TROELEMS. 



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PROBLEM XVII, 

 ^0 find a mean Proporirjua! betivccji tivo given Lines K B, B C 



Join A B and B C in one A — 

 straight line AC, and bisect ■^'~~ 

 it in the pvoint o. With the 

 centre o, and radius o A or 

 o C, descrijbe a semicircle. 

 Erect the perpendicular BD, 

 »nd it will be the mean pro- j\ '— 

 portional required. 



That is, AB ; BD : : BD : BC. 



B 



-C 



b ii 



PROBLEM XVIIT. 

 To divide a Line A B in Extreme and Mean Ratis. 



Raise B C perpendicular to A B, 

 and equal to half A B. Join A C. 

 With centre C, and radius C B, 

 cross AC in D. Lastly, with cen- 

 tre A, and radius A D, crois A B 

 in E, which will divide the line A 

 B in extreme and mean ratio, name- 

 ly, so that the whole line is to the 

 greater part, as the greater part is 

 to the less part. 



That is, AB : AE 



Ail : Ljj. 



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Ccc 



PROBLEM 



