The Legacy of Greece Part 6

The lost treatise _Sectio Spatii_ dealt similarly with the like problem in which the intercepts cut off have to contain a given rectangle.

The other treatises included in Pappus's account are (1) On _Determinate Section_; (2) _Contacts_ or _Tangencies_, Book II of which is entirely devoted to the problem of drawing a circle to touch three given circles (Apollonius's solution can, with the aid of Pappus's auxiliary propositions, be satisfactorily restored); (3) _Plane Loci_, i. e. loci which are straight lines or circles; (4) ?e?se?? {Neuseis}, _Inclinationes_ (the general problem called a ?e?s?? {neusis} being to insert between two lines, straight or curved, a straight line of given length _verging_ to a given point, i. e. so that, if produced, it pa.s.ses through the point, Apollonius restricted himself to cases which could be solved by 'plane' methods, i. e. by the straight line and circle only).

Apollonius is also said to have written (5) a _Comparison of the dodecahedron with the icosahedron_ (inscribed in the same sphere), in which he proved that their surfaces are in the same ratio as their volumes; (6) _On the cochlias_ or cylindrical helix; (7) a 'General Treatise', which apparently dealt with the fundamental a.s.sumptions, &c., of elementary geometry; (8) a work on _unordered irrationals_, i. e.

irrationals of more complicated form than those of Eucl. Book X; (9) _On the burning-mirror_, dealing with spherical mirrors and probably with mirrors of parabolic section also; (10) ???t????? {okytokion} ('quick delivery'). In the last-named work Apollonius found an approximation to p {p} closer than that in Archimedes's _Measurement of a Circle_; and possibly the book also contained Apollonius's exposition of his notation for large numbers according to 'tetrads' (successive powers of the myriad).

In astronomy Apollonius is said to have made special researches regarding the moon, and to have been called e {e} (Epsilon) because the form of that letter is a.s.sociated with the moon. He was also a master of the theory of epicycles and eccentrics.

With Archimedes and Apollonius Greek geometry reached its culminating point; indeed, without some more elastic notation and machinery such as algebra provides, geometry was practically at the end of its resources.

For some time, however, there were capable geometers who kept up the tradition, filling in details, devising alternative solutions of problems, or discovering new curves for use or investigation.

Nicomedes, probably intermediate in date between Eratosthenes and Apollonius, was the inventor of the _conchoid_ or _cochloid_, of which, according to Pappus, there were three varieties. Diocles (about the end of the second century B. C.) is known as the discoverer of the _cissoid_ which was used for duplicating the cube. He also wrote a book pe??

p??e??? {peri pyreion}, _On burning-mirrors_, which probably discussed, among other forms of mirror, surfaces of parabolic or elliptic section, and used the focal properties of the two conics; it was in this work that Diocles gave an independent and clever solution (by means of an ellipse and a rectangular hyperbola) of Archimedes's problem of cutting a sphere into two segments in a given ratio. Dionysodorus gave a solution by means of conics of the auxiliary cubic equation to which Archimedes reduced this problem; he also found the solid content of a _tore_ or anchor-ring.

Perseus is known as the discoverer and investigator of the _spiric sections_, i. e. certain sections of the spe??a {speira}, one variety of which is the _tore_. The _spire_ is generated by the revolution of a circle about a straight line in its plane, which straight line may either be external to the circle (in which case the figure produced is the tore), or may cut or touch the circle.

Zenodorus was the author of a treatise on _Isometric figures_, the problem in which was to compare the content of different figures, plane or solid, having equal contours or surfaces respectively.

Hypsicles (second half of second century B. C.) wrote what became known as 'Book XIV' of the _Elements_ containing supplementary propositions on the regular solids (partly drawn from Aristaeus and Apollonius); he seems also to have written on polygonal numbers. A mediocre astronomical work (??af?????? {Anaphorikos}) attributed to him is the first Greek book in which we find the division of the zodiac circle into 360 parts or degrees.

Posidonius the Stoic (about 135-51 B. C.) wrote on geography and astronomy under the t.i.tles _On the Ocean_ and pe?? ete???? {peri meteoron}. He made a new but faulty calculation of the circ.u.mference of the earth (240,000 stades). _Per contra_, in a separate tract on the size of the sun (in refutation of the Epicurean view that it is as big as it _looks_), he made a.s.sumptions (partly guesswork) which give for the diameter of the sun a figure of 3,000,000 stades (39-1/4 times the diameter of the earth), a result much nearer the truth than those obtained by Aristarchus, Hipparchus, and Ptolemy. In elementary geometry Posidonius gave certain definitions (notably of parallels, based on the idea of equidistance).

Geminus of Rhodes, a pupil of Posidonius, wrote (about 70 B. C.) an encyclopaedic work on the cla.s.sification and content of mathematics, including the history of each subject, from which Proclus and others have preserved notable extracts. An-Nairizi (an Arabian commentator on Euclid) reproduces an attempt by one 'Aganis', who appears to be Geminus, to prove the parallel-postulate.

But from this time onwards the study of higher geometry (except sphaeric) seems to have languished, until that admirable mathematician, Pappus, arose (towards the end of the third century A. D.) to revive interest in the subject. From the way in which, in his great _Collection_, Pappus thinks it necessary to describe in detail the contents of the cla.s.sical works belonging to the 'Treasury of a.n.a.lysis'

we gather that by his time many of them had been lost or forgotten, and that he aimed at nothing less than re-establishing geometry at its former level. No one could have been better qualified for the task.

Presumably such interest as Pappus was able to arouse soon flickered out; but his _Collection_ remains, after the original works of the great mathematicians, the most comprehensive and valuable of all our sources, being a handbook or guide to Greek geometry and covering practically the whole field. Among the original things in Pappus's _Collection_ is an enunciation which amounts to an antic.i.p.ation of what is known as Guldin's Theorem.

It remains to speak of three subjects, trigonometry (represented by Hipparchus, Menelaus, and Ptolemy), mensuration (in Heron of Alexandria), and algebra (Diophantus).

Although, in a sense, the beginnings of trigonometry go back to Archimedes (_Measurement of a Circle_), Hipparchus was the first person who can be proved to have used trigonometry systematically. Hipparchus, the greatest astronomer of antiquity, whose observations were made between 161 and 126 B. C., discovered the precession of the equinoxes, calculated the mean lunar month at 29 days, 12 hours, 44 minutes, 2-1/2 seconds (which differs by less than a second from the present accepted figure!), made more correct estimates of the sizes and distances of the sun and moon, introduced great improvements in the instruments used for observations, and compiled a catalogue of some 850 stars; he seems to have been the first to state the position of these stars in terms of lat.i.tude and longitude (in relation to the ecliptic). He wrote a treatise in twelve Books on Chords in a Circle, equivalent to a table of trigonometrical sines. For calculating arcs in astronomy from other arcs given by means of tables he used propositions in spherical trigonometry.

The _Sphaerica_ of Theodosius of Bithynia (written, say, 20 B. C.) contains no trigonometry. It is otherwise with the _Sphaerica_ of Menelaus (fl. A. D. 100) extant in Arabic; Book I of this work contains propositions about spherical triangles corresponding to the main propositions of Euclid about plane triangles (e.g. congruence theorems and the proposition that in a spherical triangle the three angles are together greater than two right angles), while Book III contains genuine spherical trigonometry, consisting of 'Menelaus's Theorem' with reference to the sphere and deductions therefrom.

Ptolemy's great work, the _Syntaxis_, written about A. D. 150 and originally called ?a??at??? s??ta??? {Mathematike syntaxis}, came to be known as ?e?a?? s??ta??? {Megale syntaxis}; the Arabs made up from the superlative e??st?? {megistos} the word al-Majisti which became _Almagest_.

Book I, containing the necessary preliminaries to the study of the Ptolemaic system, gives a Table of Chords in a circle subtended by angles at the centre of increasing by half-degrees to 180. The circle is divided into 360 ???a? {moirai}, parts or degrees, and the diameter into 120 parts (t?ata {tmemata}); the chords are given in terms of the latter with s.e.xagesimal fractions (e. g. the chord subtended by an angle of 120 is 103^{p} 53' 23?). The Table of Chords is equivalent to a table of the _sines_ of the halves of the angles in the table, for, if (crd. 2 a {a}) represents the chord subtended by an angle of 2 a {a} (crd. 2 a {a})/120 = sin a {a}. Ptolemy first gives the minimum number of geometrical propositions required for the calculation of the chords. The first of these finds (crd. 36) and (crd. 72) from the geometry of the inscribed pentagon and decagon; the second ('Ptolemy's Theorem' about a quadrilateral in a circle) is equivalent to the formula for sin (?-f) {th-ph}, the third to that for sin ? {th}.

From (crd. 72) and (crd. 60) Ptolemy, by using these propositions successively, deduces (crd. 1) and (crd. ), from which he obtains (crd. 1) by a clever interpolation. To complete the table he only needs his fourth proposition, which is equivalent to the formula for cos (?+f) {th+ph}.

Ptolemy wrote other minor astronomical works, most of which survive in Greek or Arabic, an _Optics_ in five Books (four Books almost complete were translated into Latin in the twelfth century), and an attempted proof of the parallel-postulate which is reproduced by Proclus.

Heron of Alexandria (date uncertain; he may have lived as late as the third century A. D.) was an almost encyclopaedic writer on mathematical and physical subjects. He aimed at practical utility rather than theoretical completeness; hence, apart from the interesting collection of _Definitions_ which has come down under his name, and his commentary on Euclid which is represented only by extracts in Proclus and an-Nairizi, his geometry is mostly mensuration in the shape of numerical examples worked out. As these could be indefinitely multiplied, there was a temptation to add to them and to use Heron's name. However much of the separate works edited by Hultsch (the _Geometrica_, _Geodaesia_, _Stereometrica_, _Mensurae_, _Liber geeponicus_) is genuine, we must now regard as more authoritative the genuine _Metrica_ discovered at Constantinople in 1896 and edited by H. Schone in 1903 (Teubner). Book I on the measurement of areas is specially interesting for (1) its statement of the formula used by Heron for finding approximations to surds, (2) the elegant geometrical proof of the formula for the area of a triangle ? {D} = v{_s (s-a) (s-b) (s-c)}, a formula now known to be due to Archimedes, (3) an allusion to limits to the value of p {p} found by Archimedes and more exact than the 3-1/7 and 3-10/71 obtained in the _Measurement of a Circle_.

Book I of the _Metrica_ calculates the areas of triangles, quadrilaterals, the regular polygons up to the dodecagon (the areas even of the heptagon, enneagon, and hendecagon are approximately evaluated), the circle and a segment of it, the ellipse, a parabolic segment, and the surfaces of a cylinder, a right cone, a sphere and a segment thereof. Book II deals with the measurement of solids, the cylinder, prisms, pyramids and cones and frusta thereof, the sphere and a segment of it, the anchor-ring or tore, the five regular solids, and finally the two special solids of Archimedes's _Method_; full use is made of all Archimedes's results. Book III is on the division of figures. The plane portion is much on the lines of Euclid's _Divisions_ (of figures). The solids divided in given ratios are the sphere, the pyramid, the cone and a frustum thereof. Incidentally Heron shows how he obtained an approximation to the cube root of a non-cube number (100). Quadratic equations are solved by Heron by a regular rule not unlike our method, and the _Geometrica_ contains two interesting indeterminate problems.

Heron also wrote _Pneumatica_ (where the reader will find such things as siphons, Heron's Fountain, penny-in-the-slot machines, a fire-engine, a water-organ, and many arrangements employing the force of steam), _Automaton-making_, _Belopoeca_ (on engines of war), _Catoptrica_, and _Mechanics_. The _Mechanics_ has been edited from the Arabic; it is (except for considerable fragments) lost in Greek. It deals with the puzzle of 'Aristotle's Wheel', the parallelogram of velocities, definitions of, and problems on, the centre of gravity, the distribution of weights between several supports, the five mechanical powers, mechanics in daily life (queries and answers). Pappus covers much the same ground in Book VIII of his _Collection_.

We come, lastly, to Algebra. Problems involving simple equations are found in the Papyrus Rhind, in the _Epanthema_ of Thymaridas already referred to, and in the arithmetical epigrams in the Greek Anthology (Plato alludes to this cla.s.s of problem in the _Laws_, 819 B, C); the Anthology even includes two cases of indeterminate equations of the first degree. The Pythagoreans gave general solutions in rational numbers of the equations _x+y=z_ and _2x-y=1_, which are indeterminate equations of the second degree.

The first to make systematic use of symbols in algebraical work was Diophantus of Alexandria (fl. about A. D. 250). He used (1) a sign for the unknown quant.i.ty, which he calls a????? {arithmos}, and compendia for its powers up to the sixth; (2) a sign ([Transcriber's Note: Symbol]) with the effect of our _minus_. The latter sign probably represents ?? {LI}, an abbreviation for the root of the word ?e?pe??

{leipein} (to be wanting); the sign for a????? {arithmos} ([Transcriber's Note: Symbol]) is most likely an abbreviation for the letters a? {ar}; the compendia for the powers of the unknown are ?^?

{D^Y} for d??a?? {dynamis}, the square, ?^? {K^Y} for ???? {kybos}, the cube, and so on. Diophantus shows that he solved quadratic equations by rule, like Heron. His _Arithmetica_, of which six books only (out of thirteen) survive, contains a certain number of problems leading to simple equations, but is mostly devoted to indeterminate or semi-determinate a.n.a.lysis, mainly of the second degree. The collection is extraordinarily varied, and the devices resorted to are highly ingenious. The problems solved are such as the following (fractional as well as integral solutions being admitted): 'Given a number, to find three others such that the sum of the three, or of any pair of them, together with the given number is a square', 'To find four numbers such that the square of the sum _plus_ or _minus_ any one of the numbers is a square', 'To find three numbers such that the product of any two _plus_ or _minus_ the sum of the three is a square'. Diophantus a.s.sumes as known certain theorems about numbers which are the sums of two and three squares respectively, and other propositions in the Theory of Numbers.

He also wrote a book _On Polygonal Numbers_ of which only a fragment survives.

With Pappus and Diophantus the list of original writers on mathematics comes to an end. After them came the commentators whose names only can be mentioned here. Theon of Alexandria, the editor of Euclid, lived towards the end of the fourth century A. D. To the fifth and sixth centuries belong Proclus, Simplicius, and Eutocius, to whom we can never be grateful enough for the precious fragments which they have preserved from works now lost, and particularly the _History of Geometry_ and the _History of Astronomy_ by Aristotle's pupil Eudemus.

Such is the story of Greek mathematical science. If anything could enhance the marvel of it, it would be the consideration of the shortness of the time (about 350 years) within which the Greeks, starting from the very beginning, brought geometry to the point of performing operations equivalent to the integral calculus and, in the realm of astronomy, actually antic.i.p.ated Copernicus.

T. L. HEATH.

NATURAL SCIENCE

_Aristotle_

There is a little essay of Goethe's called, simply, _Die Natur_. It comes among those tracts on Natural Science in which the poet and philosopher turned his restless mind to problems of light and colour, of leaf and flower, of bony skull and kindred vertebra; and it sounds like a prose-poem, a n.o.ble paean, eulogizing the love and glorifying the study of Nature. Some twenty-five hundred years before, Anaximander had written a book with the same t.i.tle, _Concerning Nature_, pe?? f?se??

{peri physeos}: but its subject was not the same. It was a variant of the old traditional cosmogonies. It told of how in the beginning the earth was without form and void. It sought to trace all things back to the Infinite, t? ape???? {to apeiron}--to That which knows no bounds of s.p.a.ce or time but is before all worlds, and to whose bosom again all things, all worlds, return. For Goethe Nature meant the beauty, the all but sensuous beauty of the world; for the older philosopher it was the mystery of the Creative Spirit.

Than Nature, in Goethe's sense, no theme is more familiar to us, for whom many a poet tells the story and many a lesser poet echoes the conceit; but if there be anywhere in Greek such overt praise and worship of Nature's beauty, I cannot call it to mind. Yet in Latin the _divini gloria ruris_ is praised and _Natura daedala rerum_ worshipped, as we are wont to praise and worship them, for their own sweet sakes. It is one of the ways, one of the simpler ways, in which the Roman world seems nearer to us than the Greek: and not only seems, but is so. For compared with the great early civilizations, Rome is modern and of the West; while, draw her close as we may to our hearts, Greece brings along with her a breath of the East and a whisper of remote antiquity. A Tuscan gentleman of to-day, like a Roman gentleman of yesterday, is at heart a husbandman, like Cato; he is _ruris amator_, like Horace; he gets him to his little farm or vineyard (_O rus, quando te aspiciam!_), like Atticus or the younger Pliny. As Bacon praised his garden, so does Pliny praise his farm, with its cornfields and meadowland, vineyard and woodland, orchard and pasture, bee-hives and flowers. That G.o.d made the country and man made the town was (long before Cowper) a saying of Varro's; but in Greek I can think of no such apophthegm.

As Schiller puts it, the Greeks looked on Nature with their minds more than with their hearts, nor ever clung to her with outspoken admiration and affection. And Humboldt, a.s.serting (as I would do) that the portrayal of nature, for her own sake and in all her manifold diversity, was foreign to the Greek idea, declares that the landscape is always the mere background of their picture, while their foreground is filled with the affairs and actions and thoughts of men. But all the while, as in some old Italian picture--of Domenichino or Albani or Leonardo himself--the subordinated background is delicately traced and exquisitely beautiful; and sometimes we come to value it in the end more than all the rest of the composition.

Deep down in the love of Nature, whether it be of the sensual or intellectual kind, and in the art of observation which is its outcome and first expression, lie the roots of all our Natural Science. All the world over these are the heritage of all men, though the inheritance be richer or poorer here and there: they are shown forth in the lore and wisdom of hunter and fisherman, of shepherd and husbandman, of artist and poet. The natural history of the ancients is not enshrined in Aristotle and Pliny. It pervades the vast literature of cla.s.sical antiquity. For all we may say of the reticence with which, the Greeks proclaim it, it greets us n.o.bly in Homer, it sings to us in Anacreon, Sicilian shepherds tune their pipes to it in Theocritus: and anon in Virgil we dream of it to the coo of doves and the sound of bees'

industrious murmur.

Not only from such great names as these do we reach the letter and the spirit of ancient Natural History. We must go a-wandering into the by-ways of literature. We must eke out the scientific treatises of Aristotle and Pliny by help of the fragments which remain of the works of such naturalists as Speusippus or Alexander the Myndian; add to the familiar stories of Herodotus the Indian tales of Ctesias and Megasthenes; sit with Athenaeus and his friends at the supper table, gleaning from cook and epicure, listening to the merry idle troop of convivial gentlemen capping verses and spinning yarns; read Xenophon's treatise on Hunting, study the didactic poems, the Cynegetica and Halieutica, of Oppian and of Ovid. And then again we may hark back to the greater world of letters, wherein poet and scholar, from petty fabulist to the great dramatists, from Homer's majesty to Lucian's wit, share in the love of Nature and enliven the delicate background of their story with allusions to beast and bird.

Such allusions, refined at first by art and hallowed at last by familiar memory, lie treasured in men's hearts and enshrine themselves in our n.o.blest literature. Take, of a thousand crowding instances, that great pa.s.sage in the _Iliad_ where the Greek host, disembarking on the plains of the Scamander, is likened to a migrating flock of cranes or geese or long-necked swans, as they fly proudly over the Asian meadows and alight screaming by Cayster's stream--and Virgil echoes more than once the familiar lines. The crane was a well-known bird. Its lofty flight brings it, again in Homer, to the very gates of heaven. Hesiod and Pindar speak of its far-off cry, heard from above the clouds: and that it 'observed the time of its coming', 'intelligent of seasons', was a proverb old in Hesiod's day--when the crane signalled the approach of winter, and when it bade the husbandman make ready to plough. It follows the plough, in Theocritus, as persistently as the wolf the kid and the peasant-lad his sweetheart. The discipline of the migrating cranes, the serried wedge of their ranks in flight, the good order of the resting flock, are often, and often fancifully, described. Aristotle records how they have an appointed leader, who keeps watch by night and in flight keeps calling to the laggards; and all this old story Euripides, the most naturalistic of the great tragedians, puts into verse:

The ordered host of Libyan birds avoids The wintry storm, obedient to the call Of their old leader, piping to his flock.

Lastly, Milton gathers up the spirit and the letter of these and many another ancient allusion to the migrating cranes:

Part loosely wing the region; part more wise, In common ranged in figure, wedge their way Intelligent of seasons, and set forth Their aery caravan, high over seas Flying, and over lands; with mutual wing Easing their flight; so steers the prudent crane.

But the natural history of the poets is a story without an end, and in our estimation, however brief it be, of ancient knowledge, there are other matters to be considered, and other points of view where we must take our stand.

When we consider the science of the Greeks, and come quickly to love it and slowly to see how great it was, we likewise see that it was restricted as compared with our own, curiously partial or particular in its limitations. The practical and 'useful' sciences of chemistry, mechanics, and engineering, which in our modern world crowd the others to the wall, are absent altogether, or so concealed that we forget and pa.s.s them by. Mathematics is enthroned high over all, as it is meet she should be; and of uncontested right she occupies her throne century after century, from Pythagoras to Proclus, from the scattered schools of early h.e.l.lenic civilization to the rise and fall of the great Alexandrine University. Near beside her sits, from of old, the daughter-science of Astronomy; and these twain were worshipped by the greatest scientific intellects of the Greeks. But though we do not hear of them nor read of them, we must not suppose for a moment that the practical or technical sciences were lacking in so rich and complex a civilization. China, that most glorious of all living monuments of Antiquity, tells us nothing of her own chemistry, but we know that it is there. Peep into a Chinese town, walk through its narrow streets, thronged but quiet, wherein there is neither rumbling of coaches nor rattling of wheels, and you shall see the nearest thing on earth to what we hear of Sybaris. To the production of those glowing silks and delicate porcelains and fine metal-work has gone a vast store of chemical knowledge, traditional and empirical. So was it, precisely, in ancient Greece; and Plato knew that it was so--that the dyer, the perfumer, and the apothecary had subtle arts, a subtle science of their own, a science not to be belittled nor despised. We may pa.s.s here and there by diligent search from conjecture to a.s.surance; a.n.a.lyse a pigment, an alloy or a slag; discover from an older record than the Greeks', the chemical prescription wherewith an Egyptian princess darkened her eyes, or study the pictured hearth, bellows, oven, crucibles with which the followers of Tubal-Cain smelted their ore. Once in a way, but seldom, do we meet with ancient chemistry even in Greek literature. There is a curious pa.s.sage (its text is faulty and the translation hard) in the story of the Argonauts, where Medea concocts a magic brew. She put divers herbs in it, herbs yielding coloured juices such as safflower and alkanet, and soapwort and fleawort to give consistency or 'body' to the lye; she put in alum and blue vitriol (or sulphate of copper), and she put in blood. The magic brew was no more and no less than a dye, a red or purple dye, and a prodigious deal of chemistry had gone to the making of it. For the copper was there to produce a 'lake' or copper-salt of the vegetable alkaloids, which copper-lakes are among the most brilliant and most permanent of colouring matters; the alum was there as a 'mordant'; and even the blood was doubtless there incorporated for better reasons than superst.i.tious ones, in all probability for the purpose of clarifying (by means of its coagulating alb.u.men) the seething and turbid brew.

The 'Orphic' version of the story, in which this pa.s.sage occurs, is probably an Alexandrine compilation, and whether the ingredients of the brew had been part of the ancient legend or were merely suggested to the poet by the knowledge of his own day we cannot tell; in either case the prescription is old enough, and is at least pre-Byzantine by a few centuries. Such as it is, it does not stand alone. Other fragments of ancient chemistry, more or less akin to it, have been gathered together; in Galen's book on _The making of Simples_, in Pliny, in Paulus Aegineta, and for that matter in certain Egyptian papyri (especially a certain very famous one, still extant, of which Clement of Alexandria speaks as a secret or 'hermetic' book), we can trace the broken and scattered stones of a great edifice of ancient chemistry.

Nevertheless, all this weight of chemical learning figures scantily in literature, and is conspicuously absent from our conception of the natural genius of the Greeks. We have no reason to suppose that ancient chemistry, or any part of it, was ever peculiarly Greek, or that this science was the especial property of any nation whatsoever; moreover it was a trade, or a bundle of trades, whose trade-secrets were too precious to be revealed, and so const.i.tuted not a science but a mystery. So has it always been with chemistry, the most cosmopolitan of sciences, the most secret of arts. Quietly and stealthily it crept through the world; the tinker brought it with his solder and his flux; the African tribes who were the first workers in iron pa.s.sed it on to the great metallurgists who forged Damascan and Toledan steel.

This 'trade' of Chemistry was never a science for a Gentleman, as philosophy and mathematics were; and Plato, greatest of philosophers, was one of the greatest of gentlemen. Long, long afterwards, Oxford said the same thing to Robert Boyle--that Chemistry was no proper avocation for a gentleman; but he thought otherwise, and the 'brother of the Earl of Cork' became the Father of scientific Chemistry.

Now I take it that in regard to biology Aristotle did much the same thing as Boyle, breaking through a similar tradition; and herein one of the greatest of his great services is to be found. There was a wealth of natural history before his time; but it belonged to the farmer, the huntsman, and the fisherman--with something over (doubtless) for the schoolboy, the idler, and the poet. But Aristotle made it a science, and won a place for it in Philosophy. He did for it just what Pythagoras had done (as Proclus tells us) for mathematics in an earlier age, when he discerned the philosophy underlying the old empirical art of 'geometry', and made it the basis of 'a liberal education'.[5]