that it was the home of a modern university in every sense of that
term, having particularly the features that many people are prone to
think of as representing modern evolution in education. The buildings
of the university were erected practically by a legacy left by the
great Conqueror himself, Alexander. The central point of interest in
the university was a great library, the nucleus of which was the
library of Aristotle, tutor of Alexander, which had been collected
with the help of that great Conqueror and was the finest collection of
books in the world of that time. The main subject of interest in the
university was physical science and its sister subject mathematics,
which raises mere nature-study into the realm of science, and this
scientific physical education was conducted in connection with the
great museum or collection of objects of interest to scientists that
had also been made partly by Aristotle himself and partly for his
loved tutor by the gratitude of Alexander during his conquering
expeditions in the far East. Finally professors were attracted to
Alexandria by the offer of a better salary than had ever been paid at
educational institutions before this, and {67} by the additional offer
of a palace to live in, supplied by the ruler of the country. It is no
wonder, then, that in attendance also, as well as in the prestige of
its professors, Alexandria resembled a modern university.
It was its devotion to science, however, that especially characterized
this first great institution of learning of which we have definite
records. This devotion to science went so far that even literature was
studied from the scientific standpoint. Such details as we have of the
instruction at Alexandria and the books that have come down to us, all
show men interested in philology, in comparative literature, in
grammar and comparative grammar, rather than in the idealistic modes
of knowledge. We have commentaries on the great authors, but no great
original works of genius in literature from the professors of
Alexandria. The translation of the Septuagint version of the Old
Testament is a typical example of the sort of work that was being done
at Alexandria. They collected the documents of the nations and
translated them for purposes of comparative study. It was an education
for information rather than for power. The main idea of the time and
place was to know as much as possible about literature, rather than to
know what it represented in terms of life, and the real meaning of
both literature and life was obscured in the study about and about
them. People studied books about books rather than the books {68}
themselves. There was much writing of books about books, and it was
nearly always comparatively trivial things in the great authors that
attracted most attention from the many scholiasts, critics, editors,
commentators, lecturers of the time.
Personally I could well understand such an incident happening at
Alexandria as is said to have happened at a well-known English (of
course not American!) university not long ago. The class was
construing Shakespeare and one of the students asked the professor
what the meaning of a particular figure used by the great dramatist
was. The professor replied that they were there to construe
Shakespeare's language and not bother about his meaning--yet it was a
class in literature. Literature in recent years as studied at the
universities has come to be quite as scientific in its modes and
methods as it was at the University of Alexandria. May I also add that
it has become quite as sterile of results of any importance. There is
very little real study of literature, practically no encouragement of
the attempt to draw inspiration from the great authors, but all
devotion to the grammar, to the philology, to comparative literature
as exemplified in the old writers.
Books were the great essentials at Alexandria. This is not surprising
seeing that the university was founded around a great library, and
that this library continued to be the greatest in the world in its
time. Every student who came to Alexandria bringing a book with him of
which there was {69} no copy in the library, was required by a decree
of the authorities to leave a copy behind him. In all the university
towns of the times--and there were many founded in the rising eastern
cities of Alexander's empire, as it gradually crumbled into smaller
pieces providing new capitals with less power but with quite as much
national feeling as the capital cities of larger states, libraries
became the fashion and a city's main claim to prestige in education
and the intellectual life was the number of its books. Antioch,
Tarsus, Cos, Cnidos and Pergamos are examples of this state of
affairs. Pergamos was so jealous of the prestige of the Alexandrian
Library that it forbade the exportation of parchment, an invention of
Pergamos which received its name from that city. Petty jealousies were
quite as much the rule among educational institutions then as they
have been at any time since.
To many people it will seem quite absurd to talk of Alexandria as
having done serious scientific work because the methods of science and
scientific investigation are supposed to have been, as they think,
discovered by Lord Bacon in the seventeenth century. It is curious how
many educated people, or at least supposedly educated people, have
this as their basic notion of the history of science. Men wandered in
the mazes of inductive reasoning utterly unable to bring observations
together in such a way as to discover laws, utterly incompetent to
note phenomena and {70} bring them into relations to one another so as
to show their scientific bearing, until Queen Elizabeth's Lord
Chancellor came to show the way out of the labyrinth and leave the
precious cord through its corridors, by which others may easily thread
their way into the free air of scientific truth. I know nothing that
is more absurd than this. It is a commonplace among educators,
however; it is frequently referred to in educational addresses as if
it were a universally accepted proposition, and to dispute it would
seem the rankest kind of scientific heresy to these narrow minds.
Fortunately there are two writers, Macaulay and Huxley, to whom even
these people are likely to listen, who have expressed themselves with
regard to this precious historic superstition that Lord Bacon invented
the inductive method of reasoning with what my long-worded friend
would call appropriate opprobrium.
Macaulay says: "The inductive method has been practised ever since the
beginning of the world by every human being. It is constantly
practised by the most ignorant clown, by the most thoughtless
schoolboy, by the very child at the breast. That method leads the
clown to the conclusion that if he sows barley he shall not reap
wheat. By that method the schoolboy learns that a cloudy day is the
best for catching trout. The very infant, we imagine, is led by
induction to expect milk from his mother or nurse, and none from his
father. Not only is it not true that {71} Bacon invented the inductive
method; but it is not true that he was the first person who correctly
analyzed that method and explained its uses. Aristotle had long before
pointed out the absurdity of supposing that syllogistic reasoning
could ever conduct men to the discovery of any new principle, had
shown that such discoveries must be made by induction, and by
induction alone, and had given the history of the inductive process,
concisely indeed, but with great perspicuity and precision."
And Huxley quite as emphatically points out: "The method of scientific
investigation is nothing but the expression of the necessary mode of
working of the human mind. It is simply the mode by which all
phenomena are reasoned about--rendered precise and exact."
While the whole trend of education, even that of literature, was
scientific at Alexandria, the principal feature of the teaching was,
as we have said, concerned with the physical sciences and mathematics.
It is in mathematics that the greatest triumphs were secured. Euclid's
"Geometry," as we use it at the present time in our colleges and
universities, was put into form by Euclid teaching at the University
of Alexandria in the early days of the institution. Euclid's setting
forth of geometry was so perfect that it has remained for over 2,000
years the model on which all text-books of geometry of all the later
times have been written. There seems no doubt that {72} writers on the
history of mathematics are quite justified in proclaiming Euclid's
"Geometry" as one of the greatest intellectual works that ever came
from the hand of man. The first Ptolemy was fortunate in having
secured this man as the founder of the mathematical department of his
university. His example, the wonderful incentive of his work, the
absolute perfection of his conclusions, must have proved marvellous
emulative factors for the students who flocked to Alexandria.
Commonly mathematicians are said to be impractical geniuses so
occupied with mathematical ideas that their influence in other ways
counts for little in university life. If we are to believe the stories
that come to us with regard to Euclid, however, and there is every
reason to believe them, for some of them come from men who are almost
contemporaries, or from men who had their information from
contemporaries, Euclid's influence in the university must have been
for all that is best in education. Proclus tells the story of King
Ptolemy once having asked Euclid, if there was any shorter way to
obtain a knowledge of geometry than through the rather difficult
avenue of Euclid's own text-book, and the great mathematician replied
that there was "no royal road to geometry." Stobaeus relates the story
of a student who, having learned the first theorem, asked "but what
shall I make by learning these things?" The question is so modern that
Euclid's {73} answer deserves to be in the memory of all those who are
interested in education. Euclid called his slave and said, "Give him
twopence, since he must make something out of everything that he does,
even the improvement of his mind."
Probably even more significant than the tradition that Euclid did his
work at this first modern university, and that besides being a
mathematician he was a man of very practical ideas in education, is
the fact that he was appreciated by the men of his time and that his
work was looked up to with highest reverence by his contemporaries and
immediate successors as representing great achievement. It is not ever
thus. Far from resenting in any way the magnificent synthesis that he
had made of many rather vague notions in mathematics before his time,
his contemporaries united in doing him honor. They realized that his
teaching created a proper scientific habit of mind. Pappus says of
Apollonius that he spent a long time as a pupil of Euclid at
Alexandria and it was thus that he acquired a thorough scientific
habit of mind. After Euclid's time the value of his discoveries as a
means of training the mind was thoroughly appreciated. The Greek
philosophers are said to have posted on the doors of their schools
"Let no one enter here who does not know his Euclid." In the midst of
the crumbling of old-fashioned methods of education in the
introduction of the elective system, in the modern time, many of our
best educators have insisted {74} that at least this portion of
mathematics, Euclid's contribution to the science, should be a
required study, and most educators feel, even when there is question
of law or medical study, that one of the best preparations is to be
found in a thorough knowledge of Euclid.
Almost as wonderful as the work of Euclid was that of the second great
mathematician of the Alexandrian school, Archimedes, who not only
developed pure mathematics but applied mathematical principles to
mechanics and proved besides to have wonderful mechanical ability and
inventive genius. It was Archimedes of whom Cicero spoke so feelingly
in his "Tusculan Disputations," when about a century and a quarter
after Archimedes' death, he succeeded in finding, his tomb in the old
cemetery at Syracuse during his quaestorship there. How curious it is
to think that after so short a time as 127 years from the date of his
death Archimedes was absolutely forgotten by his fellow-Syracusans,
who resolutely denied that any trace of Archimedes' tomb existed. This
stranger from Rome knew much more of Archimedes than his
fellow-citizens a scant four generations after his time. Not how men
advance, but how they forget even great advance that has been made,
lose sight of it entirely at times and only too often have to
rediscover it, is the most interesting phase of history. Cicero says,
"Thus one of the noblest cities of Greece and one which at one time
had been very {75} celebrated for learning, knew nothing of the
monument of its greatest genius until it was rediscovered for them by
a native of Arpinum"--Cicero's modest designation for himself.
We have known much more about Archimedes' inventions than about his
mathematical works. The Archimedian screw, a spiral tube for pumping
water, invented by him, is still used in Egypt. The old story with
regard to his having succeeded in making burning mirrors by which he
was enabled to set the Roman vessels on fire during the siege of
Syracuse, used to be doubted very seriously and, indeed, by many
considered a quite incredible feat, clearly an historical
exaggeration, until Cuvier and others in the early part of the
nineteenth century succeeded in making a mirror by which in an
experiment in the Jardin des Plantes in Paris wood was set on fire at
a distance of 140 feet. As the Roman vessels were very small,
propelled only by oars or at least with very small sail capacity, and
as their means of offence was most crude and they had to approach
surely within 100 feet of the wall to be effective, the old story
therefore is probably entirely true. The other phase of history
according to which Archimedes succeeded in constructing instruments by
which the Roman vessels were lifted bodily out of the water, is
probably also true, and certainly comes with great credibility of the
man of whom it is told that, after having studied the lever, he
declared that if he only had {76} some place to rest his lever, he
could move the world.
The well-known story of his discovery in hydrostatics, by which he was
enabled to tell the King whether the royal goldsmiths had made his
crown of solid gold or not, is very well authenticated. Archimedes
realized the application of the principle of specific gravity in the
solution of such problems while he was taking a bath. Quite forgetful
of his state of nudity he ran through the streets, crying "Eureka!
Eureka! I have found it! I have found it!" There are many other
significant developments of hydrostatics and mechanics, besides
specific gravity and the lever, the germs of which are at least
attributed to Archimedes. He seems to have been one of the world's
great eminent practical geniuses. That he should have been a product
of Alexandria and should even have been a professor there would be a
great surprise if we did not know Alexandria as a great scientific
university. As it is, it is quite easy to understand how naturally he
finds his place in the history of that university and how proud any
modern university would be to have on the rolls of its students and
professors a man who not only developed pure science but who made a
series of practical applications that are of great value to mankind.
Such men our modern universities appropriately claim the right to
vaunt proudly as the products of their training.
When we analyze something of the work in {77} pure mathematics that
was accomplished by Archimedes our estimation of him is greatly
enhanced. His work "On the Quadrature," that is the finding of the
area of a segment of the parabola, is probably his most significant
contribution to mathematical knowledge. His proof of the principal
theorem in this is obtained by the "method of exhaustion," which had
been invented by Eudoxus but was greatly developed by Archimedes. This
method contains in itself the germ of that most powerful instrument of
mathematical analysis in the modern time, the calculus.
Another very important work was "The Sphere and the Cylinder." This
was more appreciated in his own time, and as a consequence, after his
death the figure of a sphere inscribed in a cylinder was cut on his
tomb in commemoration of his favorite theorem, that the volume of the
sphere is two-thirds that of the cylinder and its surface is four
times that of the base of the cylinder. It was by searching for this
symbol, famous in antiquity, that Cicero was enabled to find his tomb
according to the story that I have already related.
Within the last few years the reputation of Archimedes in pure
mathematics has been greatly enhanced by the discovery by Professor
Heiberg of a lost work of the great Alexandrian professor in
Constantinople. Archimedes himself stated in a dedication of the work
to Eratosthenes the method employed in this. He says: "I have thought
it well to analyze and lay down for you {78} in this same book a
peculiar method by means of which it will be possible for you to
derive instruction as to how certain mathematical questions may be
investigated by means of mechanics. And I am convinced that this is
equally profitable in demonstrating a proposition itself, for much
that was made evident to me through the medium of mechanics was later
proved by means of geometry, because the treatment by the former
method had not yet been established by way of a demonstration. For of
course it is easier to establish a proof, if one has in this way
previously obtained a conception of the questions, than for him to
seek it without such a preliminary notion. . . . Indeed, I assume that
some one among the investigators of to-day or in the future, will
discover by the method here set forth still other propositions which
have not yet occurred to me." On this Professor Smith comments:
"Perhaps in all the history of mathematics no such prophetic truth was
ever put into words. It would almost seem as if Archimedes must have
seen as in a vision the methods of Galileo, Cavalieri, Pascal, Newton,
and many other great makers of the mathematics of the Renaissance and
the present time."
Many other distinguished professors of mathematics have, since this
declaration of Archimedes came under their notice, declared that he
must have had almost a prophetic vision of certain developments of
mathematics and especially applied {79} mathematics and mechanics and
their relation to one another, that were only to come in much later
and indeed comparatively modern times. Undoubtedly Archimedes' works
proved the germ of magnificent development not only immediately after
his own time but in the long-after time of the Renaissance, when their
translation awakened minds to mathematical problems and their
solutions that would not otherwise have come.
We know much less of the life of the third of the great trio of
teachers and students of Alexandria, Apollonius of Perga. Perhaps it
should be enough for us to know that his contemporaries spoke of him
as "the great geometer," though they were familiar with Euclid's book
and with Archimedes' mighty work. Apollonius was surely a student of
Alexandria for many years and he was probably also a professor of
mathematics there. He developed especially what we know now as conic
sections. His book on the subject contains practically all of the
theorems to be found in our text-books of analytical geometry or conic
sections of the present time. It was developed with rigorous
mathematical logic and Euclidean conclusiveness. These three men show
us beyond all doubt how finely the mathematical side of the university
developed.
After Archimedes the greatest mechanical genius of the University of
Alexandria was Heron. To him we owe a series of inventions and
discoveries in hydrostatics and the {80} construction of various
mechanical toys that have been used in the laboratories since. There
is even a little engine run by steam--the aeolipile--invented by him,
which shows how close the old Greeks were to the underlying principles
of discoveries that were destined to come only after the development
of industries created a demand for them in the after time. Heron's
engine is a globe of copper mounted on pivots, containing water, which
on being heated produces steam that finds its way out through tubes
bent so as to open in opposite directions on each side of the globe.
The impact of the escaping steam on the air sets the globe revolving,
and the principle of the turbine engine at work is clear. We have used
steam for nearly 200 years always with a reciprocating type of
movement, so that to apply energy in one direction the engine has had
to move its parts backwards and forwards, but here was a direct-motion
turbine engine in the long ago. Our great steamboats, the _Lusitania_
and the _Mauretania,_ now cross the ocean by the use of this principle
and not by the reciprocating engine, and it is evident that it is
along these lines the future developments of the application of steam
are to take place.
Another extremely interesting invention made by Heron is the famous
fountain called by his name, and which still is used to illustrate
principles in pneumatics in our classrooms and laboratories. By means
of condensed air water is made {81} to spring from a jet in a
continuous stream and seems paradoxically to rise higher than its
source. Probably his best work in the domain of physics is that on
pneumatics in which are given not only a series of discussions, but of
experiments and demonstrations on the elasticity of air and of steam.
These experiments could only have been conducted in what we now call a
physical laboratory. Indeed these inventions of his are still used in
laboratories for demonstration purposes. While we may think, then,
that the foundation of laboratories was reserved to our day, there is
abundant evidence for their existence at the University of Alexandria.
We shall return to this subject a little later, when the evidence from
other departments has been presented, and then it will be clear, I
think, that the laboratory methods were favorite modes of teaching at
the University of Alexandria and were in use in nearly all departments
of science both for research and for demonstration purposes.
The work of the other great teacher at Alexandria which was to
influence mankind next to that of Euclid, was not destined to
withstand the critical study of succeeding generations, though it
served for some 1,500 years as the basis of their thinking in
astronomy. This was the work of Ptolemy, the great professor of
astronomy at Alexandria of the first century after Christ. It is easy
for us now to see the absurdity of Ptolemy's system. It is even hard
for us to {82} understand how men could have accepted it. It must not
be forgotten, however, that it solved all the astronomical problems of
fifteen centuries and that it even enabled men, by its application, to
foretell events in the heavens, and scientific prophecy is sometimes
claimed to be the highest test of the truth of a system of scientific
thought. Even so late as 1620 Francis Bacon refused to accept
Copernicanism, already before the world for more than a century,
because it did not, as it seemed to him, solve all the difficulties,
while Ptolemy's system did. As great an astronomer as Tycho Brahe
living in the century after Copernicus still clung to Ptolemy's
teaching. It must not be forgotten that when Galileo restated
Copernicanism, the reason for the rejection of his teaching by all the
astronomers of Europe almost without exception, was that his reasons
were not conclusive. They preferred to hold on to the old which had
been so satisfying than to accept the new which seemed dubious. Their
wisdom in this will be best appreciated from the fact that none of
Galileo's reasons maintained themselves.