Operations of the Geometric and Military Compass

catchword: rare

the same rule in very small numbers, although on the Instrument the points from 15 downwards could not be noted because of the nut that joins and connects the legs of the Instrument. But on this occasion, we will use the tens of the points as if they were units, so that, saying for example if 10 gives 7, what will 13 give? Not being able to take 7 to throw it at 10, we will take 70, that is 7 tens, and we will throw it at 10 tens, that is at 100, and immediately taking 13 tens, we will return to measure this distance directly and we will find it to contain 91 points, which are 9 and one-tenth, acting as has been said, that every ten counts as one. And with all these warnings, when they are well in practice, one will be able to easily investigate the solution of all the difficulties that could occur in any case.

Rule of Three inverse Solved by means of the same lines. Oper. V.

With no dissimilar operation, the questions of the inverse rule of three will be solved; here is an example. That provision which would suffice to maintain 100 soldiers for 60 days, to how many would it suffice for 75 days? These numbers arranged for the rule would stand in this order: 60, 100, 75.

And the operation of the Instrument requires that you take the first number directly, that is 60, and apply it transversally to the third number, that is 75, and without moving the Instrument, you take transversally the 100, which is the second, and

measure it directly, and you will find 80, which is the number sought. Where it must likewise be noted that we will find the same 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 in this one exactly.

By means of these same Arithmetical lines we can transmute any species of money into another in a very easy and fast manner, which will be achieved by first adjusting the Instrument, taking directly the price of the money that we want to transmute, and adjusting 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 want, for example, to transmute gold scudi into Venetian ducats, and because the price or value of the gold scudo 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, entering into it four soldi) to resolve one and the other money and evaluate it in soldi, considering how the price of the scudo is 160 soldi and that of the ducat 124. To adjust the Instrument for the transmutation of gold scudi into ducats, take directly the value of the scudo, that is 160, and apply it, opening the Instrument, transversally