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At the mention of dead-lights, the meaning of which he did not understand, the poor governor's heart died within him: he shivered with despair, his recollection forsaking him, he fell upon his knees in the bed, and, fixing his eyes upon the book which was in his hand, began to pronounce aloud with great fervour, "The time of a complete oscillation in the cycloid, is to the time in which a body would fall through the axis of the cycloid DV, as the circumference of a circle to its diameter."
Then also as 3 to 2 will the sum of the one set be to the sum of the other; that is to say, TF to AS, and DE to AK, and BE to SK or DV, supposing V to be the intersection of the curve EK and the ray FO. But, making FB perpendicular to DE, the ratio of 3 to 2 is also that of BE to the semi-diameter of the spherical wave which emanated from the point F while the light outside the transparent body traversed the space BE. Then it appears that this wave will intersect the ray FM at the same point V where it is intersected at right angles by the curve EK, and consequently that the wave will touch this curve.
All that you mean to say, therefore, is that the present state of the system is defined by equations into which differential coefficients enter, such as ds|dt, dv|dt, that is to say, at bottom, present velocities and present accelerations. You are therefore really speaking only of the present a present, it is true, considered along with its tendency.
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