William John Macquorn Rankine quote: “[T]he symbols of algebra, when employed in abstruse and complex theoretical investigations, constitute a sort of though…”

“When we speak of the early history of algebra it is necessary to consider… the meaning of the term. If… we mean the science that allows us to solve the equation ax^2 + bx + c = 0, expressed in these symbols, then the history begins in the 17th century; if we remove the restriction as to these particular signs, and allow for other and less convenient symbols, we might properly begin the history in the 3rd century; if we allow for the solution of the above equation by geometric methods, without algebraic symbols of any kind, we might say that algebra begins with the Alexandrian School or a little earlier; and if we say that we should class as algebra any problem that we should now solve with algebra (even though it was as first solved by mere guessing or by some cumbersome arithmetic process), the the science was known about 1800 B. C., and probably still earlier.<”

David Eugene Smith (1860–1944) American mathematician

Source: History of Mathematics (1925) Vol.2, Ch. 6: Algebra, p. 378

“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. 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 1⁄0 for its limit.”

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

Introductory Chapter, pp.9-10
The Differential and Integral Calculus (1836)

“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

“Not bodies produce sensations, but element-complexes (sensation-complexes) constitute the bodies. When the physicist considers the bodies as the permanent reality, the `elements' as the transient appearance, he does not realise that all `bodies' are only mental symbols for element-complexes”

Ernst Mach (1838–1916) Austrian physicist and university educator

sensation-complexes
Source: 20th century, The Analysis of Sensations (1902), p. 23, as quoted in Lenin as Philosopher: A Critical Examination of the Philosophical Basis of Leninism (1948) by Anton Pannekoek, p. 33

“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.
The Differential and Integral Calculus (1836)