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I have been trying, without success, to find a vaguely-remembered quotation: the quadratic equation (or perhaps the quadratic formula), given in (Latin?) prose, along lines like “Consider that quantity, which, when multiplied by itself and under multiplication by the first constant, …”

The purpose is just to contrast with the clarity and compactness of modern algebraic notation — so it doesn’t need to be the quadratic equation or formula, and it doesn’t need to be in Latin; any similar historical quotation to illustrate the point would do.

(Two relevant meta threads: Are history of maths questions acceptable?, and Area 51 proposal: history of science and maths. Also, this question as a sample question on that area 51 proposal.)

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  • $\begingroup$ This discussion has links showing the lengths it took Sluse (1668), Barrow (1670), and Bernoulli (1689) to express $(1+x)^n\geqslant 1+nx$. $\endgroup$
    – Francois Ziegler
    Commented Aug 14, 2017 at 19:17

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This was quite normal before the invention of the modern notation. You can pretty much take any text from the 16th century. Let me give you a somewhat well known example from Stifel's "Arithmetica integra", 1544, p. 240:

Primo. A numero radicum incipe, eumque dimidiatum, loco eius pone dimidium illius, quod in loco suo stet, donec consumata sit tota operatio.

which loosely translates to (my translation)

First. Start with the root number, half it, and put the half in the place, where it should remain, until the whole operation is performed.

so in formulas that would be $$\frac{x}{2}$$ which is a lot shorter. He goes on to explain how to solve quadratic equations in general and even gives a nice Mnemonic to remember how it works: AMASIAS. Here is a picture of the whole passage:enter image description here

I think even Descartes used quite long sentences to explain formulas.

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    $\begingroup$ I object to the last sentence: Descartes is amazingly modern. You can read The Geometry as easily as any modern textbook. $\endgroup$
    – abx
    Commented Feb 24, 2014 at 21:22
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    $\begingroup$ @abx: Really? Check out p. 22 on "the question begun by Euclid", which is awfully hard to understand, despite being advertised by Descartes as a major success of his. ia600200.us.archive.org/19/items/geometryofrene00desc/… $\endgroup$
    – user44143
    Commented Feb 24, 2014 at 21:40
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    $\begingroup$ As to the invention of the modern notation, it is worth recalling that it was initially the result of a natural shortening process of the above mentioned sentences, by brachylogies and shorthands also used elsewhere in writing. For instance, the symbol ${\bf +}$ comes from the letter "t" in "et" after atrophy of "e". The symbol ${\bf \sqrt{}} $ is a lowercase ${\bf r}$ for $root$, and so on. $\endgroup$
    – Pietro Majer
    Commented Feb 25, 2014 at 16:31
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    $\begingroup$ :) A wonderful classic is Florian Cajori's "A History of Mathematical Notation", archive.org/details/historyofmathema031756mbp . I don't know of more recent works; Wikipedia has a nice article with references. $\endgroup$
    – Pietro Majer
    Commented Feb 26, 2014 at 8:29
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    $\begingroup$ If you look up the $\sqrt{}$ symbol in Cajori's book, you will see that it is not derived from an r. Somewhere on MO there is a fuller account of this. $\endgroup$
    – Paul Taylor
    Commented Mar 27, 2014 at 22:40
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A better known figure than the 16th century Stifel is the 17th century Pierre de Fermat who still used notation that was not fully symbolic. Thus, in his work anticipating the calculus, he used the terms aequalitat and adaequalitat rather than the familiar equality symbol. An example may be found in section 8.8 of this text.

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