442 



PROPORTION 



ami curiosity, at which are delivered recitations 

 in every language represented in the College or 

 its missions, amounting often to fifty or sixty. Of 

 thin festival Cardinal Mezzofanti (q.v.) used to be 

 the guiding spirit. 



I'roprrfiiiK. SBXTUS (for the second family 

 name, Aurelius, often given him there is no 

 authority), the most impassioned of the Homan 

 elegiac |>oet8, was a younger contemporary of 

 Tihullus, born about 48 B.C. in Unihria. probably 

 at Asisium ( the modern Assisi ). Nearly all we know 

 of him is gleaned from his writings, according to 

 which he came of an undistinguished, comparatively 

 poor family, lost his father in boyhood, and hod a 

 portion of his patrimony confiscated, after Philippi, 

 by the Triumvirs, to reward their veterans, but 

 retained means enough to proceed to Koine for 

 education, and, having chosen his residence, like 

 Virgil and Maecenas, on the Esquiline, to make 

 poetry the business of his life. The school tln>n 

 fashionable was the Alexandrian, represented by 

 Callimachus and Philetas, and these he made his 

 models, drawing from them his learned tone and 

 his wealth of mythological colouring. In the 

 political and martial movements of the time he 

 took no part, though his patriotism was pure and 

 strong witness his exultation over the victory off 

 Actium, his scorn of Cleopatra and her presump- 

 tuous ambition to dominate the mistress of the 

 world, almve all, his appeal to the Romans to 

 renounce self-indulgence and to return to their 

 neglected legends for the civic virtues and the 

 heroism of 'Uie brave days of old.' Such was his 

 precept; while his practice was the emotional 

 poetic life, in the congenial society of Ovid, Virgil 

 (whose Mneid he has nobly eulogised), the epic 

 poet Ponticus, and Julius liossus. Like them lie 

 won the favour of Ma-cenas, to whom be dedicated 

 a I look of his poems, and even ingratiated himself 

 with Augustus, whose achievements he duly cele- 

 brated. But the central figure of his inspiVation 

 was his mistress Cynthia, a lady somewhat older 

 than he, whose real name was Hostio. For many 

 y eai - In- cherished a glowing passion for this highly 

 gifted and beautiful, hut far from virtuous woman, 

 till alioui 24 li.c. lie disentangled himself from her 

 spells. She died liefore him ; but even after death 

 sin' lived in his memory as she still lives in the 

 poem- that have immortalised her. Proper! ins left 

 Koine, it would appear, only once, on a visit to 

 Athens, when he may have experienced the ship- 

 wreck he box so vividlv described. The year of his 

 death has, with probability. !>een placed about 14 

 B.C. 'Of his poems only the first Uiok, devoted 

 entirely to Cynthia, was published during his life- 

 time; certainly the last of the four was given to 

 the light, in terms of bis will, by his friends. Its 

 contents are youthful pieces, in which he celebrates 

 the legends of early Koine in the style of Calli 

 niarhus, and have a special interest in having most 

 likely inspired Ovid to the composition of his Fa*ti 



|HTha|w even of his l/rroulu. As a poet Pro 

 perliiis ranks high in Unman literature the tone 

 of the later criticism (with (ioethe at its head) 

 being one of increasing admiration for his native 

 fuive. his eye for dramatic situation, bis power 

 over the reader's sympathies, giving the effect of 

 reality to what in the hands of Tihullus or even 

 Ovid is merely conventional. He bos more in 

 common with ('.-11111111- than with either of them, 

 while he lacks the artistic graces peculiar to the 

 three, being often rough to harshness and obscure 

 from defect of finish. 



For the F.nlish student there u an admirable text by 

 Palmer (Dublin, 18HO), and good critical note* by Paley 

 and Postdate in their respective edition*. There U no 

 adequate translation of him in any language, Cranstoun't, 

 in Engluh ( 1875 ), being about the moit faithful. 



Property. See HERITABLE AND MOVABLE, 

 LAND LAWS, PERSONAI.TV, POSSESSION, REAL. 



Prophecy. For the dot-trine of prophecy and 

 its relation to prediction, see I'.IIII.K, Vol. II. 

 p. 119. _ See also the works on the several pm- 

 phets cited at the articles ISAIAH. JKKI MIAII. 

 .\r. ; the works on prophecy by Ilofmann, 

 Delitzucb, Tholuck, Kwald, Kuerten, Reuss ; Fair- 

 bairn, Prophecy (1S56; 2d ed. 1864); Stanley 

 Leathes, Old fatament 1'rophecy (1880); \V. l: 

 Smith, The Prophet* of Israel (1882); Kiehm, 

 Messianic Prophecy ( Eng. trans. 1891 ). 



Propolis. See BKE, Vol. II. p. 21. 



Proportion, in Arithmetic and Geometry, is 

 a particular species of relation subsisting lietween 

 groups of numben or quantities. Notwithstanding 

 that the idea of proportion is found to exist in 

 perfection in the mind of every one, yet a good 

 definition of it is a matter of extreme dilliculty. 

 The two definitions which, on the whole, are found 

 to be least objectionable are that of Euclid and 

 the ordinary arithmetical definition. The latter 

 states proportion to be the 'equality of ratios,' 

 and throws us back on a definition of the term 

 ratio, which may most simply be considered as 

 the relation of two numbers to each other, shown 

 by a division of the one by the other. Thus, the 

 ratio of 12 to 3, expressed by V. or *, denotes that 

 12 contains 3 four times ; and the ratio of 8 to _' 

 being also 4, we have from our definition a state- 

 ment that the four immlwrs, 12, 3, 8, and 2. are in 

 proportion, or, as it is commonly expressed, 12 

 bears to 3 the same ratio that 8 does to 2, or 

 12:3::8:2. In the same way it is shown that 

 3 : 8 : : 13J : 36 ; for J expresses the ratio of the first 



to the second, and ~* = *' = \. It will Ixj 



TO I & o 



gathered from the two arithmetical proportion* 

 here given, and from any others that can be 

 formed, that 'the product of the first mid /</.%/ 

 terms (the extremes) is ei/nal to the /iriM/m-f <if the 

 second and third terms ( the means ) ; ' and upon t his 

 property of proportional numlieis directly depends 

 the arithmetical rule called ' proportion," &o. The 

 object of this rule is to find a fourth proportional 

 to three given numbers i.e. a number to which 

 the third bears the same ratio that the first does to 

 the second ; and the number is at once found by 

 multiplying together the second atwl third terms, 

 and dividing the iirodurt by the first. Proportion 

 is illustrated arithmetically by such problems as, 

 ' If four yards cost six shillings, what will ten co 

 Here, 15 Iwing the fourth proportional to 4, i, and 

 10, fifteen shillings is the answer. The distinction 

 of proportion into direct and inrcrsr. is not only 

 quite unnecessary, but highly mischievous, its it 

 tends to create the idea that it is possible for more 

 than ime kind of proportion to subsist. I'mitiiiiirtl 

 proportion indicates a property of every three con- 

 secutive or equidistant terms in a 'Geometrical 

 Progression' (q.v.) for instance, in the series 

 2, 4, H, 10, 32. .. , 2:4: :4:8, 4:8::S : 16, &<.., or 

 2:8::8:32, &c. In the almve remarks all con- 

 sidciation of incommensurable quantities has 

 been omitted. The definition given by Knclid is 

 as follows: Four magnitudes are proportional 

 when, any equimultiples whatever lieing taken of 

 the first and third, and any whatever of tne second 

 and fourth, according as toe multiple of the first is 

 greater, equal to, or less than that of the second, 

 the multiple of the third is also greater, equal to, 

 or less than that of the fourth ; i.e. A, B, C, D are 

 proportionals when, if rn\ is greater than nB, mC 

 is greater than P ; if iA is 'equal to i/B, mC is 

 equal to I); if )A is less than B, mC is less 

 than nD ; m and n being any multiples whatso- 

 ever. The apparent cumbrousness and circum- 



