Does anyone know where the proportionality symbol $ \propto $ originates from (historically)?

As someone who is eager to learn about the history of physics & mathematics, this question popped into my mind out of the blue. I can't seem to find the answer on Wikipedia, so here I am asking you guys (and girls).

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    $\begingroup$ I'm voting to close this question as off-topic because it's about the origin/history of mathematical notation and not physics. History of Science and Mathematics might be more appropriate. $\endgroup$ – Kyle Kanos Jun 15 '18 at 12:45
  • $\begingroup$ Thanks for the information. I'll delete the post as soon as my "cool down" for posting questions is over! $\endgroup$ – Markus Hays Jun 15 '18 at 12:55

The proportionality symbol was first used by William Emerson in his “Doctrine of Fluxions,” (3rd ed., London, 1768) [1].

He says on p. 4:—“To the common Algebraic Characters already received I add this”, which signifies a general Proportion; thus, A∝BC/D, signifies that A is in a constant Ratio to BC/D; that is (if a, b, c, d be other Values of these Quantities) A:BC/D::a:bc/d; and thus every general Proportion is to be understood.”

Prior to this a double colon (::) was used, as seen in the quoted text (line 3 - A:BC/D::a:bc/d ). The double colon is described in Jeff Miller's "Earliest Uses of Symbols of Relation":

Proportion. The symbol :: was introduced by William Oughtred (1574-1660) in Clavis Mathematicae, composed about 1628 and published in London in 1631. He wrote a proportion as a.b::c.d (Gullberg) [2].

The astronomer Vincent Wing (1619-1668) used colons to write a proportion in the modern notation, as A:B::C:D, in 1651 in Harmonicon Celeste (Cajori vol. 1, page 286) [3].

The symbol for variation (an eight lying on its side with a piece removed) was introduced in 1768 by W. Emerson in Doctrine of Fluxions (3d ed., London) (Cajori vol. 1, page 297) [3].

[1] Cajori, Florian. Origin of a Mathematical Symbol for Variation. Nature 95(562) (22 July 1915).

[2] Gullberg, Jan. Mathematics: From the Birth of Numbers. New York: W. W. Norton & Co., 1997.

[3] Cajori, Florian. A History of Mathematical Notations. 2 volumes. Lasalle, Illinois: The Open Court Publishing Co., 1928-1929.


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