_Positive Philosophy [Martineau], Bk. 1, chap. 1._ =1438.= The great advantage of the mathematical sciences over the moral consists in this, that the ideas of the former, being sensible, are always clear and determinate, the smallest distinction between them being immediately perceptible, and the same terms are still expressive of the same ideas, without ambiguity or variation. An oval is never mistaken for a circle, nor an hyperbola for an ellipsis. The isosceles and scalenum are distinguished by boundaries more exact than vice and virtue, right or wrong. If any term be defined in geometry, the mind readily, of itself, substitutes on all occasions, the definition for the thing defined: Or even when no definition is employed, the object itself may be represented to the senses, and by that means be steadily and clearly apprehended. But the finer sentiments of the mind, the operations of the understanding, the various agitations of the passions, though really in themselves distinct, easily escape us, when surveyed by reflection; nor is it in our power to recall the original object, so often as we have occasion to contemplate it. Ambiguity, by this means, is gradually introduced into our reasonings: Similar objects are readily taken to be the same: And the conclusion becomes at last very wide off the premises.--HUME, DAVID. _An Inquiry concerning Human Understanding, sect. 7, part 1._ =1439.= One part of these disadvantages in moral ideas which has made them be thought not capable of demonstration, may in a good measure be remedied by definitions, setting down that collection of simple ideas, which every term shall stand for; and then using the terms steadily and constantly for that precise collection. And what methods algebra, or something of that kind, may hereafter suggest, to remove the other difficulties, it is not easy to foretell. Confident, I am, that if men would in the same method, and with the same indifferency, search after moral as they do mathematical truths, they would find them have a stronger connexion one with another, and a more necessary consequence from our clear and distinct ideas, and to come nearer perfect demonstration than is commonly imagined.--LOCKE, JOHN. _An Essay concerning Human Understanding, Bk. 4, chap. 3, sect. 20._ =1440.= That which in this respect has given the advantage to the ideas of quantity, and made them thought more capable of certainty and demonstration [than moral ideas], is,