READINGS IN GR1 



EXAMPLES. 

 The sum of 3v/fc un<l ~ ^ / .^ in :i \'1> f 



It in manifest that three times the root of I, and twice the 



root of a, are neither fire times the root of b, nor five 



timos the root of a, unless b and a are equal. 



The sum of * A/ o and ' A/ a, i* * v/ a + * A/ a. 



The square root of a, and the cube root of a, are neither 



twioo the square root, nor twice the cube root of a. 

 From the preceding principles we deduce the following 



GENERAL RULES FOR ADDITION OF RADICALS. 

 //' the radical parts are the same, add their coefficients, and 



- t,,< annex the common radical parts. 

 If 'he radicals are i>. iiii.<, //(/ I 'led by 



i'j them one afli-r <tu(hrr, n-ithtntt altering their signs. 

 \ MPLE. Add A/28 to ^ 



A/28 = A'(4X 7>= 2^7. 

 = A/(9 x 7) = 3jv/7. 

 Sum = 5 A/7. 



EXERCISE 51. 



197243 to 10 7363. 



7. Add 78lb to 7 



8. Add 70i',i t<> 7J 



9. Add *725*c to 73&r<c. 

 10. Add3>/o6 to4o7a6. 



1. Add 727 to 748. 



2. Add 772 to 7128. 



3. Add ^180 to 7405. 



4. Add 3 740 to '7135. 



5. Add 4 '754 to 5 '7128. 



SUBTRACTION OF RADICAL QUANTITIES. 

 RULE. Subtraction of radicals is performed in the same 

 / o addition, except that the si<jns of the subtrahend 

 must be changed as in subtraction of other quantities. 

 EXAMPLE. From s A/ 81.r take * A/ 24*. 



3 A/ 81* = A/(27 X 3z) = 3 8 A/3z. 

 = 3 A/(8 X 3x) = 



1. From 7 ay take 3 7ay. 



2. From 4*7 a + x take 3 , 



3. From 3A* take - 57i*. 



4. From a (x + y)^ take b (* 



j i 



5. From o ' take 2u . 



Difference = 3 A/3x. 

 EXERCISE 52. 



6. From 750 take 78. 



7. From 7 by take 7by. 



8. From 7 * take 7" *. 



9. From 2 750 take 71 s. 



10. From 7 320 take ' 7 40. 



11. From 5 720 take 3 745. 



12. From 780o*Je take 720oz. 



KEY TO EXERCISES IN LESSONS IN ALGEBRA.-XXVII. 

 EXERCISE 47. 



10. z. 



11. x'. 



4. (a-*)*. 



5. a". 



7.' IV ' 



8. *'. 



9. v. 



18. ^1? 



and 



is. f^y 



20. x - 1. 



21. o + i. 



22. a + |. 



24. 



*. 



READINGS IN GREEK. IX. 



HOMER. 



So far ore we from being able to speak with any accuracy re- 

 specting the date at which Homer flourished, that we even are 

 unable to assert with any degree of certainty whether he ever 

 existed at all. That the poema which are commonly ascribed 

 to him are among the earliest specimens of Greek poetry is 

 evident, both from the style and manner in which they are 

 itten, and from tlio terms in which they are alluded to by other 

 Greek writers of an early period, whose date is pretty accu- 

 rately ascertained. Without going into the controversy at any 

 length, it may be stated briefly that almost all the ancient 

 writers looked upon the Homeric poems, the chief of which are 

 the " Iliad " and ths " Odyssey," as the work of an individual 

 Homer, about whose date, however, they differ very widely. 



Other*, again, bettered that wnile the " Iliad " WM the work of 

 the true Homer, the "Odyssey" WM by another band; while 

 in later times it has been bald by many that there WM no on* 

 poet called Homer to whom either of these works can be 

 Moribed in their entirety, but that they were the work of num- 

 bers of bards, banded down by oral tradition, and afterwards 

 collected together. It is quite imposiiible to decide which, if 

 any, of these is the correct view to take. For ourselves, we 

 prefer to beliuvo in the existence of Homer, and bis authorship 

 both of the " Iliad " and " Odyssey." The former of these is 

 an epic poem, in twenty-four books, describing the ten years' 

 siege of Troy by the Greeks, who bad been Msembled for the 

 purpose by Agamemnon and Menelans, to revenge the injury 

 done to the latter by Paris, the son of Pram, King of Troy, 

 who had carried away his wife, Helen, the fairest of the Greeks. 

 By far the greater part of the "Iliad" is purely mythical, 

 both in substance and treatment ; but there appears to be every 

 reason to believe that there WM at an early period some expe- 

 dition of the sort undertaken by the Greeks against the people 

 of the west coast of Ania Minor. Thncydides, a careful reader, 

 and eminently cautions in forming bin opinion, believed in it, 

 and observes that it WM the first CMC on record of the Greek* 

 acting as a united people. The "Ouyssey" is an account of 

 the wanderings of Odysseus, one of the Grecian leaders, about 

 the greater part of the then known world, on his return from 

 the siege of Troy. Both these poems are written in the Ionic 

 dialect, one of those early forms in which the Greek language 

 was spoken before it was welded into one common united 

 speech. The style of Homer is simple without being trivial, 

 and grand without being bombastic. As is the manner of epic 

 poetry, it presents a series of episodes, all minutely and care- 

 fully described. The fights are not the battle* of armies, bot 

 the hand-to-hand combats of heroes. " The great chiefs stalk 

 before the rank and file, and sustain almost alone the fortunes 

 of the day. It is the oligarchy of battle the monopoly of car- 

 nage ! Ajax is a battalion on one side, Hector a corps d'armfe 

 on the other ; while Achilles, when he does condescend to sally 

 forth, slaughters Trojans by the score. The combatants proclaim 

 their own merits like Bed Indians, and insult the dead with bitter 

 and barbarous taunts. There is a thoroughly savage element 

 about the actual combats, which takes us back, indeed, to pre- 

 civilised times." " Poets of Greece," by Edwin Arnold, p. 22. 



It would take much more space than we have at our command 

 to go fully into the various peculiarities of diction and style 

 which are to be noticed in the writings of Homer, but the most 

 prominent of them will be pointed out as we proceed. 



The following extract is from the first book of the " Iliad," 

 in which Chryses, the priest of Apollo, prays for vengeance on 

 the Greeks, who had stolen away his daughter Chryseis, as a 

 prize for Agamemnon : 



HOMER. " ILIAD," I. 37 58. 



K\v6i fjitv, ' A.pyvp6ro , 

 KiAAai/ rt faBtiiv, Tfft'Soid rt 1<pi avdaffm, 

 'S.fj.tvQfv- t?jroT rot \apitin-' iirl 

 ff (I Si) irort roi Kara iriova firipi 

 ravpwv f)5' alywv, r6$t >ioi tcprfrj 

 riffftav Aafao! ffi.a odicpva ffoitri 



>s t<par' tvx&H*vor TOV 8' fic 

 /3"; 5f /car' Oi'\vfj.iroio 



40 



45 



50 



TTJ Sf Karri 8' ayoprivSt Ka.\tffffttTo \a6v ' 

 rtf yap jirl <ppTi Orixt Ota \t\>K<i'\tiros''ttprr 65 



(c^Sero yap &ava>v, Sri pa OvriffKovras 6paro. 

 ol 8' tVfl o$v jytpOtv, &priy*p<ts r' iytrorro, 

 rotfi 8" aviffrdufvos fitrityi] troSa; aitvs *AxAA^f 

 NOTES. 



37. M<v. Homeric penitire for /u.r. 



'Ap-)ri>p6ToF. God of tht tilvtr Unc. A frequent epithet of Apollo In 

 Somer. 



'Au0i/3t'/JnKar, tf ho haft stood around, and so dtfmdtfi. 



5' &p' oiffTol T fuav \taoftLfvoio, 



ailTOV KIVT]8(VTOS- & 8" Ijlt WKT\ t'oiKCUS. 



^T" iiirtn' inrdixvdf vtHiv, JITO 8" Ibv frjKf 

 otty}] 8* K\ayyi) yivtr' ap-yupfoto /3to!o. 

 owpf/oy ftfv irpurov iftfx*' ro i *** twos apyovt. 

 aurop fiTfir' avrolffi /3Ao; ix (T(l>K * 

 aid 8 irvpal vtKvuv xaiovro 



