CHAPTER I.

On the Arithmetical Method of constructing the Caliber Rule.

Ornamental woodcut initial 'M' featuring foliage and architectural motifs.

There is a multiple and varied way and method for constructing a cubic or stereometric line (from which our Caliber Rule—which takes its origin and name from calibrating or measuring the globes and orifices of war engines—derives). This method is found everywhere among almost all arithmeticians and cultivators of geometry, both theoretical and practical, and many mechanics. For this work, however, only the knowledge of doubling, tripling, and increasing the first cube as much as one pleases is required. Since this cannot be obtained more accurately or surely by any other method than by carrying out the proposed work using arithmetical calculation, it has seemed best to place the arithmetical method in the first position, as it is more excellent and noble than the others. Manual craftsmen and other mechanics have learned to evade this due to the troublesome extraction of the cubic root, and instead only deduce tables calculated by other skilled arithmeticians into their work, using these to divide any proposed lines in stereometric proportionality. But since it is of great importance for a perfect craftsman not to be inexperienced in this method either, we shall here subjoin some very briefly written rules for extracting the cubic root and for the method of constructing stereometric tables. Once these are had, we shall be able to construct our rule without any difficulty at all.

A very brief method for extracting the cubic root, comprised in the following rules.

A cubic number is said by arithmeticians to be that which is made from the multiplication of a number by itself, and then by the multiplication of that same number by the product. As if 10 are multiplied by themselves, that is, by 10, they become 100: which, multiplied again by 10, produces 1000. This number is therefore called a cube, and 10 is its cubic root. With these things known, you will easily extract the cubic root from any offered number if you observe the following precepts.

1. One must have at hand a table of the first nine cubes and their roots. This is made from the cubic multiplication of the first simple numbers continued from unity up to the number nine, as follows: