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the prestige of authority； and produce mere Sorbonnes； and schools of
pedants。 To literature； too； they do some good； that is； in a literary age
an age of reflection rather than of production； of antiquarian research；
criticism； imitation； when book…making has become an easy and
respectable pursuit for the many who cannot dig； and are ashamed to beg。
And yet； by adding that same prestige of authority； not to mention of good
society and Court favour； to the popular mania for literature； they help on
the growing evil； and increase the multitude of prophets who prophesy out
of their own heart and have seen nothing。
And this was； it must be said； the outcome of all the Ptolemaean
appliances。
In Physics they did little。 In Art nothing。 In Metaphysics less than
nothing。
We will first examine； as the more pleasant spectacle of the two； that
branch of thought in which some progress was really made； and in which
the Ptolemaic schools helped forward the development of men who have
become world…famous； and will remain so； I suppose； until the end of
time。
Four names at once attract us： Euclid； Aristarchus； Eratosthenes；
Hipparchus。 Archimedes； also； should be included in the list； for he was
a pupil of the Alexandrian school； having studied （if 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
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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
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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