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Updated: May 20, 2025
Newton began by an assumption that the force which at each instant deflects a planet from its rectilineal course, and makes it describe a curve round the sun, is a force tending directly toward the sun.
In fact, this is the reason why we call the habit of perfected self-mastery by the name which in Greek it bears, etymologically signifying "that which preserves the Practical Wisdom:" for what it does preserve is the Notion I have mentioned, i.e. of one's own true interest, For it is not every kind of Notion which the pleasant and the painful corrupt and pervert, as, for instance, that "the three angles of every rectilineal triangle are equal to two right angles," but only those bearing on moral action.
If the outline be rectilineal, simplicity of law produces symmetry, and variety of result can be attained only at the expense of simplicity in the law. But in curved outlines it frequently happens, that, with equally simple laws, we can obtain much greater variety by dispensing with symmetry; and then, by the canon, we thus obtain the higher beauty.
In the circumference of the circle, then, no two of the points equidistant from the centre can touch each other; and the circumference must be made up of infinite all rectilineal sides joining these points.
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