tomb. This was ordered done by Marcellus." 1 As Cajori points 

 out the most wonderful of his works is, perhaps, his treatise "On 

 Spirals". He was deprived of the use of the infinitesimal calculus, 

 but this only served to display the fertility of his genius. In its 

 stead, he used in a masterly manner the so-called "method of 

 exhaustion". The geometry of the Greeks had reached a high 

 degree of attainment, and though Archimedes was to be followed 

 by other great scholars such as Apollonius of Perga, Hipparchus, 

 Ptolemy and Pappus, yet, geometry, as a science, was already 

 established and well-differentiated. 



But there was another study, which engaged the fertile brain of 

 this master mathematician, and that is the science we call mechan- 

 ics. In this particular realm, Archimedes had far fewer predeces- 

 sors than in geometry. And yet it is true that ancient Egyptian 

 and Assyrian monuments contain pictorial representations of many 

 kinds of implements and mechanical devices. Very early in his 

 history, man was able to fashion crude implements, and, in the 

 excavations which have been made, many interesting discoveries 

 have resulted, discoveries which have enabled anthropologists 

 materially in constructing a theory of the development of primitive 

 man. The lever, the inclined plane and the wedge were known from 

 a remote antiquity, and their practical use takes us back to the 

 dawn of history. But apparently little effort was made to under- 

 stand the principles of these instruments until many centuries after 

 their invention. Indeed, it was not till the time of Archimedes that 

 mechanical science became, in any sense, properly formulated. 

 Archytas, of the school of Pythagoras, is said to have invented the 

 screw and the pulley, and Aristotle, in his Mechanica Problemata, 

 c. 18, describes in a rather vague way a compound pulley. It is 

 evident, from the same work, that, before Archimedes, the mathe- 

 matical theory of the lever was under consideration. Some con- 

 ception of the parallelogram of forces had also appeared and, it is 

 possible, since Archimedes uses the concept "centre of gravity", 

 without defining it, that it was already in use. His investigations 

 into mechanics, contained in his " Equiponderance of Planes", and 

 his book, "On Floating Bodies", are fashioned somewhat after the 

 method which Euclid had used so successfully. Book 1 of the latter 



1 F. Cajori, A History of Mathematics, P. 42. 



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