Ml 



APOLLO N'lt'S, HEK 



APOLLONIUS RHODIUS. 



I i 



Philoptor, who died ac. 205. Apt'llonius and Hannibal wore nearly 

 contemporary both u to birth and achievements in their different 

 line*. ArchtaMdM died B.C. S12, at which time Apollouiiu was living ; 



:-.ot kuown who the Utter died. 



The life of Apolloniiu was pawed at Alexandria, in the school of 

 the miOMMon of Euclid, under whom be rtudied. With reiiwct to 

 charge of |.liarUni from Archimedes, brought against Apollonius, 

 it u said by Kutocius, liu commentator (about AD. 640), who ciU-s 

 UM charge, that it was well known that nritlirr Arohimedei nor 

 Apollouiu* prvUnded to bo the flnt investigators of the couio 



Of the mo*t interesting part of an eminent man, his opinions on 

 disputed isubjecu. we know I nt little in the cafe of Apollouius. 

 Ownudi, in hit life of Copernicus, mention* an opinion attributed 

 by the latter to the Grecian geometer, and which U said to have been 

 .(^. that of rhilulaui, that the mn and moon only moved round the 

 earth, but all the other planets round the run. We cannot find any 

 other authority for attributing thii opinion to Apollonian, except 

 VTeidler in hi* ' HistorU Astronomic,' who however cites Gass-udi 

 aa Ua authority. Vieta conjectures with great probability that there 

 ia a confusion of wordt. That this system was called 'Apollonian' 

 from iu reference to the sun (Apollo.) But Apollonius certainly paid 

 attention, at least, to the then received system, since known by the 

 name of the Ptolemaic, for I'tolemicus has preserved some theorems 

 of his on the method of finding the stationary points of the planet", 

 supposed to move in epicycles. Proclus, in his commentary on Euclid, 

 mentions that Apollonius attempted to prove the axioms, and cites 

 bis investigation of the theorem, that things which are equal to the 

 same are equal to one another, iu which, as may be supposed, propo- 

 sitions are assumed not more obvious than the theorem itself. Vitnt- 

 vios cites Apollonius as the inventor of a species of clock which he 

 terms 'pbaietra.' 



The great work of Apollonius which now remains is seven books 

 of bis treatise on conic sections, of which we shall presently speak. 

 Bat besides this, he is known to have written treatises, according to 

 Pappus, ' De Itationis Sectionc,' ' l)e Spatii Sectione,' ' De Sectione 

 determinate,' ' De Tactionibus,' ' De Inclinationibu.V ' De Planis 

 Locis,' and according to Proclus, 'De Cochlea,' and 'De pertnrbatis 

 Rationibus.' Of these, the first only U known to us, having been 

 found in Arabic, and published in Latin by Halley in 1703, with an 

 attempt to restore the second. But Mursenne, cited by Vossius, says 

 be read, in an Arabian author, Aben Eddin, on assertion that all the 

 works of Apollonius, more in number than those mentioned by 

 Pappus, were in Arabic at the beginning of the llth century. 



About the end of the 16th century, it was a very common exercise 

 of mathematical ingenuity to endeavour to restore these and other lost 

 that is, from the fullest notion which could be gathered, to 



gas** at the propositions which they might have contained. Such 

 attempts gave rise to the ' Apollonius Gallus ' of Vieta, the 'Apol- 

 loniiu Batavus' of Snellius, and other works of Haurolico, Qbetaldi, 

 Adrianus Komanus, rVrmat, Schooten, Anderson, Halley, R, Siinson, 

 and others. 



The conic sections of Apollonius are iu seven books, the first four 

 of which are extant in Oreek, with the commentary of Eutocius of 

 Ascalon, above-mentioned. The next three were supposed to be lost, 

 till the middle of the 17th century, when James Golius, a celebrated 

 oriental professor of Leyden, returned from tlio East, with tho whole 

 seven books in Arabia Some delay took place iu their translation 

 and publication, during which, in 1658, liorvlli accidentally discovered 

 an Arabic manuscript in the Medici library at Florence, of the same 

 seven books. It does not a little serve to illustrate the use made of 

 public libraries, that while one author after another had for years 

 nprsssed regret at the lots of the lost four books, three of them 

 should be lying in one of the most celebrated libraries in Europe, in 

 the heart of a capital city, with an Italian title-page. Borelli, and 

 Abraham Echellcwis, an oriental professor at Rome, translated it from 

 the Arabic, aod published their version in 1661. At the time of the 

 discovery, Viviani was engaged in restoring the lost books, and when 

 it was made known, he prevailed on the Grand Duke of Tuscany to 

 mark all bis popen, and to order Itorelli to k<-ep the contents of tho 

 new books secret The work of Viviani, well known as an acute and 

 sthematleian. was found (Montucls, L, 250) to fall 



. of that of Apollonius on several important ]x>inU, though, as 

 might be expected, the views of the Italian of the 17th century were 

 more extensive in uisny eases than those of the Greek. The eighth 

 book was mill wanting, and a note to the version imported by Golius 

 informed the reader that it bad never been found, even by the Arabs, 

 in the Greek. Bat when the Oxford press, at the commencement of 

 UM last century, was employed upon the magnificent versions of the 

 Oiwk geometers, which an still the best in public use, Dr. Aldrich, 

 that the preliminary Lemmas of Pappus to the seventh 

 I asserted to belong to the eighth, and also that the latter 

 from the words of Apollonius himself in his introduction. 



appeared, 

 to be a co 



, , 



to be a continuation 'of the former, proposed to Halley that he should 

 Bdeavour with these lights to re-entablish the miming book. H..II. y 

 wee then employed in completing the edition of the work, which the 

 *atb of Dr. Gregory had interrupted, and he acceded to tho sug- 

 gestion. The whole appeared at Oxford, iu 1710, with the commentary 



of Eutocius, the Lemmas of Pappus, and iu addition, the work of 

 Srreuus on the sanio subject. This is tho only edition of the Greek 

 toxt 



The content* of the work are thus briefly described by Apollonius, 

 of whose words we give a free translation. " The first four books are 

 elementary : the first contains the generation of thu three sections of 

 the cone, and of the sections which are styled opposite, and th ir 

 principal distiuctivo properties, which have been treated by us more 

 fnUy and generally than by any of our predecessor*. The second 

 book contains the properties of the diameters and axes, as well as of 

 the asymptotes, and other matters of general utility : you will hence 

 see what I have called diameters, and what axes. Tho third book 

 contains many and wonderful theorems, which are useful in the compo- 

 sition of solid loci, of which the majority arc both new and beautiful. 

 The fourth book shows iu what manner sections of a cone, or of 

 opposite cones, may cut one another, and the circumference of a circle, 

 on the whole of which nothing bos been delivered by those who went 

 before us. The remaining four books treat of the higher part of the 

 science : the fifth, on maxima and minima : the sixth, on equal and 

 similar sections : the seventh, on diorutic theorems or theorems 

 useful in the solution of problems : and the eighth, on the problems 

 thus solved." 



Apollonius was the first who used the words ellipse and hyperbola, 

 of which Archimedes does not take notice, though he uses the term, 

 parabola. He also, as we see above, first distinguishes the diameters 

 of the section from tho axes. It was, moreover, iu his time, and 

 perhaps first by himself, that the general sections of the cone were 

 considered ; for previously it had been usual to treat only of those, 

 the planes of which were at right angles to one of the sides of the 

 cone ; so that an ellipse could only coma from an acute-angled cone, 

 and so on. 



The most remarkable book in the whole work is the fifth, 

 treats of maxima and minima. With a little licence it might be called 

 a complete treatise on the curvature of the three sections, for in c m- 

 sidering the number of maxima and minima which can be drawn to 

 the section from any point in its plane, the space in.-ide and outside 

 of the ovolute has different properties. There is only wanting the 

 addition of a name for the curve which separates t'ue spaces (which 

 we now call the evolute). This book, and the quadrature of Archi- 

 medes, are the highest points of tho Grecian geometry. 



The work of Apollouiua was lightly spoken of by Descartes, who is 

 supposed to have seen the first four books only ; but it was held in 

 particular estimation by Newton, and Cardan places its author seventh 

 among all the men who have ever lived : in his own age be was called 

 the great geometer. 



We now briefly mention some of the principal editions of the ' 

 conies. The celebrated Hypati.i, daughter of Theon, wrote a com- 

 mentary upon them. We have already mentioned Pappus and Euto- 

 cius as commentators, Borelli and Halley as editors. Among the 

 Arabs, it was first translated by Thebit-ben-Cora, under tho Kalif Al- 

 Maimun in the Uth century : by Abalphut in the 10th century ; and 

 two editions, of little celebrity, appeared in Persian in the 13th 

 century. In Europe, it w;n first translated, but badly, by Memmius, 

 a Venetian, in 1537 ; by Maccolyco about tho Bamo time, but we 

 cannot learn that this edition was ever published ; also by Coin- 

 maudiut) in 15o'<5 (misprinted 1006, in .Murhnrd), and by 

 Claude Richard iu 1655. Montucla is incorrect in saying that this 

 edition was announced and never published. In 167!*, Harrow pub- 

 lished the first four books. 



Apollonius appears to have improved the notation of arithmetic, 

 if we may judge from tho praise given to him by Eutocius, iu his 

 commentary upon the quadrature of Archimedes, for a work which 

 he calls nuirrdftoov. Pappus more explicitly states that the improve- 

 ment consisted iu a simplification of the method proposed by A rchi- 

 medes for representing very large numbers, which brought tho system 

 nearer to that of the modems. (Delambre, ' Hist Ast Aue. 

 Eutocius also says, that Apollonius extended the quadrature of the 

 circle given by Archimedes. 



APULLO'MUS DY'SCOLUS, or ALEXANDR1N0S MINOR, a 

 grammarian, who was born at Alexandrine in the 2nd century of the 

 Christian era. He was tha sou of Mnesithous and Ariadne, and is 

 said to have been so poor that bo was unable to afford money su: 

 even to purchase paper. It was probably this state of poverty wliich 

 had an effect on his temper, and procured him the name of Dyscolus, 

 or tho moroae. He was the author of many works; he wan called by 

 Priscian ' Priuoeps Grammaticorum,' and afforded to that grammarian 

 many hints for his ' Latin Grammar.' Uf his four remaining works 

 the chief is a 'Treatise ou Syntax,' in four books, the first edition 

 of which is by Aldus, 1495, Venice. An improved edition was made 

 by Sylburgiu*, with a Latin translation of .Km. Portua, 1590 ; tin 

 lait is by Uckker, Berlin, 1817. At the end of the ' Treatise on 

 Greek Dialects,' by Haittaire, Hague, 1718, Lips. 1807, there ore some 

 extracts of tho Grammar of Apollonius, which were procured by 

 Voesius from a manuscript of the Royal Library of Paris. 



.U'OI-LO'NIUS RHO'DIUS, a Greek epic poet It is not ascer- 

 tained whether ho was a native of Alexandria in Egy pt, or of Naucritis, 

 a small town on the Canopic branch of tho Nile, but from his long 

 residence in the island of Rhodes he obtained his surname, lie wnu 



