LESSONS IN GEOMETRY. 



211 



The verb ease in made up of part* of two separate verbs ; first, 



is the root; and secondly, of a verb, the ttem 



of whi'-h i.s/u (compare fio in Latin, and <fuw, fu'-o, in Greek). 



i .n originally for man) came the present, the imper- 



future tenses ; from fuo oamo the perfect, the 



lilupi-rl'i (, and second future tenses. 



'!'!. rarb sum has neither gerund nor supine, and is in other 

 respects defective, as appears from the paradigm just given. 



takes before it certain prepositions, and is modified by 



them in its meaning ; thus, with ad, adsum, it means I am at 



; with ab, absum, it means I am from, away from, absent ; 



<>, prosum,' it means / ant for, that is, / aid or benefit. 



In prosum, the letter d is inserted to prevent the hiatus which 



would be caused if two vowels came in succession ; thus, 



pro-(d)-es, pronounced prodes ; also prodest, proderam, protZero, 



-iom. 



From the root mentioned above namely, fu, fuo come two 

 forms not so common as those given in the table namely, 

 forem and fore; forem (-es, -et ; -emus, -etia, -ent) is the imperfect 

 subjunctive, and signifies I might be; corresponding to essem 

 of th<> table ; fore is the infinitive future, to be about to be ; corre- 

 sponding with the futurum esse of the table. 



VOCABULARY. 



Observe that these compounds of sum require their object to 

 be in the dative case ; as, prodest MIHI, he does good TO ME, or 

 he benefits ME. 



EXERCISE 73. LATIN-ENGLISH. 



1. Deus omnibus locia adest. 2. Parvi pretii (of little avail), sunt 

 anna foris, nisi est cousilium domi. 3. Contemnuntur ii qui nee sibi 

 nee alteri prosunt. 4. Ut magistratibus leges, ita populo preesunt 

 magistrates. 5. Batio et oratio conciliat inter se homines, neque nlla 

 re longi us absamus a natura ferarnm. 6. Ego sum leetus, tu es tristis. 

 7. Si sorte vestra contenti estis, beati estis. 8. Dum nos in schola 

 erainus, sorores nostns in horto crant. 9. Quum CarSlus her! domi 

 nostra erat, ego pfiregre eram. 10. Quamdiu tu et frater tuus domi 

 nostrtB eratis, tu Icetus eras, sed frater tuus erat tristis. 11 . Quamdiu 

 tu abCras, ego eram tristis. 12. Cur heri in schola non fuisti ? 13. Quia 

 cum patre pPregre f ui. 14. Quamdiu tu et pater tuus domo abf uistis ? 

 15. Sex menses abfuimus. 16. Cur milites nostri pugnae non iiiter- 

 faerunt ? 17. Quia longins abfufirunt 18. Ubi heri fueras quum 

 domi tuse eram ? 



EXERCISE 74. ENGLISH-LATIN. 



1. I am useful to thee. 2. Thou art useful to me. 3. The boys are 

 not useful to (their) mothers. 4 Why are the girls not useful to 

 (their) fathers? 5. When thouwast absent, I was sad. 6. How long 

 has your father been absent ? 7. Charles took part in the fight. 8. 

 Wast tbou yesterday at my house ? 9. I shall be at thy house to-day. 

 10. Unless thou art happy at home, thou art not joyful abroad. 



VOCABULARY. 



Pretium, -i, n., a re- 



. ward (E. B. price, 

 precious). 



Propterfa, on account of 



Provideo, 2, 1 see be/ore- 

 hand, foretee (E. B. 

 provide). 



Prudens, -tut, prudent. 



Quod, because. 



Bectus, -a, -um, right. 



BepPto, 3, 1 seek again, 

 I repeat. 



Sed, but. 



Solum, alone. 



Studeo, 2, I endeavour. 



Voluntas, -itis, f., will 

 (E. B. loluntari/.) 



EXBBCIRI 75. LATIN-EMOLUH. 



1. Quamdiu fulix eritt, multi tibi erunt amlci. 2. Pofna fnit atroofcv 

 Hima, propterea quod utriusqua exurcitus imhu* fortiasimi fulrunt. 

 3. Ante belli initium in urbe fuertmus. 4. Demoathanis aHate mnltt 

 oratorea magni et clari f uerunt, et ante* fomrant, nao poataa df urunt. 

 5. HBO res non profuit nobis sod obfuit. 6. 81 quis rirtotu compos 

 erit, semper beatus erit. 7. Quamdiu sorte mea contentus ero, ero 

 felix. 8. Actio recta non erit, nisi recta fuerit voluntas. 9. 81 probi 

 fuerlmus, non deerit hoininum laus. 10. Attenti eate, discipuli. 11. 

 Homines mortis memores sunto. 12. Contenti eatota sorte vestri ! 

 13. Mi fili, semper virtutis prceptorummemoreto! 14. Virprudeaa 

 non solum prasentia curat, sod etiam pneterita mente repetit, et futora 

 ex preeteritis provrdet. 15. Boni bouis prodesae student. 



EXERCISE 76. ENGLISH-LATIN. 



1. Our soldiers were very brave in tb.3 fight. 2. Why were out 

 soldiers braver thau yours in the fight ? 3. So long as you are happy, 

 friends will not fail you. 4. Friends fail the wretched. 5. Before the 

 beginning of the fight, I was in the city. 6. The brave will always be 

 useful to the brave. 7. My enemies injure me. 8. If you are partaken 

 of virtue, you will be happy. 9. So long as I am content with my lot, 

 I shall be bappy. 10. O scholars, you ought to be attentive in school ! 

 11. They endeavour to be very brave. 12. Be brave, my son. 13. 

 Prudent men foresee the future (pi.) from the past. 



VOCABULARY. 



Prius, adv., be/ore. 

 Quails, -e, of what kind 



(E. B. quality). 

 Qua mente sis, of 



what disposition you 



are, what your feel ing 



is. 



Quantum, how much. 

 Quantus, -a, -um, 

 how great (E.U.quan- 



Wy). 



Scio, 4, I know (E. B. 



science) . 

 Turn, them. 



Et et, and and (and 

 also), both. 



In, towards. 



Nescio, I know not. 



Nescius, -a, -um, ig- 

 norant. 



Non sum nescius, I am 

 aware of. 



Observe that in indirect questions the dependent verb must 

 be in the subjunctive (or dependent) mood; as, for example, 

 narra mihi ubi fueris, tell me where you have been. Such a form 

 is called an indirect question. The direct question would stand 

 thus ubi fuisti ? narra mihi, where hast thou been ? tell me. In 

 the latter case the question is direct, and the verb, as not being 

 dependent, is in the indicative mood ; but put narra mihi first, 

 and then your question is implied rather than stated; it is, 

 therefore, an indirect question. In both direct and indirect ques- 

 tions the English is in the indicative; consequently, in putting 

 the dependent verb into English, yon must in English nse the 

 indicative mood ; but in putting the dependent verb into Latin, 

 you must in Latin use the subjunctive mood. Compare what 

 is said of the sequence of tenses, and similar and dissimilar 

 tenses, in the last lesson. 



EXERCISE 77. LATIN-ENGLISH. 



1. Non sum nescius qua mente tu in nos sis. 2. Scio qua mente tn 

 in uos semper fueris. 3. Nou sum uescius qua mente tu et prius in 

 nos fueris et nunc sis. 4. Non eram nescius qua mente tu in nos oases. 

 5. Scio quain slut mcerti animi houinum. 6. Cogita quam brevis sit 

 vita ! 7. Qualis sit animus, ipse animus nescit. 8. Cogita quantum 

 nobis bona exempla prosint. 9. Incertus sum ubi frater meus nunc 

 sit. 10. Incertus sum ubi amicus meus et fuerit et nunc sit. 11. In- 

 certua eram ubi heri esses. 12. Narra nobis ubi heri fueritifl. 



EXERCISE 78. ENGLISH-LATIN. 



1. Tell me where thou art. 2. Tell me where thy father and mother 

 are. 3. I know not where my sister is. 4. Dost thou know how much 

 good boys do good (prosum) to their parents ? 5. I know where my 

 son is. 6. My sou, where art thou ? 7. I knew where my son was. 

 8. I am uncertain where the enemies are. 9. Is the general ignorant 

 where the army is ? 10. I know of what mind thou art toward the 

 king. 



LESSONS IN GEOMETRY. XX. 



THERE is a curious connection between the proportions of the 

 sides of a hexagon and a heptagon inscribed in the same circle, 

 and that is, that the length of the side of the heptagon is equal 

 to the perpendicular let fall from the centre of the circle on any 

 side of the hexagon. This may be seen from the following 

 problem : 



PROBLEM LII. To inscribe a heptagon in a given eirde. 



Let ACE (Fig. 74) be the given circle in which it is required to 

 describe a heptagon. Draw any diameter A K, passing through 

 L, the centre of the given circle ACE; and from one of ita 

 extremities A as centre, with the distance A L, describe the arc 

 B L K, cutting the circumference of the circle A c K ir the 

 points B and M. Join B M, putting A K at right angles in the 



