For these reasons I would advise a melancholy person to use both secular and religious authors, and voluntarily set himself a task to turn aside his melancholy thoughts: to study the art of memory—Cosmus Rosselius, Petrus Ravennas, Scenkelius Detected—or practise shorthand, and the like, which will demand close attention. Or let him demonstrate a proposition from the last five books of Euclid, extract a square root, or study algebra.

As Clavius holds, nothing in all human learning can be more excellent or pleasing: so profound and hidden, so enchanting, so marvellous, so captivating, yet so easy and full of delight, that “it seems to surpass all human understanding.”

By this means you can determine “the lion from its claw,” as the proverb goes: Hercules’ size from his thumb alone, or the true dimensions of the great Colossus, Solomon’s Temple, and Domitian’s amphitheatre from one small part.

By this art you can contemplate the permutations of the twenty-three letters, which can be varied so endlessly that the words combined and derived from them would not fit within the compass of the heavens. Ten words can be arranged in 40,320 different ways.

By this art you can examine how many people could stand side by side over the entire surface of the earth—some say 148,456,800,000,000, “allowing each a square pace”; how many could be born in 60,000 years, supposing the whole world as habitable as France, as fertile and its people as long-lived. And, with Archimedes, you can demonstrate how many grains of sand the entire bulk of the world might contain if it were all sand, provided you first knew how many a small cube the size of a mustard seed could hold—and countless other such questions.

But in all nature, what is so astonishing as examining and calculating the motions of the planets, their sizes, apogees, perigees, eccentricities, and distances from the earth; the size, thickness, and extent of the firmament; each star, with its diameters, circumference, apparent area, and surface—using those ingenious aids, glasses, astrolabes, sextants, and quadrants, which Tycho Brahe discusses in his work on instruments; optics—divine optics!—arithmetic, geometry, and similar arts and instruments?

What is so intricate and at the same time so delightful as studying and putting into practice the works of Hero of Alexandria on pneumatics, war machines, and self-moving machinery; proposition 13 of Jordanus Nemorarius’s On Weights; that delightful treatise by Machometes Bragdedinus, On the Division of Surfaces; Apollonius’s Conics; or Commandinus’s work in this field, On the Centre of Gravity, with many similar geometrical theorems and problems?

Those remarkable instruments and mechanical inventions of Jacques Besson and Cardano for such purposes, with many similar experiments suggested long ago by Roger Bacon in his treatise On the Secrets of Art and Nature: making a carriage move without an animal; diving boats; walking on water by artifice and flying through the air; making various cranes and pulleys “by which one man may draw a thousand men towards himself”; lifting and moving great weights; mills that move themselves; Archytas’s dove, Albertus’s brass head, and other such wonder-working devices.

But above all, performing extraordinary wonders with glasses, of which Proclus and Bacon wrote long ago: burning glasses, multiplying glasses, perspective instruments, “so that one man appears an army”; seeing far away; representing solid bodies by cylindrical and concave surfaces; walking in the air; “so that they really see,” says Bacon, “gold and silver and whatever else they wish, and when they come to the place where the image appeared, find nothing.” These glasses have lately been greatly improved by Giambattista della Porta and Galileo, and Maginus and Midorgius promise much more to be accomplished in this field.

Some speak of hearing instruments to strengthen hearing as the others do sight. Marcellus Vrencken, a Dutchman, mentions in his letter to Burgravius a friend who is working on an instrument “with which he will see what lies on the other horizon.”

But our alchemists and Rosicrucians, I think, offer the greatest marvels and are richest in experiments: they can make gold, separate and transform metals, extract oils, salts, and residues, and perform more extraordinary works than Geber, Lullius, Bacon, or any of those earlier masters.

Following his master Paracelsus, Crollius has made “fulminating gold,” or “volatile gold,” which will imitate thunder and lightning and explode more loudly than any gunpowder. Cornelius Drebbel has made a perpetual-motion device, inextinguishable lights, cloth that will not burn, and many similar wonders; see his book On the Nature of the Elements. Besides hail, wind, snow, thunder, lightning, and so forth, there are those extraordinary fireworks, devilish petards, and similar engines of war derived from these arts, about which you may read Tartaglia and others.

Ernestus Burgravius, a disciple of Paracelsus, has published a discourse describing a lamp to be made from human blood. He calls it “a lamp that indicates life and death.” Chemically prepared for forty days and afterwards kept in a glass vessel, it will reveal all the changes in that person’s life: “If this lamp is bright, the man is cheerful and healthy in body and mind; if cloudy and dim, he is unwell; and so it varies with the condition of the man from whom the blood was taken.” Most wonderful of all, it dies with the person: “It perishes and vanishes with the man.” The lamp and the man whose blood supplied it are extinguished together.