ARCHIMEDES. 



ARCHIMFT1ES. 



M 



etna. It WM after this that Arehilochu* 



rattoThaso*. H. then went to Sparta, to Siris in Lower Italy, and 

 at lessjth returned to Paras, where be fell in an action between the 

 Parian* sod Naxian*. (Pint -de Sec* Ham. VfaoV o. 17.) It WM in 

 Iambic vene that the poet chiefly exotUed; be is said, indeed, to 

 have been the inventor of it, sod WM one of the three poete whom 

 Arietarchu* eetsemid most highly in this species of poetry (Veil. 

 Palm. i. 5 ; QuintiL x. 1). Some) spedmea* of Arehilochus. trans- 

 sated with much spirit, may be seen in Men vale'* Anthology,' London, 

 188S. Some fragments an feond in the 'Analeeta Vat. Poet. Onto.' 

 of Branch, Anrent, 1785, and they an publUhed separately by Liebel, 

 Reiiqui. Archilochi,' Vienna, 1819. 8vo.; al*o in Gaisford's < Minor 

 Greek Poets.' vol i. ; and in Bosswanade's Collection,' vol. xv. 



ARCH 1 MOTES, the most celebrated of the Greek geometers, and 

 OM of the few men whose writings form a standard epoch in the 

 liissnrr of the nioftieas of knowledge, WM born in Sicily, in the Corin- 

 thian colony of Syracuse, in the year sxc. 287 : be WM killed when that 



I taken by the Roman* under Marcellus, B.C. 212. aged seventy- 

 ftve yean. Eoclid died about the Urn* of the birth of Archimedes, 

 and Apollooiua of Perga WM about forty yean hi* junior. Erato*- 

 theoea WM born about tea yean before him. 



The life of Arehimedee WM written, according to Eutocius, hi* 

 aomnMatator, by Haracliiln, but the work baa not come down to UK, 

 and all that i* known of him ha* been collected from various author*, 

 of whom the principal an Polvbiu* hi* contemporary, Livy, Plutarch, 

 and Cicero. We acknowledge) our obligation* to the life of Archimede* 

 in RiTault'* edition of hi* work*, Paris, 1615 ; and also to that in 

 K. Peynrd'a translation. Pari*. 1809. 



Arobimedea WM related to Hieron, the eecond- prince of that name, 

 who came to the throne of Syracuse when Archimede* WM a very 

 young man. The reign of thin prince, including the time that hi* con 

 Ocion also bore the royal title, lasted about fifty-fire yean, during 

 the t prater part of which Archimedo* remained at Syracuae under 

 thru- patronage. All that we know of hi* life during thin period, inde- 

 prudently of the remits of hi* atudie*. of which we (hall presently 

 apeak, U contained in the following incident*. The well-known story 

 of Hieron'i crown (or Oelon'* crown, according to some), i* M follow* : 

 Hieron, or Oelon, had delivered a certain weight of gold to a work- 

 man, to be made into a retire crown. The Utter brought back a 

 crown of the proper weight, which WM afterward* suspected to hare 

 been alloyed with .ilrer. The king aaked Archimede. how he might 

 delect the cheat ; the difficulty being to measure the bulk of the crown 

 without melting it into a regular figure ; for *ilrer being, weight for 

 weight, of greater bulk than gold, any alloy of the former, in place of 

 an equal weight of the latter, would necessarily increase the bulk of 

 the crown. While thinking on thia nutter, Archimede* went to bathe, 

 and on stepping into the bath, which WM full, obaerred the very 

 eimple fact, that a quantity of water of the aame bulk M hi* body 

 before be cou 



flow over before he could immerse himself. It immediately 

 track him that by immening a weight of real gold, equal to that 

 which the crown ought to have contained, in a vessel full of water, 

 and observing how much water WM left when the weight WM taken 

 out again, and by afterwards doing the same thing with the crown 

 Heelf, be could ascertain whether the latter exceeded the former in 

 balk. In the words of Vitruvius, " As soon M he had hit upon this 

 method of detection, be did not wait a moment, but jumped joyfully 

 oat of the bath, and running naked towards his own house, called out 

 with a loud voice that be had found what be sought ; for M he ran he 

 called oat in Greek, *>, l(pvn (' I have found it, I have found 

 it')." According to Proclus, Hieron declared that from that moment 

 be could never refuse to believe anything that Archimedes told him. 



The apophthegm attributed to him. that if he had a point to stand 

 upon, be could move the world, arose from his knowledge of the pos- 

 sible effect* of machinery, and however it might aitonish a Greek of 

 Us day, would now be readily admitted to be M theoretically possible 

 M it is practically impossible. 



He is said to have travelled into Egypt, sad while there, observing 

 the nicsssity of raisins; the water of the Nile to points which the river 

 did not reach, to have invented the screw which bean hi* name, lie 

 also invented a screw, according to Proclus, which ensbled HJ.T..H 

 himself to move a ship which all the Syrsctuans were unable to stir. 

 The screw now applied to steam-vessels, and which ha* been connected 

 with the name of Archimedes, ha* only thia in common with the great 

 S^OOMUT, that he is said to have been the fint who moved a ship with 



After the death of Hieron, the misconduct of hi* successor Hiero 

 nymus, the son of Galon, provoked a rebellion, in which he WM killed. 

 The roeofsaful party sided with the Carthaginians, and the Romans 

 eccordisejly dispatched a land and naval armament against Syracuse 

 under Appios sad Marcelln*. Among all the extraordinary stories 

 which have been told of the siege, so much seems clear : that it 

 lasted three yean in spite of the utmost efforts of the besieger* ; that 

 this soeonsjfnl resistance WM principally owing to the machine* con- 

 stmoted by ArobimedM; aad that the city, after the siege had been 

 soaae time converted into a blockade, WM finally taken by surprise, 

 owing to the carelessness of the besieged daring the festival of Diana. 

 Polybins states that catapult* and batiste of various sites were suc- 

 cessfully need against the enemy ; that in their nesrer approach they 



were galled by arrow* shot not only from the top of the walls, but 

 through port-holes constructed in numerous places; that machines, 

 which threw mssses of stone or lead of a weight not leu than ton 

 talent*, discharged their contents upon the Roman engines, which had 

 been previously caught by ropes ; that iron hand* (or hooks) attached 

 to chains, were thrown so M to catch the prows of the vessels, which 

 were then overturned by the besieged ; and that the same machines 

 were used to catch the awailanta on the land side, and throw them to 

 the ground. Liry and Plutarch give much the same account ; but 

 the curious story of setting the Roman ships on fire by mirrors, is 

 fint mentioned by John Tsetses and Zonaras, writers of the 12th 

 century, who cite Diodoru* and others for the fact. But Galen, in the 

 2nd century, though he mention* that Archimedes set the enemy's 

 hip* on fire, says it WM done with i-i/pio, which may refer to any 

 machine or contrivance throwing lighted materials. Lucian also, who 

 ired in the 2nd century, mention* the burning of the ships, but with- 

 out saying how it WM effected. 



After the storming of Syracuse, Archimedes WM killed by a Roman 

 soldier, who did not know who he WM ; Maroellus, it is said, had given 

 strict orders to preserve him alive. According to Valerius Mazimus, 

 when the soldier axked who he wan, Archimedes, being intent upon a 

 problem, begged that his diagram might not be disturbed ; upon which 

 .be soldier put him to death. According to another account, he was 

 M the act of carrying his instruments to Marcellug, when he WM killed 

 by some soldiers who suspected he WM concealing treasure. At his 

 own request, expressed during his life, a sphere inscribed in a cylinder 

 WM engraved on hi* tomb, in memory of hi* discovery that the solid 

 content of a sphere is exactly two-thirds of that of the circumscribing 

 cylinder. By this mark it was afterwards found, covered with weeds, 

 by Cicero, when he was residing in Sicily as qua-stor. 



The fame of Archimede* rests upon the extraordinary advances 

 which he made, considering the time in which he lived, in pure geo- 

 metry, in the theory of equilibrium, and in numerical approximation. 

 In pure geometry be made a* near an approach to the fluxional or 

 differential calculus as can possibly be done without the aid of alge- 

 braic transformations. In the theory of mechanics be was the only 

 one among the ancients who reduced anything to demonstration from 

 evident first principles ; indeed, up to the time of Sterinus and Galileo, 

 no further advance was made. The works of Archimedes which have 

 come down to us, of which the fint seven are in Greek, are : 



1. Two books 'On the Sphere and Cylinder.' 2. ' On the Measure- 

 ment of the Circle.' In this work is given the celebrated approximation 

 to the proportion existing between the circumference and the diameter 

 of a circle. Archimedes gives the ratio M between 3-1428 and 3-1408. 

 It is now known to be 3'1416 very nearly. 3. ' On Conoids and Sphe- 

 roids.' In this treatise is shown, probably for the first time, how to 

 find the area of an ellipse by means of that of a circle. 4. ' On Spirals.' 

 6. Two books ' On the Equilibrium and Centre of Gravity of Plane 

 Surfaces.' 6. ' Psammites,' better known by its Latin name ' Areua- 

 riua.' 7. ' On the Quadrature of the Parabola.' 8. Two books ' On 

 Bodies Floating in a Fluid.' There i* also a book of ' Lemmas ' attri- 

 buted to Archimedes, translated from the Arabic in 1 659, and repub- 

 lished by Borelli in 1661. The works of Archimedes an- written in 

 Doric Greek, the prevailing dinlect in Sicily. The text is for the moat 

 part in tolerably good preservation ; the style is clear, and has been 

 considered better than that of any of the other Greek geometers. M. 

 Peyrard, in calling Archimedes the Homer of Geometry, has made a 

 simile which is perfectly admissible M to the strength of praise it 

 conveys, if in no other point. The commentaries of Eutocius which 

 hare come down to us are tboee on the ' Sphere and Cylinder,' the 

 ' Measurement of the Circle,' and the ' Equilibrium of Planes.' 



We can only briefly touch upon several remaining points. It is 

 known from Ptolemy that Archimedes observed or calculated several 

 solstices, for the determination of the length of the year. He is said 

 to hare been the first who constructed a machine for representing the 

 motions of the sun, moon, stars, and perhaps of the planets. A large 

 number of works which hare not come down to us is attributed to 

 him, a list of which may be found in Fabriciu* ; particularly a treatise 

 on ' Burning Mirrors,' and a treatise on the ' Parabola,' published at 

 Louvain in 1548. There is no great evidence in farour of the genuine- 

 ness of either. The ancients attributed to him more than forty mecha- 

 nical inventions, among which are the endless screw ; the combination 

 of pulleys ; an hydraulic organ, according to Tertullian ; a machine 

 called the helix, or screw, for launching ship*, according to Athenicus ; 

 and a machine called loculux, which appears to have consisted of forty 

 pieces, by the putting together of which various object* could be 

 framed, and which was used by boys M a sort of artificial memory. 

 It is impossible to understand what is meant by such a description. 

 This constant tendency to attribute inventions to Archimedes suffi- 

 ciently show* the impresiion which hi* name left on posterity. 



Among the principal editions of the works of Archimedes wo must 

 notice the partial edition of Tartaglia, Venice, 1643 ; the fint com- 

 plete edition, reviewed by Regiomontanus, accompanied by the com- 

 mentary of Eutocius; the whole Greek and Latin, Basle, 1544. 

 There are editions by Commanding Venice, 1558 (containing only part 

 of his works) ; by Kivault, Paris, 1615 (containing the Greek of Archi- 

 medes in the preliminary addresses nnd enunciations only, the demon- 

 stration* being the Latin of Rirault, except in the ' ArenariuR,' which 



