“Over and above the specific theorems created by men such as Desargues, Pascal and La Hire, several new ideas and outlooks were beginning to appear. The first is the idea of continuous change of a mathematical entity from one state to another… [i. e., of a] a geometrical figure. It was Kepler, in his Astronomiae Optica of 1604, who first seemed to grasp the fact that parabola, ellipse, hyperbola, circle, and the degenerate conic consisting of a pair of lines are continuously derivable from each other…. The notion of a continuous change in a figure was also employed by Pascal. He allowed two consecutive vertices of his hexagon to approach each other so that the figure became a pentagon. In the same manner he passed from pentagons to quadrilaterals.
The second idea to emerge from the work of the projective geometers is that of transformation and invariance. To project a figure from some point and then take a section of that projection is to transform the figure to a new one. The properties… of interest are those that remain invariant under transformation. Other geometers of the seventeenth century, for example, Gregory of St. Vincent… and Newton, introduced transformations other than projection and section.”

Source: Les Misérables

The Method of Mechanical Theorems

p, 125
Arithmetica Universalis (1707)

On War (1832), Book 3

The Law of Mind (1892)

From Italian: La filosofia è scritta in questo grandissimo libro, che continuamente ci sta aperto innanzi agli occhi (io dico l'Universo), ma non si può intendere, se prima non il sapere a intender la lingua, e conoscer i caratteri ne quali è scritto. Egli è scritto in lingua matematica, e i caratteri son triangoli, cerchi ed altre figure geometriche, senza i quali mezzi è impossibile intenderne umanamente parola; senza questi è un aggirarsi vanamente per un oscuro labirinto.
Other translations:
Philosophy is written in that great book which ever lies before our eyes — I mean the universe — but we cannot understand it if we do not first learn the language and grasp the symbols, in which it is written. This book is written in the mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.
The Assayer (1623), as translated by Thomas Salusbury (1661), p. 178, as quoted in The Metaphysical Foundations of Modern Science (2003) by Edwin Arthur Burtt, p. 75.
Philosophy is written in this grand book — I mean the universe — which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering about in a dark labyrinth.
As translated in The Philosophy of the Sixteenth and Seventeenth Centuries (1966) by Richard Henry Popkin, p. 65
Il Saggiatore (1623)
Source: Galilei, Galileo. Il Saggiatore: Nel Quale Con Bilancia Efquifita E Giufta Si Ponderano Le Cofe Contenute Nellalibra Astronomica E Filosofica Di Lotario Sarsi Sigensano, Scritto in Forma Di Lettera All'Illustr. Et Rever. Mons. D. Virginio Cesarini. In Roma: G. Mascardi, 1623. Google Play. Google. Web. 22 Dec. 2015. <https://play.google.com/store/books/details?id=-U0ZAAAAYAAJ>.

Source: Mathematics and the Physical World (1959), pp. 224-225

Source: Disturbing the Peace (1986), Ch. 1 : Growing Up "Outside", p. 12

Curriculum Vitae (1843)
Context: What attracted me so strongly and exclusively to mathematics, apart from the actual content, was particularly the specific nature of the mental processes by which mathematical concepts are handled. This way of deducing and discovering new truths from old ones, and the extraordinary clarity and self-evidence of the theorems, the ingeniousness of the ideas... had an irresistible fascination for me. Beginning from the individual theorems, I grew accustomed to delve more deeply into their relationships and to grasp whole theories as a single entity. That is how I conceived the idea of mathematical beauty...