Pleasure with Profit

portion :

Epimanondas did. King Henry the Fifth of England was so swift in running, that he, with two of his Nobles (without Bow, or other Engine) would take a Wild Buck or Doe in a large Park. Allo Harold, the Son of Canutus the Second, was Sirnamed Harefoot for his swift running. And Ethus, King of Scotland, was of that swiftness, that he almost reached that of Stags or Grayhounds; and was therefore called Alipes , or Wing’d-foot. Philippides an Athenian, in the space of two days, did run 150 Roman Miles. And one Euclides, another of the same Countrey, went and returned in one day 125 of the like Miles.

But those are the best Exercises, which (besides the refreshing of the Body) enable men to some other good Ends: As Bowling, ] It teaches Mens Hands and Eyes Mathematical Pros

- And (for a Home-Diversion) the Play at the Billiard Table hath not its Peer : It exercises the whole Body moderately ; the strength of the Arm juliciously : It directs the Hand Geometrically, and the Eye Optically : For the attaining to be an Exquisite Proficient in playing at it, depends wholly upon putting in practice that Axiome of Euclid in his Catoptignes ; which demonstrates, that, The Angles of Incidence and Reflection are ever more equal.

Swimming ] hath saved many a man's Life, when himself hath been both the Ship and the Cargozoon. And single Persons, by their dexterity in this Art, have not saved their own Lives only, but their Countrey also. For (as Livie relates ) One Horatius Cocles, That, after a long time, he alone, had defended the Bridge over Tyber against the Hetruscans, the Ro. mans brake it down behind him ; wherewith, in his Armour, he cast himself into the River, and (notwithstanding a shower of Darts and Arrows were sent after him) swam with safety into the City; which rewarded him with a Statue erected in the Market-place, and as much Land as he could encompass with a Plough in one day. And as resolute an Attempt was that of Gerrard and Harvey, two Gentlemen of our own Nation, who in the Fight at Sea in 1588. swam in the Night-time, and pierced with Augres, or such like Instruments, the sides of the Spanish

, Gallions, and returned back safe to the English Fleet. And Vincent in his Travails reports, That at Barlavento, Calo and Hispaniola, he hath seen men stay under water the space of three quarters of an Hour ; and hath heard of those that would continue an whole Hour. The forementioned Exercises are such as are generally used,

and

and do tend to the health of Mens Bodies ; and for the prevention of several Maladies to which by Nature they are inclin'd. But there are other Corporeal Exercises which are more Heroical, and fit only for the Recreation of Princes, and such Noble Heroes, whose principal Ambitions tend to the defence of their King and Countrey: And such are, Horsemanship, Tilting, Tornamenting, Throwing the Bar, Wrestling, &c. Of which instances might be given of many Emperors, Kings and Generals, who have performed great Exploits thereby. But leaving those of the Body, Ishall proceed to such Recreations as adorn the Mind; of which those of the Mathematicks are inferior to none.

Now the Excellency of any Science (says the Philosopher) may be judged of, (1.) By the Excellency of the Object : And (2.) by the Certainty of its Demonstrations.

First, for the Object; It is no less than the whole World : No only of the Terrestrial, but the Cælestial part thereof also. So that in this respect it far exceeds all those empty and barren Speculations about Materia Prima, or Universale: In the Study of which so many do mispend their Younger Years.

Secondly, For the Demonstrations of these Sciences, they are as infallible as Truth it self: And for this reason also doth it exceed all other Knowledge which depend upon Conjectures and Uncertainty. Since therefore in these respects, it is one of the most Excellent Sciences in Nature, it may best become the Industry of Man, who is one of the best Works of Nature. And for that end was he made with an Elevated Aspect, with Head and Eyes exalted: And for what reason, the Poet tells you,

Os Homini sublime dedit, Celumque tueri

Jufit, e erectos ad Sydera tollere vultus.
God gave to Man an upright Face, thar He

Mighe view the Stars, and learn Astronomy. And thus the Kingly Prophet David, Pfal. 8. v. 3, 4. falls ouc into this Admiration, When I consider the Heavens, the Works of thy Fingers ; the Moon and the Stars which thou hast created; Whát is Man, that thou art mindful of him, and the Son of Man that thou visitest him! Upon which Text, Sandys thus excellently Paraphrases.

When I pure Heaven, thy Fabrick see ;
The Moon and Stars, create by Thee

Ö! what is Man, and his frail Race;

That Thou should'st such a shadow grace ! Now these Sciences being so excellent in themselves, and of such benefit to us, we cannot spend our leisure hours better, than in these Sublime Sciences. It was so with Julius Cæsar, who amongst the Broils and Tumults of the Camp, made choice of this for his Recreation : As Lucan says of him, Lib. 1o.

Media inter prelia semper
Stellarum, Cælique plagis, superisque vacavit.
He always leisure found amidst his Wars,
To mark the course of Heaven, and learn the Stars.

And for this reason likewise did Seneca, amidst the continual Noise andBustle of the Court, becake himself to this Recreation.

O quam juvabat, &c.

O what a Pleasure was it to Survey Natures Chief Work, the Heavens! Where we may View the alternate Courses of the Sun, The Sacred Chariots, how the World does run : The Moon's bright Orb, when she's attended by Those scattered Stars, whose Light adorns the Sky. And thus let what I have already said concerning the Excellency,Utility and Benefit of these Mathematical Arts fuffice. It may be expected I should say something concerning those which I have selected in the following Tra&tates: But for that I refer you only to the Table of Contents following : And for the using of them, make them as Ballast to a Ship; to fix it, not to stall it ; so as to justle out its other Cargo of less weight, though of greater ima portance to Mundane subsistence. But I will deter thee (Reader) no longer in the Porch, but invite thee into the Inner Rooms; into which Ingredere ut Proficias : And so, for this time,

Farewell.

The

and Order of the Whole BOOK.

upon them.

O problems.

TRACT. J. Numerical Recreations. Cochlea : Of the Wheel.

Većtis : Of the Leaver.

F Digit, Article, Mixt, Square and Of Archimedes his Water-Screw.

Cubc Numbers, and some Observa- From thence a Perpetual Motion attempted. 10

tions

Pag. I' A Mechanical Paradox.

Of Comparative Arithmetick, or of the Relation of other Engines for the moving of Heavy Bodies ;

of Numbers in Quantity.

12 and other for Violent Morions.

Of Arithmetical, Geometrical and Musical Pro- Of Engines of War.

portions.

14 Of Automata : Or Sell-Movers.

Numerical Theorems.

17 of divers Magnificent Works of the Ancients. 20

Concerning the Golden Rule, both Simple and The height of several Obelisks, Steeples, Pyramids

Compound.

and Pillars in the World, according to our Eng.

Of the Increase of Swine, Corn, Sheep, doc. 23 lish Measure.

Of Changes in Bells, Mulical Instruments, Of Some such admirable Pieces of Work of several

Voices, &c.

kinds, as have been made by Artists both Ancient

Of Numerical Versifying. :

32 and Modern.

Of Numbers thought upon.

TRACT. IV. Statical Recreations.

Numerical

33
F the Art Statical.

Pag. I

Of Extracting ,

ibid.

without Multiplication or Divisjon.

Statical Theorems.

A moft Compendious way of Multiplication. 50

Of the Rule of Ceres and Virginum.

of the Ballance of Signeur Galileo Galilei. 5

Six Statical Theorems of Archimedes, taken

Numerical Devices.

from bis Tractate, De Incidentibus Aqua. 8

TRACT. II. Geometrical Recreations.

The Comparison of several Metals in Quantity and

E. Geometrical Definitions, and Practical

Weight.

Problems.

Pag. I Of the Roman and English Foot.

Home ( without Compuses) having only a common The Ancient Roman Weights, and our English,

Fork, and a Pliin Rule, to perform many plea compared.

Sant Geometrical Conclusions.

16 The weight of Spheres of several Metals compared.

Geometrical Arithmetick in all its Rules. 28

Mechanical ways of measuring of Heigbes, Depths of the worth, weight, magnitude, &c. of several

and Distances.

Metals and Liquors.

of Alcimetria ; or of the Mensuration of Heights Of the weight of Water and other things in weight

Accessible or Inaccessible.

and magnitude compared.

Of Longimetria : Or of the Mensuration of Di- A Comparative Table of the weight of Metals,
stànces, Accessible or Inaccesible.
41 Grains, Liqours, &c.