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I guess the use of arrows to visualise vectors came before the general notion of vectors, so a more precise question is: when where arrows first used to visualise physical (or mathematical) quantities which are nowadays considered to be vectors? For instance: when where arrows first used to visualise forces, velocities, tuples of numbers etc.? And were there ever competing ways to visualise vectors?

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    $\begingroup$ Good question. Neither pseudo-Aristotle in Mechanics, nor Newton in Principia used arrows where we would. Possibly, it originated with Monge's technical drawing and then spread in 19th century. I'd consult Booker's History of Engineering Drawing, but I do not have access to it. $\endgroup$
    – Conifold
    Commented Sep 13, 2023 at 10:50

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