The Preface to the Reader.

As for plans, symmetry, and proportion of forts, camps, towns, countries, coasts, and harbors, I think there are none so unskilled but will confess these geometrical measurements are most necessary. But if there be any so rude, ignorant, and unlearned, or so blinded by self-conceit, that cannot be content to acknowledge anything necessary in a perfect soldier that is missing in themselves (for such surely they are that most arrogantly maintain this foolish opinion), let them but observe and mark the renowned Captain Alexander the Great. He held this knowledge in such high estimation that he seldom or never in his manifold conquests would attempt any action—whether against a fort, town, or country—without first having an exact topography (the mapping of a place) thereof, and thereupon invent, devise, and execute his warlike policies.

On the contrary, due to negligence of this knowledge, we may read how Hannibal—the most worthy and famous soldier that ever has been (all circumstances duly weighed)—was, by that painstaking, grave, and right valiant Captain Quintus Fabius Maximus, led and trained into a field enclosed with steep hills and deep rivers. There, this noble consul had so surrounded his host by fortifying two mountains that Hannibal and his entire army were in marvelous jeopardy of perishing from famine, had not the crafty wit of Hannibal invented an immediate policy to escape such imminent calamity.

Cyrus also, that great king and mighty monarch, was he not, through ignorance of topography, even while pursuing victory, trapped and defeated with all his power by the Scythian Queen Thomiris at the river Araxis? I pass over innumerable examples from all ages that manifestly declare the great advantage or disadvantage a captain may receive, whether invading or defending, by the strong or weak situation of places, and by the foreknowledge or ignorance of them.

Neither is there any liberal or free mind, whether of warlike or civil profession, that will not take great delight and pleasure to see how by art a man may measure the distances of places remote and far asunder—approaching near none of them—and doing so as well as, or even more exactly than, if he should painfully pass over them with cord or pole. Hereupon did the poets feign Atlas to be of such huge and mighty stature, sustaining and upholding the earth and the mighty mass of the heavenly spheres. For although this man, notwithstanding he was imprisoned in a mortal carcass and thereby detained in this inferior and vilest portion of the universal world—farthest distant from that passing pleasant and beautiful frame of celestial orbs—yet his divine mind, aided by this science of geometrical mensurations, found out the quantities, distances, courses, and strange, intricate, miraculous motions of these resplendent heavenly globes of the sun, moon, planets, and fixed stars, leaving the rules and precepts thereof to his posterity. Archimedes also (as some suppose), with a glass framed by the revolution of a parabolic section, set the Roman navy on fire in the sea while they were coming to the siege of Syracuse.

But to leave these celestial causes and things done in antiquity long ago, my father, by his continual, painstaking practices assisted with mathematical demonstrations, was able—and sundry times has, by proportional glasses duly situated at convenient angles—not only to discover things far off, read letters, and number pieces of money (including the very coin and inscription thereof) cast by some of his friends on purpose upon downs in open fields, but also seven miles away, he declared what was being done at that instant in private places. He has also sundry times, by the sun’s beams, set powder on fire and discharged ordnance half a mile or more away. These things I am the bolder to report, for there are yet living diverse oculati testes (eyewitnesses) of these his doings, and many other matters far more strange and rare, which I omit as irrelevant to this place.

But for the invention of these conclusions, I have heard him say that nothing ever helped him so much as the exquisite knowledge he had attained through continual practice in geometrical mensurations. And for science in great ordnance, especially to shoot exactly at randons (a quality not unmeet for a gentleman), without geometrical rules and perfect skill in these measurements, he shall never know anything. Thus have I partly declared the pleasure and commodity that any well-disposed mind may reap by these three books of my father’s. But somewhat to say concerning the last treatise of the five regular bodies...