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with a describing point. If it move for the least interval in a straight line, so far the line is not curved; if it begins to bend before it has traced the least portion of a line, it has nothing from which to bend or curve. It must begin to move and curve at once, and an image of this the fancy can not form. Even a point, in order that progress may be made by passing through it, must have some breadth, and this breadth, if it is to give an initiatory direction from which the curve is to depart, must be straight. In analytic conception we resolve the descriptive process into motion and departure, or bending from that motion; we can not conceive these two to be absolutely and constantly synchronous, yet without this the circle is imperfect. The imagination follows after the hand and eye, and as these are not exact, neither is it.

Lesson 56 - 14. Criteria of regulative ideas - p.254

14. Having presented the twelve intuitive ideas which constitute the mind's intellectual furniture, and also the grounds of proof in each case, we propose further to draw attention to some considerations which belong to all of them, establishing their character, and separating them from generalizations. Necessity and universality have been fixed on as the criteria of these notions. The two tests are liable to be mistaken for one, and are so under a certain rendering of them. To distinguish these from each other, we should understand by necessity, that certainty of conviction which attaches in all minds to truths purely dependent on intuitive ideas. Thus there are in the definitions and axioms of Geometry many secondary intuitions, referable to the primary intuition, space. From these there spring convictions, in the certainty with which the mind receives them, wholly unlike those dependent on experience. That two straight lines, lying in the same plane, and for a space equally distant, will remain so through their entire length, is an assertion which the mind accepts at