“Although there is no study which presents so simple a beginning as that of geometry, there is none in which difficulties grow more rapidly as we proceed, and what may appear at first rather paradoxical, the more acute the student the more serious will the impediments in the way of his progress appear. This necessarily follows in a science which consists of reasoning from the very commencement, for it is evident that every student will feel a claim to have his objections answered, not by authority, but by argument, and that the intelligent student will perceive more readily than another the force of an objection and the obscurity arising from an unexplained difficulty, as the greater is the ordinary light the more will occasional darkness be felt. To remove some of these difficulties is the principal object of this Treatise.”

Ben Yamen's Song of Geometry (1853)
Context: There is proof enough furnished by every science, but by none more than geometry, that the world to which we have been allotted is peculiarly adapted to our minds, and admirably fitted to promote our intellectual progress. There can be no reasonable doubt that it was part of the Creator's plan. How easily might the whole order have been transposed! How readily might we have been assigned to some complicated system which our feeble and finite powers could not have unravelled!

What is Knowledge? (1971)

A.1, 184a.16 sqq, source: http://classics.mit.edu//Aristotle/physics.html, Book I, Part 1, Tr. R. P. Hardie, R. K. Gaye.
Physics

Source: The Light of Day (1900), Ch. II: From the Artificial to the Natural

Source: On the Study and Difficulties of Mathematics (1831), Chapter I. Introductory Remarks on the Nature and Objects of Mathematics.

The Differential and Integral Calculus (1836)

Source: A System of Logic (1843), p. 4
Context: [W]e may fancy that we see or feel what we in reality infer. Newton saw the truth of many propositions of geometry without reading the demonstrations, but not, we may be sure, without their flashing through his mind. A truth, or supposed truth, which is really the result of a very rapid inference, may seem to be apprehended intuitively. It has long been agreed by thinkers of the most opposite schools, that this mistake is actually made in so familiar an instance as that of the eyesight. There is nothing of which we appear to ourselves to be more directly conscious, than the distance of an object from us. Yet it has long been ascertained, that what is perceived by the eye, is at most nothing more than a variously coloured surface; that when we fancy we see distance, all we really see is certain variations of apparent size, and degrees of faintness of colour; and that our estimate of the object's distance from us is the result of a comparison (made with so much rapidity that we are unconscious of making it) between the size and colour of the object as they appear at the time, and the size and colour of the same or of similar objects as they appeared when close at hand, or when their degree of remoteness was known by other evidence. The perception of distance by the eye, which seems so like intuition, is thus, in reality, an inference grounded on experience; an inference, too, which we learn to make; and which we make with more and more correctness as our experience increases; though in familiar cases it takes place, so rapidly as to appear exactly on a par with those perceptions of sight which are really intuitive, our perceptions of colour.

Author, Third Day. Change of Position<!--p.153 [190]-->
Dialogues and Mathematical Demonstrations Concerning Two New Sciences (1638)
Context: It has been observed that missiles and projectiles describe a curved path of some sort; however no one has pointed out the fact that this path is a parabola. But this and other facts, not few in number or less worth knowing, I have succeeded in proving; and what I consider more important, there have been opened up to this vast and most excellent science, of which my work is merely the beginning, ways and means by which other minds more acute than mine will explore its remote corners.

Source: A Treatise On Political Economy (Fourth Edition) (1832), Book I, On Production, Chapter XV, p. 133 (See also: Say's Law)
Context: A man who applies his labour to the investing of objects with value by the creation of utility of some sort, can not expect such a value to be appreciated and paid for, unless where other men have the means of purchasing it. Now, of what do these means consist? Of other values of other products, likewise the fruits of industry, capital, and land. Which leads us to a conclusion that may at first appear paradoxical, namely, that it is production which opens a demand for products.