The Operations of the Geometric and Military Compass

and measure it directly, and you will find 80, which is the number sought; where it must be equally noted that we will find the same result by applying the second directly to the third transversally, and then measuring directly the first taken transversally. One must, besides this, note that all the warnings placed above concerning the rule of three must still be observed precisely in this one as well.

Rule for transmuting currencies.

Operat. VI.

With the help of these same arithmetic lines, we can transmute every species of money into another in a very easy and fast manner. This will be accomplished by first adjusting the instrument, taking directly the price of the money we wish to transmute, and accommodating it transversally to the price of that into which the transmutation is to be made. As, so that everything is understood more distinctly, we will declare with an example: we wish, for example, to transmute gold scudi into Venetian ducats, and because the price or value of the gold scudi is 8 lire, and the value of the ducat is 6 lire and 4 soldi, it is necessary (since the ducat is not measured precisely by the lire, as there are four soldi in it) to resolve one and the other currency, and evaluate it in soldi, considering how the price of the scudo is 160 soldi, and that of the ducat is 124. To adjust the instrument then for the transmutation of gold scudi into ducats, take directly the value of the scudo, that is 160, and apply it, opening the instrument, transversal-