QUOTATIONS.-See Deuteronomy, viii. 11–17.

If I have made gold my hope, or have said to fine gold, "thou art my confidence," I should have denied

the God that is above.-Job, xxxi. 24. 28.

Having food and raiment let us be therewith content. But they that will be rich fall into temptation and a snare, and into many foolish and hurtful lusts, which drown men in destruction and perdition.-1 Tim. vi. 9.

The love of money is the root of all evil, which while some coveted after, they have erred from the faith, and pierced themselves through with many sorrows.-1 Tim. vi. 10.

It is easier for a camel to go through the eye of a needle, than for a rich man to enter into the kingdom of God.— Matt. xix. 24.

The middle station of life is called, by the consent of all nations, THE GOLDEN MEAN.

Avoid extremes.

Virtue lies in the medium, Vice in the extremes; and every virtue has its attendant vice.-Addison.

I deem an equal mediocrity of life

Most to be wished; if not in gorgeous state,
Yet without danger glides it on to age;

There is protection in its very name,

And happiness dwells with it.

Potter's Euripides, "Medea."

Is there no Temperate region to be shown
Betwixt the Torrid and the Frigid zone?
Remote from sordid filth and gilded care,
Health, virtue, wisdom, competence, dwell there.
Know all the good that individuals find,
Or God and Nature meant to mere mankind,
Reason's whole pleasure, all the joys of sense,
Lie in three words, HEALTH, PEACE, and COMPETENCE.

Pope.

For aught I see, they are as sick that surfeit with too much, as they that starve with nothing: It is no mean

happiness, therefore, to be seated in the mean. Superfluity comes sooner by white hairs, but competency lives longer. Shakspeare.

Est modus in rebus, sunt certi denique fines,

Quos ultra citraque nequit consistere rectum.-Horace. Medio tutissimus ibis.

Curæ lacqueata circum tecta.-Horace.

Id arbitror adprime in vita est utile NE QUID NIMIS.— Terence.

Auream mediocritatem dilige.

Auream quisquis mediocritatem
Diligit, tutus caret obsoleti
"Sordibus tecti, caret invidenda
Sobrius aula.-Horace.

Media via est tutissima.

In plerisque rebus optima est mediocritas.- Cicero.

CONCLUSION.

THEME XLII. The Usefulness of Mathematical Learning.

INTRODUCTION.-Mathematics may be called the art of arguing by numbers and quantities; the benefits of this science, as a branch of education, are very great.

1ST REASON. The study of mathematics accustoms the mind to minute attention, by entertaining it with a variety of truths, indisputable and demonstrable, though often obscure and greatly involved.

2ND REASON.--It is the only science which cannot admit of error: opinion, prejudice, fraud, and falsity may, in some measure, affect all other sciences, but can have no influence whatsoever upon the deductions of mathematics.

3RD REASON.-The study of mathematics habituates the mind to clear methodical reasoning; and, by early training, it may be taught to argue logically, and discern acutely, as well as it may be trained to any other exercise.

4TH REASON. It disengages the mind from foolish credulity, by compelling it to examine minutely every statement, and to take nothing upon trust.

5TH REASON. As vice and superstition are founded and upheld by error and false reasoning, the study of mathematics must be friendly to the cause of religion, by purging the mind from all sophisms, and engrafting in it a love of truth.

6TH REASON. The science of pure mathematics is so intimately connected with natural philosophy, that mechanics, astronomy, optics, and other physical subjects, are both investigated and explained by it; and, without a knowledge of mathematics, natural philosophy can neither be appreciated nor understood.

7TH REASON. Many of the arts depend upon mathematics for their development, as architecture, surveying, engineering, navigation, &c., and no one can be qualified for these pursuits, who has not been trained to the study of mathematics.

8TH REASON. The study of mathematics trains the mind to industry and perseverance, by leading it to an important result by the slow process of minute gradations.

SIMILES. As a winnowing fan blows away the chaff, and renders corn more clear and valuable; so the study of mathematics frees the mind from error and frivolity.

As drilling and gymnastic exercises render the body more graceful, healthy, and erect, by training it to selfdenying labour, driving out superfluous humours, and correcting bad habits; so the study of mathematics may be called a mental drilling, or gymnastic exercise, which makes the mind more healthy and straight-forward.

As the use of the hoe and spade brings the soil into better cultivation, by keeping down weeds, bringing forth latent properties, breaking up the hard clods, and admitting air below the surface; so the study of mathematics is beneficial to the mind, by excluding error, and admitting only truth.

Mathematics may be compared to a still, every drop that falls into the recipient is perfectly pure; and by no other means can perfectly pure water be obtained.

As metals are tested by a crucible, so truth and error are tested by mathematics.

As gold is refined in the furnace, so a proposition is sifted by the refining fire of mathematics.

Mathematics may be compared to the ordeals of our forefathers, which only the innocent and undefiled could pass innocuously through.

Mathematics may be compared to the fabulous well of St. Agnes, in which only the chaste could see their reflection, or taste its delicious waters.

HISTORICAL ILLUSTRATIONS. Sir Isaac Newton, the greatest mathematician of modern times, was remarkable for his urbanity of manners, his humility of mind, his extensive information, and his devout piety.

Many of our greatest divines, and most eminent statesmen, have been high wranglers at the University of Cambridge.

Richard Porson, one of the finest classical scholars that England ever produced, was trained by his father from earliest youth to mental arithmetic; to which he always ascribed his literary eminence.

Pythagoras, the celebrated philosopher of Samos, was one of the finest mathematicians of antiquity. His love of numbers made him an admirable musician, astronomer, and philosopher. He reduced music and even ethics to a mathematical science; and taught that happiness, as well as piety, consisted in the perfect science of numbers.

No philosopher of Greece ever stood higher than Pythagoras, or was more honoured for learning, consistency, moral rectitude, and devotion.

Napoleon, the greatest genius of France, was celebrated for his mathematical lore.

Simeon of Durham was the best mathematician in the reign of Henry I.; and to this peculiar talent is to be ascribed his patient researches and admirable digest of ancient records, between the seventh and twelfth centuries.

Archimedes, the Syracusan philosopher, was no less noted for his mathematical knowledge than for his scientific discoveries, his patriotic zeal, his humility of mind, and his extensive information.

QUOTATIONS. The weakness and effeminacy of mankind, in being persuaded where they are delighted, have made them the sport of orators, poets, and men of wit.Dr. Arbuthnot.

In the search of truth, an imitation of the method of the geometers will carry a man further than all the dialectical rules.-Dr. Arbuthnot.

If a man's wits be wandering let him study the mathematics; for in demonstration, if his wit be called away never so little, he must begin again.-Lord Bacon.

Mathematics is a ballast for the soul to fix it, not to stall it; and not to jostle out other arts.-Fuller.

The study of the mathematics will make our natural faculty of reason both the better and the sooner to judge rightly between truth and error, good and evil.-Hooker.

Mathematics and the severer sciences, with logic and metaphysics, bestow an acuteness and an endurance upon the mind which serve essentially to call forth and strengthen the abstract reason.-Dr. Jones.

Quicquid difficile est hoc superare decet.

CONCLUSION.