3A Review of the Principia of Newteu. 
root of the equation, consequently the n r of the roots 
will be infinite, ation only of infinite dimensions 
will express that number. The area, there in relation 
« 
cendental curve, assumed by our author, is the cycloid; but 
apparently sensible « i 
analytical solution of this famous problem, with a reference 
to the improvement of that sublime science, which appeared 
most to attract him. This has been made more practical by 
Dr. Keil, by reducing our author’s principles to a form more 
susceptible of logarithmic calculation. But even this solu« 
tion, if facility of theory and practice both be regarded, may 
be still further simplified ; for, suppose x to be the eccentric 
anomaly to the radius a, and 6 the eccentricity, or the dis- 
‘tance of the focus from the centre of the ellipse,-we shall 
then have Sin. 6 x + a «=A, the arc of the circle represent 
ing the mean anomaly, which is given. By reducing Sin. 
bx to terms of the arc x, by the known series for that pur- 
pose, and by reverting the series the value of x, the eccen- 
tric anomaly will be | n, from which the true or co- 
ard supposes the angles to be equally described about the 
focus of the ellipse, This has been shown, by Bulli- 
