnad^vfq^js oJ a^uoii aljiil jud avig lliw i'l ^las^dus oih 

 „j.i 1 !. c r. . r. r , ^ ■' i'j79wut[ ;-^nf« 



9 od \n(n aina'io^dt 

 n lo noJJfioifqqij odJ 



i vd ogfi 8*i«3'^ smoa badeil 



C\ 



III. Through the points B B', the extremities of the minor 

 axe in the ellipse, or of the transverse axe in the hyperbola, 

 and any other point P on the curve, let there be drawn two 

 cords meeting one of the minor directrices in the points tttt', 

 the segment tttt' subtends a right angle at the centre; hence 

 the angle in a semicircle is a right angle. ; 



IV. Through the centre of a conic section let two right 

 lines be drawn at right angles to each other, one meeting the 



adjlo 

 -drjq axiw 



