Now he should acquaint the youth with mathematics; and to invite him to it, he should begin quickly to show him some of the more pleasant mechanical performances in mathematicks. That which is necessarily to be known to one that would study these sciences is Euclid’s Elements, at least his first six books, arithmetick and trigonometr; and without one’s understanding these, one may be a mechanist, but a mathematician shall he never be. For stereometry, algebra, and conic sections, they require more subtlety and patience, than is to be expected from youth, neither are they of such use.
For the subalternate sciences of the mathematicks, it is necessary to give a youth a taste of them. All of the parts of geometry and astronomy, he should know exactly, and be prompt in using and managing instruments. The theories of musick, fortification, dioptricks, and the art of dialling, if the governour understand them well himselfe, will be easily learned; but the architecture and statues are these which he must know as his fingers; they being so necessary to humane life. Since all mechanisme depends upon the force of motion; and in these there will be no difficulty. If the youth have a delight in problemes and theoremes, and be of ane active fancy, it will be good to hook him as much as can be to them; for this is by wise men judged a good advice for preserving a state quiet, to engage young nobility, who have active spirits, to mathematical sciences, which carrying their thoughts after them, will preserve them from ambition, and medling with the state. But in this, moderation is to be observed, least their brains be too much stretched with these curiosities.