When John Napier and Joost Burgi developed logarithms in the 16th century, they succeeded in replacing long, tedious, error-prone multiplications with table-look-up and addition, giving other mathematicians the benefit of their stored work in the form of their extensive tables.

So what makes this better than developing extensive multiplication tables, which would replace multiplication with table-look-up only, instead of table-look-up and addition, as with logarithms?

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    $\begingroup$ The time it would take to compose those tables and to leaf through them, and the space it would take to print them? You'd need square tables instead of just a pair of columns. $\endgroup$ – Conifold Jul 5 '19 at 23:57

I am explaining the comment of Conifold. The main point is that log tables tabulate a function of ONE variable. For example, Napier's original table is organized in 1230 lines and occupies 41 pages (30 lines per page). And it permits interpolation. Imagine a similar table for a function of TWO variables. Calculation of such a table by hand is impossible, and its use is impractical. The sheer volume will be like 1230 of Napier's volumes. Not even mentioning interpolation.

  • $\begingroup$ Thanks Alexandre and Conifold. I came to a similar conclusion after posting the question. $\endgroup$ – mjc Jul 6 '19 at 12:27

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