=1441.= It has been generally taken for granted, that mathematics alone are capable of demonstrative certainty: but to have such an agreement or disagreement as may be intuitively perceived, being, as I imagine, not the privileges of the ideas of number, extension, and figure alone, it may possibly be the want of due method and application in us, and not of sufficient evidence in things, that demonstration has been thought to have so little to do in other parts of knowledge, and been scarce so much as aimed at by any but mathematicians. For whatever ideas we have wherein the mind can perceive the immediate agreement or disagreement that is between them, there the mind is capable of intuitive knowledge, and where it can perceive the agreement or disagreement of any two ideas, by an intuitive perception of the agreement or disagreement they have with any intermediate ideas, there the mind is capable of demonstration: which is not limited to the idea of extension, figure, number, and their modes.--LOCKE, JOHN. _An Essay concerning Human Understanding, Bk. 4, chap. 2, sect. 9._ =1442.= Now I shall remark again what I have already touched upon more than once, that it is a common opinion that only mathematical sciences are capable of a demonstrative certainty; but as the agreement and disagreement which may be known intuitively is not a privilege belonging only to the ideas of numbers and figures, it is perhaps for want of application on our part that mathematics alone have attained to demonstrations. --LEIBNITZ. _New Essay concerning Human Understanding, Bk. 4, chap. 2, sect. 9 [Langley]._ CHAPTER XV MATHEMATICS AND SCIENCE =1501.= How comes it about that the knowledge of other sciences, which depend upon this [mathematics], is painfully sought, and that no one puts himself to the trouble of studying this science itself? I should certainly be surprised, if I did not know that everybody regarded it as being very easy, and if I had not long ago observed that the human mind, neglecting what it believes to be easy, is always in haste to run after what is novel and advanced.--DESCARTES. _Rules for the Direction of the Mind; Philosophy of Descartes [Torrey], (New York, 1892), p. 72._