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None of us happened to remember what it was that Archimedes had dreamed, and the subject was dropped. For a considerable time afterwards we saw nothing of Stonewall. He did not come to the club, and we were beginning to think of looking him up, when one evening, quite unexpectedly, he dropped in, wearing an unusually cheerful expression.
The germ of algebra may be discerned in the works of Diophantus of Alexandria, who is supposed to have lived in the second century of our era. In that Egyptian school Euclid had formerly collected the great truths of geometry, and arranged them in logical sequence. Archimedes, in Syracuse, had attempted the solution of the higher problems by the method of exhaustions.
It will be observed that the chief principle involved in all these mechanisms was a capacity to transmit great power through levers and pulleys, and this brings us to the most important field of the Syracusan philosopher's activity. It was as a student of the lever and the pulley that Archimedes was led to some of his greatest mechanical discoveries.
* It may be useful to mention some of the scientific facts and mechanical principles which were known to Europeans at this time. More than one learned essay has been written to prove the mechanical indebtedness of the modern world to the ancient, particularly to the works of those mechanically minded Greeks: Archimedes, Aristotle, Ctesibius, and Hero of Alexandria.
"But before I could deprive you of that pleasure, I ought to have been made acquainted with your intention of doing so." "You came to Belle-Isle without knowing anything?" "Of you! yes. How the devil could I imagine that Aramis had become so clever an engineer as to be able to fortify like Polybius, or Archimedes?" "True. And yet you smelt me out over yonder?" "Oh! yes." "And Porthos, too?"
The names of Hipparchus, of Apollonius, of Ptolemy, of Archimedes, will be mentioned with reverence by men of every religious profession, as long as there are men to speak. THE MUSEUM AND MODERN SCIENCE. The Museum of Alexandria was thus the birthplace of modern science.
III Ideal Husbands and Wives. IV Happiness as an End of Human Action. I The Battle of Cannæ. II Hannibal's Advance on Rome. III The Defense of Syracuse by Archimedes. I Demosthenes and Cicero Compared. II The Assassination of Cæsar. III Cleopatra's Barge. IV The Death of Antony and Cleopatra. I Of Freedom. II Of Friendship. III The Philosopher and the Crowd. I A Descent to the Unknown.
I might mention the subjects of his various works, but they would not be understood except by those familiar with mathematics. Other famous geometers could also be named, but such men as Euclid, Archimedes, and Apollonius are enough to show that geometry was cultivated to a great extent by the philosophers of antiquity.
The land forces were conducted by Appius: Marcellus, with sixty galleys, each with five rows of oars, furnished with all sorts of arms and missiles, and a huge bridge of planks laid upon eight ships chained together, upon which was carried the engine to cast stones and darts, assaulted the walls, relying on the abundance and magnificence of his preparations, and on his own previous glory; all which, however, were, it would seem, but trifles for Archimedes and his machines.
It also contains the important reference to the heliocentric theory of the universe put forward by Aristarchus of Samos in a book of 'hypotheses', as well as historical details of previous attempts to measure the size of the earth and to give the sizes and distances of the sun and moon. Lastly, Archimedes invented the whole science of hydrostatics.
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