But while the mathematical principles of the Newtonian system were ably expounded in our seats of learning, its physical truths were generally studied, and were explained and communicated to the public by various lecturers on experimental philosophy. The celebrated Locke, who was incapable of understanding the Principia from his want of mathematical knowledge, inquired of Huygens if all the mathematical propositions in that work were true. When he was assured that he might depend upon their certainty, he took them for granted, and carefully examined the reasonings and corollaries deduced from them. In this manner he acquired a knowledge of the physical truths in the Principia, and became a firm believer in the discoveries which it contained. In the same manner he studied the treatise on Optics, and made himself master of every part of it which was not mathematical.[52] From a manuscript of Sir Isaac Newton’s, entitled “A demonstration that the planets, by their gravity towards the sun, may move in ellipses,[53] found among the papers of Mr. Locke, and published by Lord King,” it would appear that he himself had been at considerable trouble in explaining to his friend that interesting doctrine. This manuscript is endorsed, “Mr. Newton, March, 1689.” It begins with three hypotheses (the first two being the two laws of motion, and the third the parallelogram of motion), which introduce the proposition of the proportionality of the areas to the times in motions round an immoveable centre of attraction.[54] Three lemmas, containing properties of the ellipse, then prepare the reader for the celebrated proposition, that when a body moves in an ellipse,[55] the attraction is reciprocally as the square of the distance of the body from the focus to which it is attracted. These propositions are demonstrated in a more popular manner than in the Principia, but there can be no doubt that, even in their present modified form, they were beyond the capacity of Mr. Locke.