Kepler, having discovered the laws that regulate the motion of a planet in its orbit, proposed the following problem, for determining the true place of a planet at any given time: “To draw a straight line DE, from an eccentric point D in the diameter of a semicircle AEB, so that the whole semicircle may be to the sector ADE, in a given ratio.”

In resolving this problem, we are to take the quadrature of the circle for granted: and therefore, if C be the centre of the circle, and if the sector ACM be taken, such, that the whole semicircle is to the sector ACM in the required given ratio, the problem may be otherwise enunciated: “ To draw a straight “ line DE from an eccentric point D, to cut off a sector ADE, that shall be equal to the given sector ACM.”