gp:ometry. 369 



in H, and with H E or H G, as radius, describe 

 the semicircle E I G. From F draw F I perpen- 

 dicular to E G, cutting' the circle in I ; and I F 

 will be the mean proportional required. 



Proh. 26. To describe an ellipsis. 



If two pins are fixed at the points E and F, a 

 string put about them, and the ends tied together 

 at C ; the point C being moved round, keeping 

 the string stretched, will describe an ellipsis. 



The points E and F, where the pins were fixed, 

 are called theyoa. 



The line A B passing through the foci, is called 

 the transverse axis. 



The point G bisecting the tranverse axis, is the 

 centre of the ellipsis. 



The line C D crossing this centre at right-angles 

 to the tranverse axis, is the conjugate axis. 



The latus rectum is a right line passing through 

 the focus at F, at right angles to the transverse 

 axis terminated by the curve : this is also called 

 the parameter. 



A diameter is any line passing through the 

 centre, and terminated by the curve. 



A coiyugate diameter to another diameter is a 

 line drawn through the centre, parallel to a tan- 

 gent at the extreme of the other diameter, and 

 terminated by the curve. 



A double ordinate is a line drawn through any 

 diameter parallel to a tangent, at the extreme of 

 that diameter terminated by the curve. 



The transverse axis A B, and conjugate axis 

 C D, of any ellipsis, being given, to find the two 

 foci, and from thence to describe the ellipsis. 



Take the semi-transverse A E, or E B, and from 

 C as a centre, describe an arc cutting A B at F 

 and G ; these are the foci. Fix pins in these 



VOL. II. * p B 



