RIvM)IN'(iS IS LATIN. 



Fig. 19. 



From A B oat off A r equal to c D (Euc. I. 3), and from contro A, 

 at distance A F, describe a circle (Post. 3). With F as centre, 

 and radius v a equal to D E, describe a circle, cutting the lost 

 described circle in o, a'. Join A a, A o ; then FA a, r A a' shall 

 be the angles required. For in the triangles FA a, FA a', since 

 A F, A a, A a' are all equal, being radii of the same circle, and 

 that A Y is rqinil to c D or c E, therefore A F, A o, A a' are equal 

 to c D or c E. Also, because F a, F a' are equal, being radii of 

 the same circle, and F a is equal to D E, therefore r o' is equal to 

 D E. Hence, since A F, A o and A F, A o' are equal to c D and 

 c E, also bases F o and F o' are equal to D E, therefore included 

 angles F A o, F A a' are equal to included angle D c E. Q. E F. 



Both positions, a, a', are given, since the enunciation does not 

 state on which side of A B the angle is to be. 



PBOPOSITION XX. In the figure of Euclid I. 15, if EF, E o 

 (Fig. 19) be drawn at right angles 

 respectively to A B and c D, the angle 

 F E a is equal to the angle B E D or 

 ABC; for since A E F is a right 

 angle, and the angle c E a is a right 

 angle, therefore A E F = c E a. From 

 each take the common part, c E F, 

 then the remainder A E c = remain- 

 der F EG. But, by Euclid 1. 15, AEC 

 = B E D ; i.e., angle F E o is equal to 

 angle A E c or B E D. Q. E. D. 

 Our next article will extend as far as Euclid I. 32, and we 

 shall prove the following propositions : 



PROPOSITION XXI. Given two straight lines, A B, A c, meet- 

 ing in A, and another line, r> E, of limited length. Required 

 to describe an isosceles triangle, A L M, such that A L may coincide 

 with A B, and A M with A c, and L M may be equal to D E. 



PROPOSITION XXII. If ABC be an isosceles triangle of 

 vertex A, with the base B c produced to D, and if from centre 

 c, at distance c A, a circle be described cutting B A produced in 

 E, then the angle BCD shall be equal to three times the angle 

 A c B or A B c. 



PROPOSITION XXIII. In the figure of Euclid I. 5, draw c L 

 at right angles to c B, meeting B A produced in L, and prove 



AL =AC. 



PROPOSITION XXIV. If in the figure of Euclid I. 5, the 

 angles F B c, B c Q be bisected by the lines c o, B o, meeting in o, 

 then o A shall bisect the angle BAG. 



PROPOSITION XXV. In the figure of Euclid I. 1, if the* 

 circles cut again in F, and c A produced cut the circle in H, then 

 H F will be equal to A B. 



PROPOSITION XXVI. If in a triangle ABC, B c be bisected 

 in a, and A a joined, and the angle B A o be equal to the angle 

 c A o, then B A shall be equal to c A. 



PROPOSITION XXVII. Given two straight lines, A B, AC, 

 meeting in A, and another straight line, x>, of limited length. 

 Required to form a right-angled triangle, of which the base 

 shall coincide with A c, one side shall coincide with A B, and the 

 other side be equal to D. 



PROPOSITION XXVIII. If in the figure of Euclid I. 1, AB 

 produced cut the circles in D, E, and the circles cut again in F, 

 the figure c E F B is a rhombus, having each of the angles at D 

 and E double the angles at c and F. 



READINGS IN LATIN. IV. 



HORACE. 



QUINTUS HORATIUS FLACcus was born at Venusium in the 

 year 65 B.C., and died 8 B.C., in his fifty-seventh year. He was 

 the greatest of all the lyric poets of Rome, and his Satires, 

 though not so biting and pungent as those of Juvenal, the ac- 

 knowledged master of that branch of literature, are marked 

 \>j as keen a sense of humour and power of observation. He 

 Las left us four books of Odes and one book of Epodes in 

 various lyric metres, two books of Satires, two books of Epistles, 

 and the " De Arte Poetica," a treatise on the art and practice 

 of versification, in hexameters. The Odes and Epodes are the 

 most beautiful of his works, though they are not the most 

 original, being, for the most part, formed upon Greek models. 

 There is an occasional obscurity in his language, and especially 

 in the Satires and Epistles there are allusions to the events 

 of his time to which it is difficult to find a key ; but for the 



most part his writing* are easy and graceful, and but few 

 of the Ode* present any bat ordinary difficulties to the reader. 

 The following extract is the ninth ode of the first book ; it ui 

 addressed to his friend Thaliarchns, and requires no further 

 introduction. It is in the Alcaic measure, so called from the 

 Greek poet Alcsaos, who employed it, and was credited with 

 its invention : 



HORACE. BOOK I., ODE ix. 

 Vide* at altA stet nive candidnm 

 Soraote, nee jam sostincant onos 

 Sflvse laborantcs, geluque 

 Flumina oonstiterint acuto. 



Dissolve frigos, ligna super fooo b 



Large reponena, atque benignios 

 Deprome quadrimum Sabina, 

 O Thaliarche, meruin diota. 



Permitte divia eastern, qni simul 

 Stravere ventos aequore fervido 10 



Deprcaliantes, nee cupressi 

 Nee veteres agitantur orni. 



Quid sit f nturum eras, f uge quasrere ; et 

 Quern sors dierum cunque dabit, lucro 



Appone : nee dulces amores 15 



Sperne puer, neque tu choreas. 



Donee virenti canities abest 

 Morosa. Nnnc et campus, et areas, 

 Lenesque sub noctem susurri 



Composita repetantur bora. 20 



None et latentis proditor intimo 

 Gratus puellse risus ab angulo, 

 Pignusque dereptum lacertia, 

 Aut digito male pcrtinaci. 



NOTES. 



1. Stet, stands out, owing to the greater clearness of the atmosphere. 

 In summer the outline of the hills would be dim aud hazy. 



2. Soracte, a hill in the territory of the Falisci, about twenty- 

 four miles from Rome, now called Monte di S. Orttte. 



4. Acuto. So Pindar speaks of x"<" . and we use the phrase 

 " piercing cold." Constiterint, as liaring a passive tense, " hare been 

 stopped," takes gelu as a kind of ablative of the agent. 



7. Sabina, generally described by Horace as a poor wine, " rile 

 Sabinum " (Ode I. XT. 1), but this would be mellowed by having been. 

 kept four yean (quadrimum). 



8. Diota, a two-handled jar (Air, oi'r, MTOT, the ear), abl. of the 

 place trfi*nc a thing proceeds. 



9. Simul more generally would be rimul ac stravere, a* MOM at Utff 

 have quitted. 



10. JEquore, abl. of place. 



11. Deproeliantes, fighting it out. The de has a tense of completing 

 a thing, doing it thoroughly. 



13. Fuge qucerere, seek not to Imoic. The infinitive is used as 

 the object of (accusative case after) fuge, by a frequent construction 

 borrowed from the Greek. So Virg. Xn. ix. 200, "adjungere rebus 

 Nise fugis ? " where adjungere is the object of fugis. 



14. The construction is quern cunque (diem) dierum Fors dabit, 

 whatever sort of day fortune gives, count it a gain. Lucro appone, ut H 

 down to the profit s\de of the account. 



18. Arete, open places, around temples, for example. 



20. Repetantur, be sought for at the appointed hour. 



23. Pignus, either a bracelet (laeertis) or a riug (digito). 



24. Male pertinaci, that ill feigns rtsittance, 



The following ode is addressed to some fickle fair one who 

 had betrayed the poet, who now congratulates hicelf on uis 

 cscupe : 



HORACE. ODES, I. T. 

 Quis molta gracilis te puer in roaa 

 Perfnsus liquidis urget odoribos 

 Grato, Pyrrha, sab antro ? 

 Cui flavam rcligas comam 



Simplex munditiis ? Heu, quotics fidem 

 Mutatosque Decs flebit, et aspera 

 Nigris aeqnora rentis 

 Emirabitnr insolens, 



Qni nunc te frnitnr credalus anreA ; 

 Qoi semper vacnam, semper amabilem 

 Sperat, nescius aurte 

 Fallacis. iliseri quibua 



10 



