416.» A Demonstration of 
ing one: geometrical property from another. 
Itis for: their assistance herein, and not from 
any supposed.excellence of the solutions above 
(though most of them are different from 
those of the original authors themselves, ) that 
I have taken the trouble to run through, and 
investigate the 60 Theorems. I believe 1 
may safely say that any person that will take 
the trouble to follow me herein, will find it 
worth his while, and may in a short time, 
from hence find out many times this number 
of theorems of like nature, and equally cu- 
rious with these. And as this may possibly 
fall into the hands of some more learned readers, 
I would wish them to think, whether or no 
this may not possibly be a specimen of a me- 
thod of investigation similar to that of the 
Ancients, which has been a desideratum ever 
since the Saracens burnt the library at Alex-_ 
andria in Egypt. 
Diacram 1.—(Plate IX.) 
Draw ED the perpendicular of the isosceles 
triangle BEC, and:AH through the vertex, 
parallel to the base; from any ‘point A in 
which, draw lines through the extremes of the 
base and perpendicular, viz. AC, AB, AD ; 
and through D, the extreme of the perpen- 
dicular, a line ad libitum, cutting AB in F, 
1 
