“The value of money is in proportion to the quantity of the necessaries of life which it will purchase.”

Source: (1776), Book V, Chapter II, Part II, Article IV.

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Adam Smith175

Scottish moral philosopher and political economist 1723–1790

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“LABOUR, like all other things which are purchased and sold, and which may be increased or diminished in quantity, has its natural and its market price. The natural price of labour is that price which is necessary to enable the labourers, on with another, to subsist and to perpetuate their race, without either increase or diminution.”

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Source: The Principles of Political Economy and Taxation (1821) (Third Edition), Chapter V, On Wages, p. 52

“Of the proportion, which the product of any region bears to the people, an estimate is commonly made according to the pecuniary price of the necessities of life; which is never certain, because it supposes what is far from truth, that the value of money is always the same, and so measures an unknown quantity by an uncertain standard. It is competent enough when the markets of the same country, at different times, and those times not too distant, are to be compared; but of very little use for the purpose of making one nation acquainted with the state of another.”

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“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.”

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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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“On symbolic use of equalities and proportions. Chapter II.
The analytical method accepts as proven the most famous [ as known from Euclid ] symbolic use of equalities and proportions that are found in items such as:
1. The whole is equal to the sum of its parts.
2. Quantities being equal to the same quantity have equality between themselves. [a = c & b = c => a = b]
3. If equal quantities are added to equal quantities the resulting sums are equal.
4. If equals are subtracted from equal quantities the remains are equal.
5. If equal equal amounts are multiplied by equal amounts the products are equal.
6. If equal amounts are divided by equal amounts, the quotients are equal.
7. If the quantities are in direct proportion so also are they are in inverse and alternate proportion. [a:b::c:d=>b:a::d:c & a:c::b:d]
8. If the quantities in the same proportion are added likewise to amounts in the same proportion, the sums are in proportion. [a:b::c:d => (a+c):(b+d)::c:d]
9. If the quantities in the same proportion are subtracted likewise from amounts in the same proportion, the differences are in proportion. [a:b::c:d => (a-c):(b-d)::c:d]
10. If proportional quantities are multiplied by proportional quantities the products are in proportion. [a:b::c:d & e:f::g:h => ae:bf::cg:dh]
11. If proportional quantities are divided by proportional quantities the quotients are in proportion. [a:b::c:d & e:f::g:h => a/e:b/f::c/g:d/h]
12. A common multiplier or divisor does not change an equality nor a proportion. [a:b::ka:kb & a:b::(a/k):(b/k)]
13. The product of different parts of the same number is equal to the product of the sum of these parts by the same number. [ka + kb = k(a+b)]
14. The result of successive multiplications or divisions of a magnitude by several others is the same regardless of the sequential order of quantities multiplied times or divided into that magnitude.
But the masterful symbolic use of equalities and proportions which the analyst may apply any time is the following:
15. If we have three or four magnitudes and the product of the extremes is equal to the product means, they are in proportion. [ad=bc => a:b::c:d OR ac=b2 => a:b::b:c]
And conversely
10. If we have three or four magnitudes and the first is to the second as the second or the third is to the last, the product of the extremes is equal to that of means. [a:b::c:d => ad=bc OR a:b::b:c => ac=b2]
We can call a proportion the establishment of an equality [equation] and an equality [equation] the resolution of a proportion.”

François Viète (1540–1603) French mathematician

From Frédéric Louis Ritter's French Tr. Introduction à l'art Analytique (1868) utilizing Google translate with reference to English translation in Jacob Klein, Greek Mathematical Thought and the Origin of Algebra (1968) Appendix
In artem analyticem Isagoge (1591)

“Buying the necessary or the important is not synonymous with avarice, but with knowing how to give the right value to money.”

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Original: (it) Acquistare il necessario o l'importante non è sinonimo di avarizia, ma di saper dare il giusto valore al denaro.
Source: prevale.net

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Pierre Louis Maupertuis (1698–1759) French mathematician, philosopher and man of letters

Histoire de l'Academie (1744) p. 423; Les Oeuvres De Mr. De Maupertuis (1752) vol. iv p. 17; as quoted by Philip Edward Bertrand Jourdain, The Principle of Least Action https://books.google.com/books?id=y3UVAQAAIAAJ (1913) p. 5.

“The value of money is in proportion to the quantity of the necessaries of life which it will purchase.”

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