Jacques Ozanam quote: “Mathematicks therefore is a Science which teaches or contemplates whatever is capable of Measure or Number as such. Whe…”

“I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of science, whatever the matter may be.”

William Thomson (1824–1907) British physicist and engineer

Lecture on "Electrical Units of Measurement" (3 May 1883), published in Lectures Vol. I, p. 73 https://archive.org/stream/popularlecturesa01kelvuoft#page/73/mode/1up|Popular

“To investigate the essence of a natural phenomenon, three conditions are necessary: We must first study and know the phenomenon itself, from all sides; we must then determine in what relation it stands to other natural phenomena; and lastly, when we have ascertained all these relations, we have to solve the problem of measuring these relations and the laws of mutual dependence—that is, of expressing them in numbers. In the first period of chemistry, all the powers of men's minds were devoted to acquiring a knowledge of the properties of bodies; it was necessary to discover, observe, and ascertain their peculiarities. This is the alchemistical period. The second period embraces the determination of the mutual relations or connections of these properties; this is the period of phlogistic chemistry. In the third period, in which we now are, we ascertain by weight and measure and express in numbers the degree in which the properties of bodies are mutually dependent. The inductive sciences begin with the substance itself, then come just ideas, and lastly, mathematics are called in, and with the aid of numbers, complete the work.”

Justus von Liebig (1803–1873) German chemist

Familiar Letters on Chemistry, Tr. Blythe, 4th ed., London, 1859, p. 60 as quoted by John Theodore Merz, A History of European Thought in the Nineteenth Century Vol.1 http://books.google.com/books?id=xqwQAAAAYAAJ (1903).

“Cause, Principle, and One eternal
From whom being, life, and movement are suspended,
And which extends itself in length, breadth, and depth,
To whatever is in Heaven, on Earth, and Hell;
With sense, with reason, with mind, I discern,
That there is no act, measure, nor calculation, which can comprehend
That force, that vastness and that number,
Which exceeds whatever is inferior, middle, and highest;
Blind error, avaricious time, adverse fortune,
Deaf envy, vile madness, jealous iniquity,
Crude heart, perverse spirit, insane audacity,
Will not be sufficient to obscure the air for me,
Will not place the veil before my eyes,
Will never bring it about that I shall not
Contemplate my beautiful Sun.”

Giordano Bruno (1548–1600) Italian philosopher, mathematician and astronomer

"Of Love" as translated in The Infinite in Giordano Bruno : With a Translation of His Dialogue, Concerning the Cause, Principle, and One (1978) by Sidney Thomas Greenburg, p. 89
Variant translation:
Cause, Principle and One, the Sempiterne,
On whom all being, motion, life, depend.
From whom, in length, breadth, depth, their paths extend
As far as heaven, earth, hell their faces turn :
With sense, with mind, with reason, I discern
That not, rule, reckoning, may not comprehend
That power and bulk and multitude which tend
Beyond all lower, middle, and superne. Blind error, ruthless time, ungentle doom,
Deaf envy, villain madness, zeal unwise,
Hard heart, unholy craft, bold deeds begun,
Shall never fill for one the air with gloom,
Or ever thrust a veil before these eyes,
Or ever hide from me my glorious sun.
As quoted in "Giordano Bruno" by Thomas Davidson, The Index Vol. VI. No. 36 (4 March 1886), p. 429
Cause, Principle, and Unity (1584)

“The Essential Parts of the Simple or Pure Mathematicks are Arithmetick and Geometry, which mutually assist one another, and are independent on any other Sciences, except perhaps on Artificial Logick: But doubtless Natural Logick may be sufficient to a Man of Sense. The other parts are chiefly Physical Subjects explained by the Principles of Arithmetics or Geometry.”

Jacques Ozanam (1640–1718) French mathematician

Source: A Mathematical Dictionary: Or; A Compendious Explication of All Mathematical Terms, 1702, p. 2, The introduction

“The success of a relationship should be measured by its depth, not by its length.”

Neil Strauss book The Truth: An Uncomfortable Book About Relationships

The Truth: An Uncomfortable Book About Relationships (2015)

“Every measurable thing except numbers is imagined in the manner of a continuous quantity. Therefore, for the mensuration of such a thing, it is necessary that points, lines, and surfaces, or their properties, be imagined. For in them… measure or ratio is initially found… Therefore, every intensity which can be acquired successively ought to be imagined by a straight line perpendicularly erected on some point of the space or subject of the intensible thing, e. g., a quality… And since the quantity or ratio of lines is better known and is more readily conceived by us—nay the line is in the first species of continua, therefore such intensity ought to be imagined by lines… Therefore, equal intensities are designated by equal lines, a double intensity by a double line, and always in the same way if one proceeds proportionally.”

Nicole Oresme (1323–1382) French philosopher

Tractatus de Configurationibus et Qualitatibus et Motuum (c. 1350)

“A prime number is one (which is) measured by a unit alone.”

Euclid book Elements

Elements, Book 7, Definition 11 (12 in certain editions)
Euclid’s Elements

“A life isn't measured in hours and minutes. It's the quality, not the length.”

Gabrielle Zevin book Elsewhere

Source: Elsewhere

“Individuality is the capacity for union. The measure of individuality is the depth and breadth of true relation. I am an individual not as far as I am apart from, but as far as I am a part of other men. Evil is non-relation.”

Mary Parker Follett The New State

Source: The New State, 1918, p. 62

“Cause, Principle, and One eternal
From whom being, life, and movement are suspended,
And which extends itself in length, breadth, and depth,
To whatever is in Heaven, on Earth, and Hell”

Giordano Bruno (1548–1600) Italian philosopher, mathematician and astronomer

"Of Love" as translated in The Infinite in Giordano Bruno : With a Translation of His Dialogue, Concerning the Cause, Principle, and One (1978) by Sidney Thomas Greenburg, p. 89
Variant translation:
Cause, Principle and One, the Sempiterne,
On whom all being, motion, life, depend.
From whom, in length, breadth, depth, their paths extend
As far as heaven, earth, hell their faces turn :
With sense, with mind, with reason, I discern
That not, rule, reckoning, may not comprehend
That power and bulk and multitude which tend
Beyond all lower, middle, and superne. Blind error, ruthless time, ungentle doom,
Deaf envy, villain madness, zeal unwise,
Hard heart, unholy craft, bold deeds begun,
Shall never fill for one the air with gloom,
Or ever thrust a veil before these eyes,
Or ever hide from me my glorious sun.
As quoted in "Giordano Bruno" by Thomas Davidson, The Index Vol. VI. No. 36 (4 March 1886), p. 429
Cause, Principle, and Unity (1584)
Context: Cause, Principle, and One eternal
From whom being, life, and movement are suspended,
And which extends itself in length, breadth, and depth,
To whatever is in Heaven, on Earth, and Hell;
With sense, with reason, with mind, I discern,
That there is no act, measure, nor calculation, which can comprehend
That force, that vastness and that number,
Which exceeds whatever is inferior, middle, and highest;
Blind error, avaricious time, adverse fortune,
Deaf envy, vile madness, jealous iniquity,
Crude heart, perverse spirit, insane audacity,
Will not be sufficient to obscure the air for me,
Will not place the veil before my eyes,
Will never bring it about that I shall not
Contemplate my beautiful Sun.

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