“Whereas in Arithmetick Questions are only resolv'd by proceeding from given Quantities to the Quantities sought, Algebra proceeds in a retrograde Order, from the Quantities sought as if they were given, to the Quantities given as if they were sought, to the End that we may some Way or other come to a Conclusion or Æquation, from which one may bring out the Quantity sought.”

— Isaac Newton , book Arithmetica Universalis

Arithmetica Universalis (1707)
Context: Whereas in Arithmetick Questions are only resolv'd by proceeding from given Quantities to the Quantities sought, Algebra proceeds in a retrograde Order, from the Quantities sought as if they were given, to the Quantities given as if they were sought, to the End that we may some Way or other come to a Conclusion or Æquation, from which one may bring out the Quantity sought. And after this Way the most difficult problems are resolv'd, the Resolutions whereof would be sought in vain from only common Arithmetick. Yet Arithmetick in all its Operations is so subservient to Algebra, as that they seem both but to make one perfect Science of Computing; and therefore I will explain them both together.<!--pp.1-2

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Isaac Newton 171

British physicist and mathematician and founder of modern c… 1643–1727

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G. I. Gurdjieff (1866–1949) influential spiritual teacher, Armenian philosopher, composer and writer

Aphorisms

“Assuming… that all available goods of higher order are employed in the most economic fashion, the value of a concrete quantity of a good of higher order is equal to the difference in importance between the satisfactions that can be attained when we have command of the given quantity of the good of higher order whose value we wish to determine and the satisfactions that would be attained if we did not have this quantity at our command.”

Carl Menger (1840–1921) founder of the Austrian School of economics

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“A function of a variable quantity is an analytic expression composed in any way whatsoever of the variable quantity and numbers or constant quantities.”

Leonhard Euler (1707–1783) Swiss mathematician

§4
Introduction to the Analysis of the Infinite (1748)

“Number is different from quantity.”

Gregory Bateson (1904–1980) English anthropologist, social scientist, linguist, visual anthropologist, semiotician and cyberneticist

Source: Mind and Nature, a necessary unity, 1988, p. 118

“When… we have a series of values of a quantity which continually diminish, and in such a way, that name any quantity we may, however small, all the values, after a certain value, are severally less than that quantity, then the symbol by which the values are denoted is said to diminish without limit. And if the series of values increase in succession, so that name any quantity we may, however great, all after a certain point will be greater, then the series is said to increase without limit.”

Augustus De Morgan (1806–1871) British mathematician, philosopher and university teacher (1806-1871)

It is also frequently said, when a quantity diminishes without limit, that it has nothing, zero or 0, for its limit: and that when it increases without limit it has infinity or ∞ or 1&frasl;0 for its limit.
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“Quantities defined in terms of measurements made at the end of the period in question are referred to as ex post; quantities defined in terms of action planned at the beginning of the period in question are referred to as .”

Gunnar Myrdal (1898–1987) Swedish economist

Source: Monetary Equilibrium (1939), p. 34
Context: An important distinction exists between prospective and retrospective methods of calculating economic quantities such as incomes, savings, and investments; and... a corresponding distinction of great theoretical importance must be drawn between two alternative methods of defining these quantities. Quantities defined in terms of measurements made at the end of the period in question are referred to as ex post; quantities defined in terms of action planned at the beginning of the period in question are referred to as.

“There are, in fact, as I began to say above, not a few principles which are the special property of mathematics, such principles as are discovered by the common light of nature, require no demonstration, and which concern quantities primarily; then they are applied to other things, so far as the latter have something in common with quantities. Now there are more of these principles in mathematics than in the other theoretical sciences because of that very characteristic of the human understanding which seems to be such from the law of creation, that nothing can be known completely except quantities or by quantities. And so it happens that the conclusions of mathematics are most certain and indubitable.”

Johannes Kepler (1571–1630) German mathematician, astronomer and astrologer

Vol. VIII, p. 148
Joannis Kepleri Astronomi Opera Omnia, ed. Christian Frisch (1858)

Augustus De Morgan (1806–1871) British mathematician, philosopher and university teacher (1806-1871)

Introductory Chapter, pp.9-10
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“An important distinction exists between prospective and retrospective methods of calculating economic quantities such as incomes, savings, and investments; and… a corresponding distinction of great theoretical importance must be drawn between two alternative methods of defining these quantities. Quantities defined in terms of measurements made at the end of the period in question are referred to as ex post; quantities defined in terms of action planned at the beginning of the period in question are referred to as ex ante.”

Gunnar Myrdal (1898–1987) Swedish economist

Source: Monetary Equilibrium (1939), p. 34

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Isaac Newton 171

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