causes; poetry with effects. The one gives scope to the exercise of judgment; the other, of imagination. Philosophy presents us with an anatomical dissection; poetry exhibits the object clothed with flesh and blood, and animated with passion. The element of philosophy is argument; that of poetry, feeling. Between philosophy and poetry there is no essential contrariety; for poetry implies, not the rejection, but the use of philosophy. It includes, however, something which philosophy alone cannot reach; and the portion of it which it employs, it disguises by art. On this account, poetry is often, but without justice, deemed incompatible with philosophy.-W. B. Clulow.

178.

Study to acquire such a philosophy as is not barren and babbling, but solid and true; not such an one as floats upon the surface of endless verbal controversies, but one that enters into the nature of things.-Abp. Leighton.

179.

The science of the mathematics performs more than it promises, but the science of metaphysics promises more than it performs. The study of the mathematics, like the Nile, begins in minuteness, but ends in magnificence; but the study of metaphysics begins with a torrent of tropes, and a copious current of words, yet loses itself at last in obscurity and conjecture, like the Niger in his barren deserts of sand.-Lacon.

180.

They [the mathematics] effectually exercise the mind, and plainly demonstrate every thing within their reach; they draw certain conclusions, instruct by profitable rules, and unfold pleasant questions. Their discipline inures and corroborates the mind to a constant diligence in study; they wholly deliver us from a credulous simplicity; they effectually

restrain us from rash presumption; most easily incline us to a due assent; and perfectly subject us to the government of right reason.-Dr Barrow.

181.

Every exercise of the mind upon Theorems of Science, like generous and manly exercise of the body, tends to strengthen and call forth Nature's original vigour. The nerves of reason are braced by the mere employ, and we become abler actors in the drama of life, whether our part be of the busier or sedater kind.-Harris.

182.

Of Geometry, it is not too much to say that it is a necessary part of a good education. There is no other study by which the Reason can be so exactly and so rigorously exercised. In learning Geometry, as I have on a former occasion said [University Education, p. 139], the Student is rendered familiar with the most perfect examples of strict inference; he is compelled habitually to fix his attention on those conditions on which the cogency of the demonstration depends; and in the mistakes and imperfect attempts at demonstration made by himself and others, he is presented with examples of the more natural fallacies, which he sees exposed and corrected. He is accustomed to a chain of deduction in which each link hangs from the preceding, yet without any insecurity in the whole; to an ascent, beginning from solid ground, on which each step, as soon as it is made, is a foundation for a further ascent, no less solid than the first self-evident truths. Hence he learns continuity of attention, coherency of thought, and confidence in the power of human reason to arrive at the truth. These great advantages, resulting from the study of Geometry, have justly made it a part of every good system of liberal education from the time of the Greeks to our own.-Dr Whewell.

183.

The value of mathematical instruction as a preparation for those more difficult investigations (physiology, society, government, &c.) consists in the applicability not of its doctrines, but of its method. Mathematics will ever remain the most perfect type of the deductive method in general; and the applications of mathematics to the simpler branches of physics, furnish the only school in which philosophers can effectually learn the most difficult and important portion of their art, the employment of the laws of simpler phenomena for explaining and predicting those of the more complex. These grounds are quite sufficient for deeming mathematical training an indispensable basis of real scientific education, and regarding, with Plato, one who is ἀγεωμέτρητος, as wanting in one of the most essential qualifications for the successful cultivation of the higher branches of philosophy.-John Stuart Mill.

184.

I remember a young man at the University who refused to read Euclid's Elements,-because he was a man of fortune, and was never likely to become a carpenter. His understanding was too narrow to conceive the utility of Geometry, &c. in strengthening the reason, and advancing science.-Dr Knox.

185.

Would you have a man reason well, you must use him to it betimes, and exercise his mind in observing the connexion of ideas, and following them in train. Nothing does this better than Mathematics; which, therefore, I think should be taught all those who have time and opportunity; not so much to make them Mathematicians, as to make them reasonable creatures.-John Locke.

186.

He that gives a portion of his time and talent

to the investigation of Mathematical truth, will come to all other questions with a decided advantage over his opponents. He will be in argument what the ancient Romans were in the field; to them the day of battle was a day of comparative recreation; because they were ever accustomed to exercise with arms much heavier than they fought with; and their reviews differed from a real battle in two respects, they encountered more fatigue, but the victory was bloodless.-Lacon.

187.

The Mathematics are either pure or mixed. To the pure Mathematics are those sciences belonging which handle quantity determinate, merely severed from any axioms of natural philosophy; and these are two, Geometry, and Arithmetic; the one handling quantity continued, and the other dissevered. Mixed hath for subject some axioms or parts of natural philosophy, and considereth quantity determined, as it is auxiliary and incident unto them. For many parts of nature can neither be invented with sufficient subtilty, nor demonstrated with sufficient perspicuity, nor accommodated unto use with sufficient dexterity, without the aid and intervening of the Mathematics; of which sort are perspective, music, astronomy, cosmography, architecture, enginery, and divers others.

In the Mathematics I can report no deficience, except it be that men do not sufficiently understand the excellent use of the pure Mathematics, in that they do remedy and cure many defects in the wit and faculties intellectual. For, if the wit be dull, they sharpen it; if too wandering, they fix it; if too inherent in the sense, they abstract it. So that as tennis is a game of no use in itself, but of great use in respect that it maketh a quick eye, and a body ready to put itself into all postures; so in the Mathematics, that use which is collateral and inter

venient, is no less worthy than that which is principal and intended. And as for the mixed Mathematics, I may only make this prediction, that there cannot fail to be more kinds of them, as nature grows further disclosed.-Bacon.

188.

The Principles of Natural Philosophy are the Principles of common sense.-Professor Daniel.

189.

Elementary Mechanics should now form a part of intellectual education, in order that the student may understand the theory of universal gravitation : for our intellectual education should cultivate such ideas as enable the student to understand the most complete and admirable portions of the knowledge which the human race has attained to.-Dr Whewell.

190.

Some dispositions evince an unbounded admiration for antiquity, others eagerly embrace novelty; and but few can preserve the just medium, so as neither to tear up what the ancients have correctly laid down, nor to despise the just innovations of the moderns. But this is very prejudicial to the sciences and philosophy, and instead of a correct judgment, we have but the factions of the ancients and moderns. Truth is not to be sought in the good fortune of any particular juncture of time which is uncertain, but in the light of nature and experience which is eternal.-Bacon.

191.

Men of strong minds, and who think for themselves, should not be discouraged on finding occasionally that some of their best ideas have been anticipated by former writers; they will neither anathematize others with a "pereant qui ante nos nostra dixerint," nor despair themselves. They will rather go on in science, like John Hunter in physics,