translated from the Dutch in Gilbert's “ Annalen |
movements
of the hearenly bodies, of which we
der Physik," vol.
der Physik," vol.
William Smith - 1844 - Dictionary of Greek and Roman Antiquities - a
The name of | there, because he bad written in his poeins, that a
8
## p. 269 (#289) ############################################
ARCIIILOCHUS.
269
ARCHILOCHUS.
Was
9
p. 5. )
man bad better throw away his arms than lose his rage," as we see in the line of llorace ( A. P.
life. But Valerius Maximus (vi. 3, ext. 1) says, 79):
that the poems of Archilochus were forbidden at “ Archilochum proprio rabies armavit iambo,"
Sparta because of their licentiousness, and especi- and in the expression of Hadrian (l. c. ), Avoo@vTAS
ally on account of the attack on the daughters of iáulous; and his bitterness passed into a proverbia
Lycambes. It must remain doubtful whether a 'Apxınó xou mateis. But there must have been
confusion has been made between the personal something more than mere sarcastic power, there
history of the poet and the fate of his works, both must bave been truth and delicate wii, in the six-
in this instance and in the story that he won the casms of the poet whom Plato does not hesitate to
prize at Olympia with his hymn to Heracles call "the very wise," (Toû Oodatátov, kepul. ii.
(Tzetzes, Chil. i. 685), of which thus much is cer- p. 365. ) Quintilian (x. 1. & 60) ascribes to him the
tain, that the Olympic victors used to sing a hymn greatest power of expression, displayed in sen-
by Archilochus in their triumphal procession. (Pin- tences sometimes strong, sometimes brief, with ra-
dar, Olymp. ix. 1. ) These traditions, and the cer-pid changes (quum validac, tum breves vibrantesquo
tain fact that the fame of Archilochus was spread, sententiue), the greatest life and nervousness (pilar
in his lifetime, over the whole of Greece, together rimum sanguinis utque nerve
ervorum), and considers
with his unsettled character, render it probable that whatever blame his works deserve is the fault
that he made many journeys of which we have no of his subjects and not of his genius. In the latter
account. It seems that he visited Siris in Lower opinion the Greek critics seem to have joined.
Italy, the only city of which he speaks well. (Plut. de Aud. 13, p. 45, a. ) Of modern writers,
(Athen. xii. p. 523, d. ) At length he returned to Archilochus has been perhaps best understood by
Paros, and, in a war between the Parians and the Müller, who says, “The ostensible object of Ar-
people of Naxos, he fell by the hand of a Naxian chilochus' lambics, like that of the later comedy,
named Calondas or Corax. The Delphian oracle, was to give reality to caricatures, every hideous
which, before the birth of Archilochus, had pro feature of which was made more striking by being
mised to his father an immortal son, now pro- magnified. But that these pictures, like carica-
nounced a curse upon the man who had killed tures from the hand of a master, bad a striking
him, because “he had slain the servant of the truth, may be inferred from the impression which
Muses. " (Dion Chrysost. Orat. 33, vol. ii. Archilochus' iambics produced, both upon contem-
poraries and posterity. Mere calumnies could
Archilochus shared with his contemporaries, never have driven the daughters of Lycambes to
Thaletas and Terpander, in the honour of esta- hang themselves,—if, indeed, this story is to be
blishing lyric poetry throughout Greece. The in- believed, and is not a gross exaggeration. But we
vention of the elegy is ascribed to him, as well as have no need of it; the universal admiration
to Callinus ; and though Callinus was somewhat which was awarded to Archilochus' iambics proves
older than Archilochus (CalliNUS), there is no the existence of a foundation of truth; for when
doubt that the latter was one of the earliest poets had a satire, which was not based on truth, uni-
who excelled in this species of composition. Me versal reputation for excellence ? When Plato
leager enumerates him among the poets in his produced his first dialogues against the sophists,
Curona. (38. )
Gorgias is said to have exclaimed “ Athens has
But it was on his satiric iambic poetry that the given birth to a new Archilochus ! " This com-
fame of Archilochus was founded. The first place parison, made by a man not unacquainted with
in this style of poetry was awarded to him by the art, shows at all events that Archilochus must have
consent of the ancient writers, who did not hesi- possessed somewhat of the keen and delicate satire
tate to compare him with Sophocles, Pindar, and which in Plato was most severe where a dull lis-
even Homer,--meaning, doubtless, that as they tener would be least sensible of it. ” (History of
stood at the head of tragic, lyric, and epic poetry, the Literature of Greece, is p. 135. )
so was Archilochus the first of iambic satirical The satire of preceding writers, as displayed for
writers; while some place him, next to Homer, example in the Margites, was less pointed, because
above all other poets. (Dion Chrysost. I. c. ; Longin. its objects were chosen out of the remote world
xiii. 3; Velleius, i. 5; Cicero, Orat. 2; Hera- which furnished all the personages of epic poetry ;
cleitus, ap. Diog. Laërt. ix. 1. ) The statues of while the iambics of Archilochus were aimed at
Archilochus and of Homer were dedicated on the those among whom he lived. Hence their per-
same day (Antip. Thessal. Epigr. 45), and two sonal bitterness and sarcastic power. This kind of
faces, which are thought to be their likenesses, are satire bad already been employed in extempora-
found placed together in a Janus-like bust. (Vis- neous effusions of wit, especially at the festivals of
conti, Icon. Grec. i. p. 62. ) The emperor Hadrian Demeter and Cora, and Dionysus. This raillery,
judged that the Muses had shown a special mark a specimen of which is preserved in some of the
of favour to Homer in leading Archilochus into a songs of the chorus in Aristophanes' Frogs, was
different department of poetry. (Epig. 5. ) Other called iambus; and the same name was applied to
testimonies are collected by Liebel (p. 43). the verse which Archilochus invented when he in-
The lambics of Archilochus expressed the troduced a new style of poetry in the place of
strongest feelings in the most unmeasured lan- these irregular effusions. For the measured more-
guage. The licence of lonian democracy and the ment of the heroic hexameter, with its arsis and
bitterness of a disappointed man were united with thesis of equal lengths, he substituted a movement
the highest degree of poetical power to give them in which the arsis was twice as long as the thesis,
force and point. In countries and ages unfamiliar the light tripping character of which was admirably
with the political and religious licence which at adapted to express the lively play of wit. Accord-
once incited and protected the poet, his satire was ing as the arsis followed or preceded the thesis, the
blamed for its severity (Liebel, p. 41); and the verse gained, in the former case, strength, in the
emotion accounted most conspicuous in his verses / latter, speed and lightness, which are the chari-
## p. 270 (#290) ############################################
270
ARCHIMEDES.
ARCHIMEDES.
|
teristics respectively of the iambus and of the tro- several places of his works. (See the introductions
chee. These shori feet he formed into continued to the Quadratura Paraboles and the De Helicibus. )
bystems, by uniting every two of them into a pair After visiting other countries, he returned to
(a metre or dipodia), in which one arsis was more Syracuse. (Diod. v. 37. ) Livy (xxiv. 34) calls
strongly accentuated than the other, and one of him a distinguished astronomer, unicus spectator
the two theses was left doubtful as to quantity, 80 coeli siderumque;" a description of which the truth
that, considered with reference to musical rhythm, is made sufficiently probable by his treatment of
cach dipod formed a lar. Hence arose the great the astronomical questions occurring in the Arena-
kindred dramatic metres, the iambic trimeter and rius. (See also Macrob. Somn. Scip. ii. 3. ) lle
the trochaic tetrameter, as well as the shorter forms was popularly best known as the inventor of
of iambic and trochaic verse. Archilochus was the several ingenious machines ; but Plutarch ( Marcell.
inventor also of the epodc, which was formed by c. 14), who, it should be observed, confounds the
subjoining to one or more verses a shorter one. application of geometry to mechanics with the
One form of the epode, in which it consists of solution of geometrical problems by mechanical
three trochees, was called the ithyphallic verse means, represents him as despising these con-
(idúpallos). He used also a kind of verse com- trivances, and only condescending to withdraw
pounded of two different metrical structures, which himself from the abstractions of pure geometry at
was called asynartete. Some writers ascribe to the request of Hiero. Certain it is, however, that
him the invention of the Saturnian verse. (Bent- Archimedes did cultivate not only pure geometry,
ley's Dissertation on Phalaris. ) Archilochus in but also the mathematical theory of several branches
troduced several improvements in music, which of physics, in a truly scientific spirit, and with
began about his time to be applied to the public a success which placed him very far in advance
recitations of poetry.
of the age in which he lived. His theory of the
The best opportunity we have of judging of the lever was the foundation of statics till the discovery
structure of Archilochus' poetry, though not of its of the composition of forces in the time of Newton,
satiric character, is furnished by the Epodes of and no essential addition was made to the princi-
Horace, as we learn from that poet himself (Epist. ples of the equilibrum of faids and floating bodies,
i. 19. 23):
established by him in his treatise “ De Insidenti-
“ Parios ego primum iambos bus," till the publication of Stevin's researches on
Ostendi Latio, numeros animosque secutus the pressure of Auids in 1608. (Lagrange, Móc.
Archilochi, non res et agentia verba Lycamben. " Anal. vol. i. pp. 11, 176. )
Some manifest translations of Archilochus may be which, many years afterwards, were so far effectual
He constructed for Hiero various engines of war,
traced in the Epodes. The fragments of Archi- in the defence of Syracuse against Marcellus, as to
lochus which remain are collected in Jacobs' Anthol.
Graec. , Gaisford's Poet. Graec. Min. , Bergk's taking of the city for a considerable time. (Plut.
convert the siege into a blockade, and delay the
Poet. Lyrici Graec. , and by Liebel, Archilochi Ro Marcell. 15-18 ; Liv. xxiv. 34; Polyb. viii. 5-9. )
liquiae, Lips. 1812, 8vo.
The accounts of the performances of these engines
Fabricius (ii. pp. 107–110) discusses fully the
are evidently exaggerated; and the story of the
passages in which other writers of the name are
burning of the Roman ships by the reflected rays
supposed to be mentioned.
[P. S. )
of the sun, though very current in later times, is
ARCHIME'DES ('Apxuundns), of. Syracuse, probably a fiction, since neither Polybius, Livy,
the most famous of ancient mathematicians, was
nor Plutarch gives the least hint of it. The earliest
born B. C. 287, if the statement of Tzetzes, which
makes him 75 years old at his death, be correct.
writers who speak of it are Galen (De Temper. iii.
Of his family little is known. Plutarch calls who (in the second century) merely allude to it as
2) and his contemporary Lucian (Hippias, c. 2),
him a relation of king Hiero; but Cicero (7’usc.
a thing well known. Zonaras (about A. D. 1100)
Disp. v. 23), contrasting him apparently not with
Dionysius (as Torelli suggests in order to avoid mentions it in relating the use of a similar appa-
the contradiction), but with Plato and Archytas, tium was besieged in the reign of Anastasius ;
ratus, contrived by a certain Proclus, when Byzan-
humilem homunculum a pulvere et radio and gives Dion as his authority, without referring
excitabo. " At any rate, his actual condition in
life does not seem to have been elevated (Silius Dion contain no allusion to it.
to the particular passage. The extant works of
Tzetzes (about
Ital. xiv. 343), though he was certainly a friend, if 1150) gives an account of the principal inventions
not a kinsman, of Hiero. A modern tradition
makes him an ancestor of the Syracusan virgin them of this burning machine, which, he says, set the
of Archimedes (Chil. ii. 103—156), and amongst
martyr St. Lucy. (Rivaltus, in vit
. Archim. Maz: Roman ships on fire when they came within a
zuchelli, p. 6. ) In the early part of his life he bow-shot of the walls; and consisted of a large
travelled into Egypt, where he is said, on the hexagonal mirror with smaller ones disposed round
authority of Proclus, to have studied under Conon
the Samian, a mathematician and astronomer
it, each of the latter being a polygon of 24 sides.
(mentioned by Virg. Ed. iii. 40), who lived under modern times, particularly by Cavalieri (in cap. 29
The subject has been a good deal discussed in
the Ptolemies, Philadelphus and Euergetes, and of a tract entitled “ Del Specchio Ustorio,” Bologna,
for whom he testifies his respect and esteem in 1650), and by Buffon, who has left an elaborate
dissertation upon it in his introduction to the his-
* These two remarks apply to the first arsis tory of minerals. (Oeuvres, tom. v. p. 301, &c. )
and the first thesis of the iamlic metre, and to the The latter author actually succeeded in igniting
second arsis and the second thesis of the trochaic : wood at a distance of 150 feet, by means of a
combination of 148 plane mirrors. The question
is also examined in vol. ij. of Peyrard's Archi-
medes; and a prize essay upon it by Capelle is
savs,
u
I lo
## p. 271 (#291) ############################################
ARCHIMEDES.
27 1
ARCHIMEDES.
translated from the Dutch in Gilbert's “ Annalen | movements of the hearenly bodies, of which we
der Physik," vol. liii. p. 242. The most pro have no particular description. (Claudian, Epigr.
bable conclusion seems to be, that Archimedes had | xxi. in Sphaeram Archimeris ; Cic. Nal. Dcor. ii. 35,
on some occasion, set fire to a ship or ships by Tusc. Disp. i. 25; Sext. Empir. adv. Math. ix. 115;
means of a burning mirror, and that later writers Lactant. Div. Inst. ii. 5; Ov. Fust. vi. 277. )
falsely connected the circumstance with the siege When Syracuse was taken, Archimedes was
of Syracuse. (See Ersch and Gruber's Cyclop. killed by the Roman soldiers, ignorant or careless
art. Archim. note, and Gibbon, chap. 40. ). who he might be. The accounts of his death vary
The following additional instances of Archi- in some particulars, but mostly agree in describing
medes' skill in the application of science have him as intent upon a mathematical problem at the
been collected from various authors by Rivaltus time. He was deeply regretted by Marcellus, who
(who edited his works in 1615) and others. directed his burial, and befriended his surviving
He detected the mixture of silver in a crown relations. (Liv. xxv. 31; Vaier. Max. viii. 7. $ 7;
which Hiero had ordered to be made of gold, and Plut. Marcell. 19; Cic. de fin. v. 19. ) Upor his
determined the proportions of the two metals, by tomb was placed the figure of a sphere inscribed
a method suggested to him by the overflowing of in a cylinder, in accordance with his known wish,
the water when he stepped into a bath. When and in commemoration of the discovery which he
the thought struck him he is said to have been so most valued. When Cicero was quaestor in Sicily
much pleased that, forgetting to put on his clothes, (B. c. 75) he found this tomb near one of the gates
he ran home shouting cúpnko, eüpnic The par- of the city, almost hid amongst briars, and forgotten
ticulars of the calculation are not preserved, but it by the Syracusans. (Tusc. Disp. v. 23. )
probably depended upon a direct comparison of the Of the general character of Archimedes we have
weights of certain volumes of silver and gold with no direct account. But his apparently disinterest-
the weight and volume of the crown ; the volumes ed devotion to his friend and admirer Hiero, in
being measured, at least in the case of the crown, whose service he was ever ready to exercise his
by the quantity of water displaced when the mass ingenuity upon objects which his own taste would
was immersed. It is not likely that Archimedes not have led him to choose (for there is doubtless
was at this time acquainted with the theorems some truth in what Plutarch says on this point);
demonstrated in his hydrostatical treatise con- the affectionate regret which he expresses for his
cerning the luss of weight of bodies immersed in deceased master Conon, in writing to his surviving
water, since he would hardly have evinced such friend Dositheus (to whom most of his works are
lively gratification at the obvious discovery that addressed); and the unaffected simplicity with
they might be applied to the problem of the crown; which he announces his own discoveries, seem to
his delight must rather have arisen from his now afford probable grounds for a favourable estimate
first catching sight of a line of investigation which of it. That his intellect was of the very highest
led immediately to the solution of the problem order is unquestionable. He possessed, in a degree
in question, and ultimately to the important never exceeded unless by Newton, the inventive
theorems referred to. (Vitruv. ix. 3. ; Proclus. genius which discovers new provinces of inquiry,
Comm. in lib. i. Eucl. ii. 3. )
and finds new points of view for old and familiar
He superintended the building of a ship of ex- objects; the clearness of conception which is
traordinary size for Hiero, of which a description essential to the resolution of complex phaenomena
is given in Athenaeus (v. p. 206, D), where he is into their constituent elements; and the power
also said to have nuoved it to the sea by the help and habit of intense and persevering thought, with-
of a screw. According to Proclus, this ship was out which other intellectual gifts are comparatively
intended by Hiero as a present to Ptolemy; it may fruitless. (See the introd. to the treatise * De Con.
possibly have been the occasion of Archimedes' et Sphaer. ") It may be noticed that he resembled
visit to Egypt
other great thinkers, in bis habit of complete ab-
He invented a machine called, from its form, straction from outward things, when reflecting on
Cochlean and now kuown as the water-screw of subjects which made considerable demands on his
Archimedes, for pumping the water out of the hola mental powers. At such times he would forget to
of this vessel ; it is said to have been also used in eat his meals, and require compulsion to take him
Egypt by the inhabitants of the Delta in irrigating to the bath. (Plut. 1. c. ) Compare the stories of
their landa. (Diod. i. 34; Vitruv. x. 11. ) An Newton sitting great part of the day half dressed
investigation of the mathematical theory of the on his bed, while composing the Principia; and of
water screw is given in Ersch and Gruber. The Socrates standing a whole day and night, thinking,
Arabian historian Abulpharagius attributes to on the same spot. (Plat. Symp. p. 220, c. d. ) The
Archimedes the raising of the dykes and bridges success of Archimedes in conquering difficulties
used as defences against the overflowing of the seems to have made the expression πρόβλημα 'Αρ-
Nile. (Pope-Blount, Censura, p. 32. ) Tzetzes xuño etov proverbial. (See Cic. ad Att. xiii. 28,
and Oribasius (de Mach. xxvi. ) speak of his Tris pro Cluent. 32. )
pasl, a machine for moving large weights; probably The following works of Archimedes have come
a combination of pulleys, or wheels and axles. A down to us : A treatise on Equiponderants and
hydraulic organ (a musical instrument) is mention Centres of Grarity, in which the theory of the
ed by Tertullian (de Anima, cap. 14), but Pliny equilibrium of the straight lever is demonstrated,
(vii. 37) attributes it to Ctesibius. (See also Pap- both for commensurable and incommensurable
pus, Muth. Coll. lib. 8, introd. ) An apparatus weights; and various properties of the centres of
called loculus, apparently somewhat resembling the gravity of plane surfaces bounded by three or four
Chinese puzzle, is also attributed to Archimedes. straight lines, or by a straight line and a parabola,
(Fortunatianus, de Arte Metrica, p. 2684. ) His are established.
most celebrated performance was the construction The Quadrature of the Parabola, in which it is
of a spluere; a kind of orrery, representing the proved, that the area cut off from a parabola by
## p. 272 (#292) ############################################
27:2
ARCHIMEDES.
ARCHIMEDES.
any chord is equal to two-thirds of the parallelo- | the modern method of logarithms, affords one of
gram of which one side is the chord in question, the most striking instances of the great mathema.
and the opposite side a tangent to the parabola. tician's genius. Having briefly discussed the
This was the first real example of the quadrature opinions of Aristarchus upon the constitution and
of a curvilinear sprce; that is, of the discovery of extent of the Universe (ARISTARCHUS), and
a rectilinear figure equal to an area not bounded described his own method of determining the air
entirely by straight lines.
parent diameter of the sun, and the magnitude of
A treatise on tinc Sphere and Cylinder, in which the pupil of the eve, he is led to assume that the
various propositions relative to the surfaces and diameter of the sphere of the fixed stars may be
volumes of the sphere, cylinder, and cone, were taken as not exceeding 100 million of millions of
demonstrated for the first time. Many of them stadia ; and that a sphere, one daktilos in diame-
are now familiarly known; for example, those ter, cannot contain more than 640 millions of
which establish the ratio (3) between the volumes, grains of sand ; then, taking the stadium, in round
and also between the surfaces, of the sphere and numbers, as not greater than 10,000 bakturou, he
circumscribing cylinder; and the ratio (1) between shews that the number of grains in question could
the area of a great circle and the surface of the not be so great as 1000 myriads multiplied by the
sphere. They are easily demonstrable by the eighth term of a geometrical progression of which
modern analytical methods; but the original dis- the first term was unity and the common ratio a
covery and geometrical proof of them required the myriad of myriads ; a number which in our nota-
genius of Archimedes. Moreover, the legitimacy tion would be expressed by unity with 63 ciphers
of the modern applications of analysis to questions annexed.
concerning curved lines and surfaces, can only be The two books On Floating Bodies (Tiepl twv
proved by a kind of geometrical reasoning, of 'Oxouuévwv) contain demonstrations of the laws
which Archimedes gave the first example. (See which determine the position of bodies immersed
Lacroix, Diff. Cal. vol. i. pp. 63 and 431; and in water; and particularly of segments of spheres
compare De Morgan, Diff. Cul. p. 32. )
and parabolic conoids. They are extant only in
The book on the Dimension of the Circle consists the Latin version of Commandine, with the ex.
of three propositions. Ist. Every circle is equal ception of a fragment Depl Twv "Tatı €0. 0TQ-
to a right-angled triangle of which the sides con- névwv in Ang. Mai's Collection, vol. i. p. 427.
taining the right angle are equal respectively to its The treatise entitled Lemmata is a collection of
radius and circumference. 2nd. The ratio of the 15 propositions in plane geometry. It is derived
area of the circle to the square of its diameter is from an Arabic MS. and its genuineness has been
nearly that of 11 to 14. 3rd. The circumference doubted. (See Torelli's preface. )
of the circle is greater than three times its diameter Eutocius of Ascalon, about A. D. 600, wrote a
by a quantity greater than l of the diameter but commentary on the Treatises on the Sphere and
less than of the same. The last two proposi- Cylinder, on the Dimension of the Circle, and on
tions are established by comparing the circum- Centres of Gravity. All the works above men-
ference of the circle with the perimeters of the tioned, together with this Commentary, were found
inscribed and circumscribed polygons of 96 sides. on the taking of Constantinople, and brought first
The treatise on Spirals contains demonstrations into Italy and then into Germany. They were
of the principal properties of the curve, now known printed at Basle in 1544, in Greek and Latin, by
as the Spiral of Archimedes, which is generated by Hervagius. Of the subsequent oditions by far the
the uniform motion of a point along a straight line best is that of Torelli, “ Archim. quae supers.
revolving uniformly in one plane about one of its omnia, cum Eutocii Ascalonitae commentariis.
extremities. It appears from the introductory Ex recens. Joseph. Torelli, Veronensis,” Oxon.
epistle to Dositheus that Archimedes had not been 1792. It was founded upon the Basle edition,
able to put these theorems in a satisfactory form except in the case of the Arenarius, the text of
without long-continued and repeated trials; and which is taken from that of Dr. Wallis, who pub-
that Conon, to whom he had sent them as pro lished this treatise and the Dimensio Circuli, with
blems along with various others, had died without a translation and notes, at Oxford, in 1679. (They
accomplishing their solution.
are reprinted in vol. vi. of his works. )
The book on Conoids and Spheroids relates The Arenarius, having been little meddled with
chiefly to the volumes cut off by planes from the by the ancient commentators, retains the Doric
solids so called ; those namely which are generated dialect, in which Archimedes, like his countryman
by the rotation of the Conic Sections about their Theocritus, wrote. (See Wallis, Op. rol. iii. pp.
principal axes. Like the work last described, it 537, 545. Tzetzes says, freye dé kad dwploti,
was the result of laborious, and at first unsuccess- φωνή Συρακουσία, Πα βω, και χαριστίωνα ταν γαν
ful, attempts. (See the introduction. )
κινήσω πάσαν. ) A French translation of the
The Arenarius (ó Vanuitis) is a short tract works of Archimedes, with notes, was published
addressed to Gelo, the eldest son of Hiero, in by F. Peyrard, Paris, 1808, 2 vols. 8vo. , and an
which Archimedes proves, that it is possible to English translation of the Arenarius by G. Ander-
assign a number greater than that of the grains of son, London, 1784.
sand which would fill the sphere of the fixed stars. (G. M. Mazuchelli, Notizie istoriche e critiche
This singular investigation was suggested by an intorno alla vita, alle intenzioni, ed agli scritti di
opinion which some persons had expressed, that Archimede, Brescia, 1737, 410.
8
## p. 269 (#289) ############################################
ARCIIILOCHUS.
269
ARCHILOCHUS.
Was
9
p. 5. )
man bad better throw away his arms than lose his rage," as we see in the line of llorace ( A. P.
life. But Valerius Maximus (vi. 3, ext. 1) says, 79):
that the poems of Archilochus were forbidden at “ Archilochum proprio rabies armavit iambo,"
Sparta because of their licentiousness, and especi- and in the expression of Hadrian (l. c. ), Avoo@vTAS
ally on account of the attack on the daughters of iáulous; and his bitterness passed into a proverbia
Lycambes. It must remain doubtful whether a 'Apxınó xou mateis. But there must have been
confusion has been made between the personal something more than mere sarcastic power, there
history of the poet and the fate of his works, both must bave been truth and delicate wii, in the six-
in this instance and in the story that he won the casms of the poet whom Plato does not hesitate to
prize at Olympia with his hymn to Heracles call "the very wise," (Toû Oodatátov, kepul. ii.
(Tzetzes, Chil. i. 685), of which thus much is cer- p. 365. ) Quintilian (x. 1. & 60) ascribes to him the
tain, that the Olympic victors used to sing a hymn greatest power of expression, displayed in sen-
by Archilochus in their triumphal procession. (Pin- tences sometimes strong, sometimes brief, with ra-
dar, Olymp. ix. 1. ) These traditions, and the cer-pid changes (quum validac, tum breves vibrantesquo
tain fact that the fame of Archilochus was spread, sententiue), the greatest life and nervousness (pilar
in his lifetime, over the whole of Greece, together rimum sanguinis utque nerve
ervorum), and considers
with his unsettled character, render it probable that whatever blame his works deserve is the fault
that he made many journeys of which we have no of his subjects and not of his genius. In the latter
account. It seems that he visited Siris in Lower opinion the Greek critics seem to have joined.
Italy, the only city of which he speaks well. (Plut. de Aud. 13, p. 45, a. ) Of modern writers,
(Athen. xii. p. 523, d. ) At length he returned to Archilochus has been perhaps best understood by
Paros, and, in a war between the Parians and the Müller, who says, “The ostensible object of Ar-
people of Naxos, he fell by the hand of a Naxian chilochus' lambics, like that of the later comedy,
named Calondas or Corax. The Delphian oracle, was to give reality to caricatures, every hideous
which, before the birth of Archilochus, had pro feature of which was made more striking by being
mised to his father an immortal son, now pro- magnified. But that these pictures, like carica-
nounced a curse upon the man who had killed tures from the hand of a master, bad a striking
him, because “he had slain the servant of the truth, may be inferred from the impression which
Muses. " (Dion Chrysost. Orat. 33, vol. ii. Archilochus' iambics produced, both upon contem-
poraries and posterity. Mere calumnies could
Archilochus shared with his contemporaries, never have driven the daughters of Lycambes to
Thaletas and Terpander, in the honour of esta- hang themselves,—if, indeed, this story is to be
blishing lyric poetry throughout Greece. The in- believed, and is not a gross exaggeration. But we
vention of the elegy is ascribed to him, as well as have no need of it; the universal admiration
to Callinus ; and though Callinus was somewhat which was awarded to Archilochus' iambics proves
older than Archilochus (CalliNUS), there is no the existence of a foundation of truth; for when
doubt that the latter was one of the earliest poets had a satire, which was not based on truth, uni-
who excelled in this species of composition. Me versal reputation for excellence ? When Plato
leager enumerates him among the poets in his produced his first dialogues against the sophists,
Curona. (38. )
Gorgias is said to have exclaimed “ Athens has
But it was on his satiric iambic poetry that the given birth to a new Archilochus ! " This com-
fame of Archilochus was founded. The first place parison, made by a man not unacquainted with
in this style of poetry was awarded to him by the art, shows at all events that Archilochus must have
consent of the ancient writers, who did not hesi- possessed somewhat of the keen and delicate satire
tate to compare him with Sophocles, Pindar, and which in Plato was most severe where a dull lis-
even Homer,--meaning, doubtless, that as they tener would be least sensible of it. ” (History of
stood at the head of tragic, lyric, and epic poetry, the Literature of Greece, is p. 135. )
so was Archilochus the first of iambic satirical The satire of preceding writers, as displayed for
writers; while some place him, next to Homer, example in the Margites, was less pointed, because
above all other poets. (Dion Chrysost. I. c. ; Longin. its objects were chosen out of the remote world
xiii. 3; Velleius, i. 5; Cicero, Orat. 2; Hera- which furnished all the personages of epic poetry ;
cleitus, ap. Diog. Laërt. ix. 1. ) The statues of while the iambics of Archilochus were aimed at
Archilochus and of Homer were dedicated on the those among whom he lived. Hence their per-
same day (Antip. Thessal. Epigr. 45), and two sonal bitterness and sarcastic power. This kind of
faces, which are thought to be their likenesses, are satire bad already been employed in extempora-
found placed together in a Janus-like bust. (Vis- neous effusions of wit, especially at the festivals of
conti, Icon. Grec. i. p. 62. ) The emperor Hadrian Demeter and Cora, and Dionysus. This raillery,
judged that the Muses had shown a special mark a specimen of which is preserved in some of the
of favour to Homer in leading Archilochus into a songs of the chorus in Aristophanes' Frogs, was
different department of poetry. (Epig. 5. ) Other called iambus; and the same name was applied to
testimonies are collected by Liebel (p. 43). the verse which Archilochus invented when he in-
The lambics of Archilochus expressed the troduced a new style of poetry in the place of
strongest feelings in the most unmeasured lan- these irregular effusions. For the measured more-
guage. The licence of lonian democracy and the ment of the heroic hexameter, with its arsis and
bitterness of a disappointed man were united with thesis of equal lengths, he substituted a movement
the highest degree of poetical power to give them in which the arsis was twice as long as the thesis,
force and point. In countries and ages unfamiliar the light tripping character of which was admirably
with the political and religious licence which at adapted to express the lively play of wit. Accord-
once incited and protected the poet, his satire was ing as the arsis followed or preceded the thesis, the
blamed for its severity (Liebel, p. 41); and the verse gained, in the former case, strength, in the
emotion accounted most conspicuous in his verses / latter, speed and lightness, which are the chari-
## p. 270 (#290) ############################################
270
ARCHIMEDES.
ARCHIMEDES.
|
teristics respectively of the iambus and of the tro- several places of his works. (See the introductions
chee. These shori feet he formed into continued to the Quadratura Paraboles and the De Helicibus. )
bystems, by uniting every two of them into a pair After visiting other countries, he returned to
(a metre or dipodia), in which one arsis was more Syracuse. (Diod. v. 37. ) Livy (xxiv. 34) calls
strongly accentuated than the other, and one of him a distinguished astronomer, unicus spectator
the two theses was left doubtful as to quantity, 80 coeli siderumque;" a description of which the truth
that, considered with reference to musical rhythm, is made sufficiently probable by his treatment of
cach dipod formed a lar. Hence arose the great the astronomical questions occurring in the Arena-
kindred dramatic metres, the iambic trimeter and rius. (See also Macrob. Somn. Scip. ii. 3. ) lle
the trochaic tetrameter, as well as the shorter forms was popularly best known as the inventor of
of iambic and trochaic verse. Archilochus was the several ingenious machines ; but Plutarch ( Marcell.
inventor also of the epodc, which was formed by c. 14), who, it should be observed, confounds the
subjoining to one or more verses a shorter one. application of geometry to mechanics with the
One form of the epode, in which it consists of solution of geometrical problems by mechanical
three trochees, was called the ithyphallic verse means, represents him as despising these con-
(idúpallos). He used also a kind of verse com- trivances, and only condescending to withdraw
pounded of two different metrical structures, which himself from the abstractions of pure geometry at
was called asynartete. Some writers ascribe to the request of Hiero. Certain it is, however, that
him the invention of the Saturnian verse. (Bent- Archimedes did cultivate not only pure geometry,
ley's Dissertation on Phalaris. ) Archilochus in but also the mathematical theory of several branches
troduced several improvements in music, which of physics, in a truly scientific spirit, and with
began about his time to be applied to the public a success which placed him very far in advance
recitations of poetry.
of the age in which he lived. His theory of the
The best opportunity we have of judging of the lever was the foundation of statics till the discovery
structure of Archilochus' poetry, though not of its of the composition of forces in the time of Newton,
satiric character, is furnished by the Epodes of and no essential addition was made to the princi-
Horace, as we learn from that poet himself (Epist. ples of the equilibrum of faids and floating bodies,
i. 19. 23):
established by him in his treatise “ De Insidenti-
“ Parios ego primum iambos bus," till the publication of Stevin's researches on
Ostendi Latio, numeros animosque secutus the pressure of Auids in 1608. (Lagrange, Móc.
Archilochi, non res et agentia verba Lycamben. " Anal. vol. i. pp. 11, 176. )
Some manifest translations of Archilochus may be which, many years afterwards, were so far effectual
He constructed for Hiero various engines of war,
traced in the Epodes. The fragments of Archi- in the defence of Syracuse against Marcellus, as to
lochus which remain are collected in Jacobs' Anthol.
Graec. , Gaisford's Poet. Graec. Min. , Bergk's taking of the city for a considerable time. (Plut.
convert the siege into a blockade, and delay the
Poet. Lyrici Graec. , and by Liebel, Archilochi Ro Marcell. 15-18 ; Liv. xxiv. 34; Polyb. viii. 5-9. )
liquiae, Lips. 1812, 8vo.
The accounts of the performances of these engines
Fabricius (ii. pp. 107–110) discusses fully the
are evidently exaggerated; and the story of the
passages in which other writers of the name are
burning of the Roman ships by the reflected rays
supposed to be mentioned.
[P. S. )
of the sun, though very current in later times, is
ARCHIME'DES ('Apxuundns), of. Syracuse, probably a fiction, since neither Polybius, Livy,
the most famous of ancient mathematicians, was
nor Plutarch gives the least hint of it. The earliest
born B. C. 287, if the statement of Tzetzes, which
makes him 75 years old at his death, be correct.
writers who speak of it are Galen (De Temper. iii.
Of his family little is known. Plutarch calls who (in the second century) merely allude to it as
2) and his contemporary Lucian (Hippias, c. 2),
him a relation of king Hiero; but Cicero (7’usc.
a thing well known. Zonaras (about A. D. 1100)
Disp. v. 23), contrasting him apparently not with
Dionysius (as Torelli suggests in order to avoid mentions it in relating the use of a similar appa-
the contradiction), but with Plato and Archytas, tium was besieged in the reign of Anastasius ;
ratus, contrived by a certain Proclus, when Byzan-
humilem homunculum a pulvere et radio and gives Dion as his authority, without referring
excitabo. " At any rate, his actual condition in
life does not seem to have been elevated (Silius Dion contain no allusion to it.
to the particular passage. The extant works of
Tzetzes (about
Ital. xiv. 343), though he was certainly a friend, if 1150) gives an account of the principal inventions
not a kinsman, of Hiero. A modern tradition
makes him an ancestor of the Syracusan virgin them of this burning machine, which, he says, set the
of Archimedes (Chil. ii. 103—156), and amongst
martyr St. Lucy. (Rivaltus, in vit
. Archim. Maz: Roman ships on fire when they came within a
zuchelli, p. 6. ) In the early part of his life he bow-shot of the walls; and consisted of a large
travelled into Egypt, where he is said, on the hexagonal mirror with smaller ones disposed round
authority of Proclus, to have studied under Conon
the Samian, a mathematician and astronomer
it, each of the latter being a polygon of 24 sides.
(mentioned by Virg. Ed. iii. 40), who lived under modern times, particularly by Cavalieri (in cap. 29
The subject has been a good deal discussed in
the Ptolemies, Philadelphus and Euergetes, and of a tract entitled “ Del Specchio Ustorio,” Bologna,
for whom he testifies his respect and esteem in 1650), and by Buffon, who has left an elaborate
dissertation upon it in his introduction to the his-
* These two remarks apply to the first arsis tory of minerals. (Oeuvres, tom. v. p. 301, &c. )
and the first thesis of the iamlic metre, and to the The latter author actually succeeded in igniting
second arsis and the second thesis of the trochaic : wood at a distance of 150 feet, by means of a
combination of 148 plane mirrors. The question
is also examined in vol. ij. of Peyrard's Archi-
medes; and a prize essay upon it by Capelle is
savs,
u
I lo
## p. 271 (#291) ############################################
ARCHIMEDES.
27 1
ARCHIMEDES.
translated from the Dutch in Gilbert's “ Annalen | movements of the hearenly bodies, of which we
der Physik," vol. liii. p. 242. The most pro have no particular description. (Claudian, Epigr.
bable conclusion seems to be, that Archimedes had | xxi. in Sphaeram Archimeris ; Cic. Nal. Dcor. ii. 35,
on some occasion, set fire to a ship or ships by Tusc. Disp. i. 25; Sext. Empir. adv. Math. ix. 115;
means of a burning mirror, and that later writers Lactant. Div. Inst. ii. 5; Ov. Fust. vi. 277. )
falsely connected the circumstance with the siege When Syracuse was taken, Archimedes was
of Syracuse. (See Ersch and Gruber's Cyclop. killed by the Roman soldiers, ignorant or careless
art. Archim. note, and Gibbon, chap. 40. ). who he might be. The accounts of his death vary
The following additional instances of Archi- in some particulars, but mostly agree in describing
medes' skill in the application of science have him as intent upon a mathematical problem at the
been collected from various authors by Rivaltus time. He was deeply regretted by Marcellus, who
(who edited his works in 1615) and others. directed his burial, and befriended his surviving
He detected the mixture of silver in a crown relations. (Liv. xxv. 31; Vaier. Max. viii. 7. $ 7;
which Hiero had ordered to be made of gold, and Plut. Marcell. 19; Cic. de fin. v. 19. ) Upor his
determined the proportions of the two metals, by tomb was placed the figure of a sphere inscribed
a method suggested to him by the overflowing of in a cylinder, in accordance with his known wish,
the water when he stepped into a bath. When and in commemoration of the discovery which he
the thought struck him he is said to have been so most valued. When Cicero was quaestor in Sicily
much pleased that, forgetting to put on his clothes, (B. c. 75) he found this tomb near one of the gates
he ran home shouting cúpnko, eüpnic The par- of the city, almost hid amongst briars, and forgotten
ticulars of the calculation are not preserved, but it by the Syracusans. (Tusc. Disp. v. 23. )
probably depended upon a direct comparison of the Of the general character of Archimedes we have
weights of certain volumes of silver and gold with no direct account. But his apparently disinterest-
the weight and volume of the crown ; the volumes ed devotion to his friend and admirer Hiero, in
being measured, at least in the case of the crown, whose service he was ever ready to exercise his
by the quantity of water displaced when the mass ingenuity upon objects which his own taste would
was immersed. It is not likely that Archimedes not have led him to choose (for there is doubtless
was at this time acquainted with the theorems some truth in what Plutarch says on this point);
demonstrated in his hydrostatical treatise con- the affectionate regret which he expresses for his
cerning the luss of weight of bodies immersed in deceased master Conon, in writing to his surviving
water, since he would hardly have evinced such friend Dositheus (to whom most of his works are
lively gratification at the obvious discovery that addressed); and the unaffected simplicity with
they might be applied to the problem of the crown; which he announces his own discoveries, seem to
his delight must rather have arisen from his now afford probable grounds for a favourable estimate
first catching sight of a line of investigation which of it. That his intellect was of the very highest
led immediately to the solution of the problem order is unquestionable. He possessed, in a degree
in question, and ultimately to the important never exceeded unless by Newton, the inventive
theorems referred to. (Vitruv. ix. 3. ; Proclus. genius which discovers new provinces of inquiry,
Comm. in lib. i. Eucl. ii. 3. )
and finds new points of view for old and familiar
He superintended the building of a ship of ex- objects; the clearness of conception which is
traordinary size for Hiero, of which a description essential to the resolution of complex phaenomena
is given in Athenaeus (v. p. 206, D), where he is into their constituent elements; and the power
also said to have nuoved it to the sea by the help and habit of intense and persevering thought, with-
of a screw. According to Proclus, this ship was out which other intellectual gifts are comparatively
intended by Hiero as a present to Ptolemy; it may fruitless. (See the introd. to the treatise * De Con.
possibly have been the occasion of Archimedes' et Sphaer. ") It may be noticed that he resembled
visit to Egypt
other great thinkers, in bis habit of complete ab-
He invented a machine called, from its form, straction from outward things, when reflecting on
Cochlean and now kuown as the water-screw of subjects which made considerable demands on his
Archimedes, for pumping the water out of the hola mental powers. At such times he would forget to
of this vessel ; it is said to have been also used in eat his meals, and require compulsion to take him
Egypt by the inhabitants of the Delta in irrigating to the bath. (Plut. 1. c. ) Compare the stories of
their landa. (Diod. i. 34; Vitruv. x. 11. ) An Newton sitting great part of the day half dressed
investigation of the mathematical theory of the on his bed, while composing the Principia; and of
water screw is given in Ersch and Gruber. The Socrates standing a whole day and night, thinking,
Arabian historian Abulpharagius attributes to on the same spot. (Plat. Symp. p. 220, c. d. ) The
Archimedes the raising of the dykes and bridges success of Archimedes in conquering difficulties
used as defences against the overflowing of the seems to have made the expression πρόβλημα 'Αρ-
Nile. (Pope-Blount, Censura, p. 32. ) Tzetzes xuño etov proverbial. (See Cic. ad Att. xiii. 28,
and Oribasius (de Mach. xxvi. ) speak of his Tris pro Cluent. 32. )
pasl, a machine for moving large weights; probably The following works of Archimedes have come
a combination of pulleys, or wheels and axles. A down to us : A treatise on Equiponderants and
hydraulic organ (a musical instrument) is mention Centres of Grarity, in which the theory of the
ed by Tertullian (de Anima, cap. 14), but Pliny equilibrium of the straight lever is demonstrated,
(vii. 37) attributes it to Ctesibius. (See also Pap- both for commensurable and incommensurable
pus, Muth. Coll. lib. 8, introd. ) An apparatus weights; and various properties of the centres of
called loculus, apparently somewhat resembling the gravity of plane surfaces bounded by three or four
Chinese puzzle, is also attributed to Archimedes. straight lines, or by a straight line and a parabola,
(Fortunatianus, de Arte Metrica, p. 2684. ) His are established.
most celebrated performance was the construction The Quadrature of the Parabola, in which it is
of a spluere; a kind of orrery, representing the proved, that the area cut off from a parabola by
## p. 272 (#292) ############################################
27:2
ARCHIMEDES.
ARCHIMEDES.
any chord is equal to two-thirds of the parallelo- | the modern method of logarithms, affords one of
gram of which one side is the chord in question, the most striking instances of the great mathema.
and the opposite side a tangent to the parabola. tician's genius. Having briefly discussed the
This was the first real example of the quadrature opinions of Aristarchus upon the constitution and
of a curvilinear sprce; that is, of the discovery of extent of the Universe (ARISTARCHUS), and
a rectilinear figure equal to an area not bounded described his own method of determining the air
entirely by straight lines.
parent diameter of the sun, and the magnitude of
A treatise on tinc Sphere and Cylinder, in which the pupil of the eve, he is led to assume that the
various propositions relative to the surfaces and diameter of the sphere of the fixed stars may be
volumes of the sphere, cylinder, and cone, were taken as not exceeding 100 million of millions of
demonstrated for the first time. Many of them stadia ; and that a sphere, one daktilos in diame-
are now familiarly known; for example, those ter, cannot contain more than 640 millions of
which establish the ratio (3) between the volumes, grains of sand ; then, taking the stadium, in round
and also between the surfaces, of the sphere and numbers, as not greater than 10,000 bakturou, he
circumscribing cylinder; and the ratio (1) between shews that the number of grains in question could
the area of a great circle and the surface of the not be so great as 1000 myriads multiplied by the
sphere. They are easily demonstrable by the eighth term of a geometrical progression of which
modern analytical methods; but the original dis- the first term was unity and the common ratio a
covery and geometrical proof of them required the myriad of myriads ; a number which in our nota-
genius of Archimedes. Moreover, the legitimacy tion would be expressed by unity with 63 ciphers
of the modern applications of analysis to questions annexed.
concerning curved lines and surfaces, can only be The two books On Floating Bodies (Tiepl twv
proved by a kind of geometrical reasoning, of 'Oxouuévwv) contain demonstrations of the laws
which Archimedes gave the first example. (See which determine the position of bodies immersed
Lacroix, Diff. Cal. vol. i. pp. 63 and 431; and in water; and particularly of segments of spheres
compare De Morgan, Diff. Cul. p. 32. )
and parabolic conoids. They are extant only in
The book on the Dimension of the Circle consists the Latin version of Commandine, with the ex.
of three propositions. Ist. Every circle is equal ception of a fragment Depl Twv "Tatı €0. 0TQ-
to a right-angled triangle of which the sides con- névwv in Ang. Mai's Collection, vol. i. p. 427.
taining the right angle are equal respectively to its The treatise entitled Lemmata is a collection of
radius and circumference. 2nd. The ratio of the 15 propositions in plane geometry. It is derived
area of the circle to the square of its diameter is from an Arabic MS. and its genuineness has been
nearly that of 11 to 14. 3rd. The circumference doubted. (See Torelli's preface. )
of the circle is greater than three times its diameter Eutocius of Ascalon, about A. D. 600, wrote a
by a quantity greater than l of the diameter but commentary on the Treatises on the Sphere and
less than of the same. The last two proposi- Cylinder, on the Dimension of the Circle, and on
tions are established by comparing the circum- Centres of Gravity. All the works above men-
ference of the circle with the perimeters of the tioned, together with this Commentary, were found
inscribed and circumscribed polygons of 96 sides. on the taking of Constantinople, and brought first
The treatise on Spirals contains demonstrations into Italy and then into Germany. They were
of the principal properties of the curve, now known printed at Basle in 1544, in Greek and Latin, by
as the Spiral of Archimedes, which is generated by Hervagius. Of the subsequent oditions by far the
the uniform motion of a point along a straight line best is that of Torelli, “ Archim. quae supers.
revolving uniformly in one plane about one of its omnia, cum Eutocii Ascalonitae commentariis.
extremities. It appears from the introductory Ex recens. Joseph. Torelli, Veronensis,” Oxon.
epistle to Dositheus that Archimedes had not been 1792. It was founded upon the Basle edition,
able to put these theorems in a satisfactory form except in the case of the Arenarius, the text of
without long-continued and repeated trials; and which is taken from that of Dr. Wallis, who pub-
that Conon, to whom he had sent them as pro lished this treatise and the Dimensio Circuli, with
blems along with various others, had died without a translation and notes, at Oxford, in 1679. (They
accomplishing their solution.
are reprinted in vol. vi. of his works. )
The book on Conoids and Spheroids relates The Arenarius, having been little meddled with
chiefly to the volumes cut off by planes from the by the ancient commentators, retains the Doric
solids so called ; those namely which are generated dialect, in which Archimedes, like his countryman
by the rotation of the Conic Sections about their Theocritus, wrote. (See Wallis, Op. rol. iii. pp.
principal axes. Like the work last described, it 537, 545. Tzetzes says, freye dé kad dwploti,
was the result of laborious, and at first unsuccess- φωνή Συρακουσία, Πα βω, και χαριστίωνα ταν γαν
ful, attempts. (See the introduction. )
κινήσω πάσαν. ) A French translation of the
The Arenarius (ó Vanuitis) is a short tract works of Archimedes, with notes, was published
addressed to Gelo, the eldest son of Hiero, in by F. Peyrard, Paris, 1808, 2 vols. 8vo. , and an
which Archimedes proves, that it is possible to English translation of the Arenarius by G. Ander-
assign a number greater than that of the grains of son, London, 1784.
sand which would fill the sphere of the fixed stars. (G. M. Mazuchelli, Notizie istoriche e critiche
This singular investigation was suggested by an intorno alla vita, alle intenzioni, ed agli scritti di
opinion which some persons had expressed, that Archimede, Brescia, 1737, 410.
