; SONS IK GEOMETRY. 



worda and the commencement* of new tenet. From cloven 



i i/t) to seventeen (aeptendecim) inclusive, each consecutive 



\\or.l is ..Mppi'iiinled of deoem and a number taken from the 



PICK. \Mn-n they oome to eighteen, instead of saying 



tit't. T tlu-ir former manner, and as we say in English, eight, ten, 



the BomaiiH said; la-it from twenty, duo de viginti. Having 



passed twenty, they made use of it to form the numbers between 



twenty and thirty; thus : nnus et viginti, one and ta-rnty ; they 



also said, viginti unus, viginti duo, viginti tres, viginti quatnor, 



and BO forth. In all cases, eight and nine are expressed by 



subtracting two and ono from tho next ensuing new term ; thu 



-eight i* duo de triginta, two from thirty ; thirty-iiim- is 



undequadraginta, one from forty ; so in the ordinals duodequadra- 



gcsirnuB, undosexageaimus. 



VOCABULARY. 





Alius is used with alias in a peculiar manner, nearly equal to 

 our one another, the one, the other, differently, in different ways, as : 

 Alius alium occidit. I Alii olio currunt. 



The <w slays the other. They run in different directions. 



EXERCISE 67. LATIN-ENGLISH. 



1. Quota hora est ? 2. Decima. 3. Estne sexta bora ? 4. Quinta 

 est hora. 5. Annus quo mine vivinms, est millesimus octingesimus 

 sexagesimus et octavus post Christum natum. 6. Pater incus agit annum 

 quartum et sexagesimum. 7. Soror tua ngit annum sexogesimum ter- 

 tium. 8. Mater mea agit annum octavum et quinquagesiinum. 9. 

 Pater tuus agit quiuquagesimum octavum annum. 10. Frater major 

 nutu agit annum tertium et tricesimum. 11. Prater minor natu agit 

 annum alterum et vicesimum. 12. Soror major natu agit annum duo- 

 detricesimum. 13. Soror minor natu agit annum vicesimum. 14. In 

 urbe aunt millo uiilites. 15. Duo milia hostium iirbem obsident. 16. 

 Aliud alii placet. 17. Aliud ulii displicet. 18. Milites utriusque exer- 

 citus suut fortissimi. 19. Utrumque est vitium et omnibus credere, 

 et nulli. 20. Perfldus homo vix ulli fldem habet. 21. Unius fidi ho- 

 minis amicitia habet plus pretii quam multorum infidorum societas. 

 22. Soli sapienti vera vis virtutis est cognita. 23. Incoloe totlus urbis 

 de victoria exercitus Iseti suut. 24. Nulling hominis vita ex omni 

 parte beata est. 25. Habeo duo amicos, ambo valde diligo. 26. Auii- 

 cus meus habet duo filios et duos fllias. 



EXERCISE 68. ENGLISH-LATIN. 



1. The enemy breaks into our country with 10,000 soldiers. 2. A 

 thousand soldiers defend the city. 3. The city is defended by 2,500 

 soldiers. 4. 28,000 cavalry and 13,500 infantry defend the country. 5. 

 My father is in his seventy-fifth year. 6. My mother is in her sixty- 

 third year. 7. My elder brother is in his thirty-seventh year. 8. My 

 younger brother is in his thirtieth year. 9. My elder sister is in her 

 thirty-fourth year. 10. My younger sister is in her eighteenth year. 

 11. What o'clock is it ? (what is the hour ?) 12. It is eleven o'clock. 

 13. How old art thou ? (in Latin, What year dost thou lead ?) 14. I am 

 fifty-two. 15. We repose confidence in neither of the two, neither the 

 faithless nor the flatterer. 16. The life of no one is happier than (the 

 life) of the sage. 17. The father takes a walk (ambulo) with his two 

 sons and two daughters. 18. Two faithful friends are one soul in 

 two bodies. 19. Some things please some (persons), some others. 

 20. This displeases some one, that another. 21. God is the governor 

 of the whole of life (in Latin, the whole life) . 



KEY TO EXERCISES IN LESSONS IN LATIN. XVI. 



EXERCISE 59. LATIN-ENGLISH. 



1. The king who governs the state ought to take care of the safety 

 of the citizens. 2. All the citizens willingly obey a king whose govern- 

 ment is mild and just. 3. The citizens respect a king to (with) whom 



the laws an sacred. 4. Happy is the king whom all the cJUzeas lov*. 



5. O king, who governest our state, thou art pleased (resolved) to 

 honour rood citizens, to terrify evil-doers, to succour the 



an I to hear the request of the rood. 



EXERCISE 60. ENGLISH-LATIN. 

 1. Beges qui civitates (ubemant omnium civinm 

 debent. 2. Boni homines libenter parent refibos 

 est mite et justum. 3. Begibus quibus 

 parent boni elves. 4. Beges qui civibos oari suit, soot fsUots. *. O 

 reges, qui civitates gubemant, colere vlrum borast mafBtnsqoe debetis. 



6. O Deus, colimus te cui placet mieeris suocurrere. 7. Hosts* fjsV 

 buscum confligitis patriam vestram devastant. 



EXSBCISE 61. LATIN-ENGLISH. 



1. Who calls me? 2. What art thou doing, my friend f 3. Who 

 writes this letter? 4. What art thou thinking of? 5. What am I 

 doing? 6. Why do I torture myself? 7. What friendship Is there 

 among the ungrateful ? 8. What poem art thoo reading ? 9. What 

 man is coming ? 10. What poet is sweeter than Homer ? 11. Whose 

 voice is sweeter than the voice of the nightingale ? 12. What stes do 

 we most easily yield to ? 13. Whatever is honourable Is useful. 14. 

 Whatever thou seest, runs (away) with (in the lapse of) time. 15. How. 

 ever the fact is, I defend my view. 16. Whatever opinion opposes 

 virtud is false. 



EXERCISE 62. ENGLISH-LATIN. 



1. Quid dicis? 2. Quis est ille homo ? 3. Qua est ifla feminaf 4. 

 Quibus cum ambulat amicus tuus ? 5. Quern qtueris ? 6. Quern librum 

 legis ? 7. Ad quern bos literas scribis ? 8. Qnocuuque modo res sees 

 habent, sententiam tuam laudamus. 



EXERCISE 63. LATIN-ENGLISH. 



1. If we fear death, some terror always hangs over us. 2. If fortune 

 takes away his money from any one (a person), be is not on that ac- 

 count miserable. 3. Greece holds a certain small space of (in) Europe. 

 4. There is (inheres) in our minds as it were an angary (presage) of 

 future ages. 5. God dwells in every good man. 6. Justice gives his 

 due to every one according to his dignity. 7. The love of life is plamted 

 in every one of us. 



EXERCISE 64. ENGLISH-LATIN. 



1. Malis aliqui terror semper impendet. 2. Quid terroris tibi im- 

 pendet? 3. Si cuipiain fortunam adimis, vituperaris. 4. Parvnm 

 quondam G rescue partem teuent. 5. In unoquoqne malorum hoinlsusi 

 habitat malum. 6. Unicuique merita ejus tribuit justitia, 7. Pecu- 

 uiaui habent quidam. 



EXERCISE 65. LATIN-ENGLISH. 



1. There are as many views as there are men. 2. That princes do 

 wrong is as great an evil as that there arise very many imitators of 

 princes. 3. As many kinds of orations as there are, so many kinds of 

 orators are found. 4. As are the generals, so are the soldiers. 5. As 

 is the king, so is the flock (people). 6. As princes are in the state, 

 so the citizens are wont to be. 7. A good man does not despise 

 wretched men, of whatever kind they are. 8. The goods of the body 

 and of fortune, how great soever, are uncertain and perishable. 9. 

 All the men that live love life. 10. All the writers there are speak of 

 the justice of Aristides. 



EXERCISE 66. ENGLISH-LATIN. 



1. Quot homines tot animi. 2. Quot pueri tot puellaj. 8. Qoot 

 patres tot matres. 4. Quantua est tuus moeror tantum est meom 

 gaudium. 5. Quales suut parentes tales sunt liberi. 6. Quails festor 

 tails grex. 7. Bes qualescunque sunt non contemno. 8. 

 scriptoribus, quotcunque sunt, Justus pnedicatur Aristides. 



LESSONS IN GEOMETKY. XVIL 



THE circle affords us a ready means of constructing regular 

 polygons of any number of sides; but before entering on this 

 part of our subject, it will be necessary to say something about 

 the inscription of the triangle and square in any given circle, 

 and the circumscription of the triangle and square about any 

 given circle, the triangle being equiangular and similar to 

 a given triangle, both in the case of inscription in a square 

 and circumscription about a square. 



First, however, let us arrive at a clear understanding of what 

 is meant when we speak of describing a figure, inscribing one 

 figure within another, and circumscribing one figure about 

 another. The latter part of each word is immediately derived 

 from the Latin word scribo, I writ* or draw; the distinctive 

 meaning of each of the three words given above depends^ on 

 the meaning of the Latin preposition with which each word is 

 commenced. In the first the prefix de C"a the * ro * d *|** 

 meaning of "writing down" or "copying off;" in the second 

 the prefix tn gives tho word the signification of drawing a 

 figure within the limits or boundary lines of another figure, bat 



