# Quotes from Oughtred's Circles of Proportion

In his book ``The Circles of Proportion and the Horizontal Instrument" London (1632) Oughtred describes two instruments. The first, with the most detailed explanation, is the Circle of Proportion. This is an early form of slide rule. The second is a type of sundial. An example of such a circle can be found in the Oxford Museum of Science.

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This is a large brass disk inscribed with a number of concentric circles. On top of this are two pointers which are fixed to the centre and are free to rotate. The circle of proportion, then, is simply a circular logarithmic scale on which a pair of compasses have been laid flat, with a pivot at the centre. In Oughtred's instrument the moving parts were not circles, but the pointers, which could be used either together with friction holding them, or separately by applying an appropriate amount of pressure. Both sides are marked with scales, one side for trigonometrical calculations and the other for settling questions relating to spherical trigonometry. Oughtred writes

The fifth circle is of equal numbers noted with 1,...,9,0. This fifth circle serveth for finding logarithmes of the true numbers upon the forth circle.
Oughtred writes, ``Numbers are multiplies by addition of their logarithms; and they are divided by subtraction of their logarithms", which reads no differently that a modern text book. One pointer is referred to as the antecedent arm and the other as the consequent arm. To use the instrument, which in modern notation is to solve for x in, ,a/b = c/x, Oughtred writes,
Open the Armes of the Instrument to the distance of the first and second numbers; then bring the Antecedent arme, or that which stood upon the first number unto the third and so the consequent arme, keeping the same opening, will shew the forth number sought for.
Circles of Proportion (1632)

[Slide rule page] [Chris Sangwin]