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point B) the angle between the course of the bodyand the line drawn from S continues to diminish, andat b this angle has its minimum value, S b a. Atthis point b, the body has recovered a portion of thevelocity it had lost, but its distance has diminished,and its course is now directed as nearly towards thebody at S as it can possibly be. After passing b thecontinual access of velocity, owing to the sun’s at-tracting force, causes the body to travel on a courseinclined at a continually increasing angle to the linefrom S, but the distance of the body continues todiminish, until at A, where the angle between thecourse of the body and the line from S is again aright angjle, the distance is reduced to the minimumvalue S A, as at first. All the circumstances are nowthe same as when the motion began.
It is to be noticed of the above explanation, thatthough it does not prove that an ellipse must bedescribed, it shows that the description of an ellipsecorresponds with the circumstances of the case,—that,in fact, in each quadrant of the ellipse forces tendingto produce motion in a curve of such a shape, are inoperation. This is all that can be done by way ofpopularly explaining a proposition whose inherentdifficulty is Such that eminent mathematicians likeWren and Halley failed to solve it.* But the above
* It has "been objected even that Newton’s demonstration isimperfect inasmuch as it only shows that the curvature at anypoint of a conic section corresponds with that due to the law offorce according to the inverse squares of the distances. But taken