alexandria and her schools-第6章
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Proclus is to be trusted） in Egypt； under Conon the Samian； during the reigns of two Ptolemies； Philadelphus and Euergetes。
Of Euclid； as the founder （according to Proclus） of the Alexandrian Mathematical school； I must of course speak first。 Those who wish to attain to a juster conception of the man and his work than they can do from any other source； will do well to read Professor De Morgan's admirable article on him in 〃Smith's Classical Dictionary；〃 which includes； also； a valuable little sketch of the rise of Geometric science； from Pythagoras and Plato； of whose school Euclid was； to the great master himself。
I shall confine myself to one observation on Euclid's genius； and on the immense influence which it exerted on after generations。 It seems to me； speaking under correction； that it exerted this； because it was so complete a type of the general tendency of the Greek mind； deductive； rather than inductive； of unrivalled subtlety in obtaining results from principles； and results again from them ad infinitum： deficient in that sturdy moral patience which is required for the examination of facts； and which has made Britain at once a land of practical craftsmen； and of earnest scientific discoverers。
Volatile； restless； 〃always children longing for something new；〃 as the Egyptian priest said of them； they were too ready to believe that they had attained laws； and then； tired with their toy； throw away those hastily assumed laws； and wander off in search of others。 Gifted； beyond all the sons of men； with the most exquisite perception of form； both physical and metaphysical； they could become geometers and logicians as they became sculptors and artists； beyond that they could hardly rise。 The were conscious of their power to build； and it made them ashamed to dig。
Four men only among them seem； as far as I can judge； to have had a great inductive power： Socrates and Plato in Metaphysics； Archimedes and Hipparchus in Physics。 But these men ran so far counter to the national genius； that their examples were not followed。 As you will hear presently； the discoveries of Archimedes and Hipparchus were allowed to remain where they were for centuries。 The Dialectic of Plato and Socrates was degraded into a mere art for making anything appear alternately true and false； and among the Megaric school； for undermining the ground of all science； and paving the way for scepticism； by denying the natural world to be the object of certain knowledge。 The only element of Plato's thought to which they clung was； as we shall find from the Neoplatonists； his physical speculations； in which； deserting his inductive method； he has fallen below himself into the popular cacoethes； and Pythagorean deductive dreams about the mysterious powers of numbers； and of the regular solids。
Such a people； when they took to studying physical science； would be； and in fact were； incapable of Chemistry； Geognosy； Comparative Anatomy； or any of that noble choir of sister sciences； which are now building up the material as well as the intellectual glory of Britain。
To Astronomy； on the other hand； the pupils of Euclid turned naturally； as to the science which required the greatest amount of their favourite geometry： but even that they were content to let pass from its inductive to its deductive stagenot as we have done now； after two centuries of inductive search for the true laws； and their final discovery by Kepler and Newton： but as soon as Hipparchus had propounded any theory which would do instead of the true laws； content there to stop their experiments； and return to their favourite work of commenting； deducing； spinning notion out of notion； ad infinitum。
Still； they were not all of this temper。 Had they been； they would have discovered； not merely a little； but absolutely nothing。 For after all； if we will consider； induction being the right path to knowledge； every man； whether he knows it or not； uses induction； more or less； by the mere fact of his having a human reason； and knowing anything at all； as M。 Jourdain talked prose all his life without being aware of it。
Aristarchus is principally famous for his attempt to discover the distance of the sun as compared with that of the moon。 His method was ingenious enough； but too rough for success； as it depended principally on the belief that the line bounding the bright part of the moon was an exact straight line。 The result was of course erroneous。 He concluded that the sun was 18 times as far as the moon； and not； as we now know； 400； but his conclusion； like his conception of the vast extent of the sphere of the fixed stars； was far enough in advance of the popular doctrine to subject him； according to Plutarch； to a charge of impiety。
Eratosthenes； again； contributed his mite to the treasure of human sciencehis one mite； and yet by that he is better known than by all the volumes which he seems to have poured out； on Ethics； Chronology； Criticism on the Old Attic Comedy； and what not； spun out of his weary brain during a long life of research and meditation。 They have all perished；like ninety…nine hundredths of the labours of that great literary age； and perhaps the world is no poorer for the loss。 But one thing； which he attempted on a sound and practical philosophic method； stands； and will stand for ever。 And after all； is not that enough to have lived for？ to have found out one true thing； and； therefore； one imperishable thing； in one's life？ If each one of us could but say when he died： 〃This one thing I have found out； this one thing I have proved to be possible； this one eternal fact I have rescued from Hela； the realm of the formless and unknown；〃 how rich one such generation might make the world for ever！
But such is not the appointed method。 The finders are few and far between； because the true seekers are few and far between； and a whole generation has often nothing to show for its existence but one solitary gem which some one manoften unnoticed in his timehas picked up for them； and so given them 〃a local habitation and a name。〃
Eratosthenes had heard that in Syene； in Upper Egypt； deep wells were enlightened to the bottom on the day of the summer solstice； and that vertical objects cast no shadows。
He had before suggested； as is supposed； to Ptolemy Euergetes； to make him the two great copper armillae； or circles for determining the equinox； which stood for centuries in 〃that which is called the Square Porch〃probably somewhere in the Museum。 By these he had calculated the obliquity of the ecliptic； closely enough to serve for a thousand years after。 That was one work done。 But what had the Syene shadows to do with that？ Syene must be under that ecliptic。 On the edge of it。 In short； just under the tropic。 Now he had ascertained exactly the latitude of one place on the earth's surface。 He had his known point from whence to start on a world…journey； and he would use it； he would calculate the circumference of the earthand he did it。 By observations made at Alexandria； he ascertained its latitude compared with that of Syene； and so ascertained what proportion to the whole circumference was borne by the 5000 stadia between Alexandria and Syene。 He fell into an error； by supposing Alexandria and Syene to be under the same meridians of longitude： but that did not prevent his arriving at a fair rough result of 252；000 stadia31；500 Roman miles； considerably too much； but still； before him； I suppose； none knew whether it was 10；000； or 10；000；000。 The right method having once been found； nothing remained but to employ it more accurately。
One other great merit of Eratosthenes is； that he first raised Geography to the rank of a science。 His Geographica were an organic collection； the first the world had ever seen； of all the travels and books of earth…description heaped together in the Great Library； of which he was for many years the keeper。 He began with a geognostic book； touched on the traces of Cataclysms and Change visible on the earth's surface； followed by two books； one a mathematical book； the other on political geography； and completed by a mapwhich one would like to see： but not a trace of all remains； save a few quoted
