LESSONS IN GEOMETRY. 



191 



TWO VOICES. 



1. Active. 2. Pauive. 



D#pon#nt belonging to the passive in form and to the active in meaning. 



SIX TENSES. 



1. Prtttnt; 2. Ptfftct; 3. Imperfect; 4. Pluperfect; 5. Firtt Futur; 

 6. Soond 1'uture, or Future Perfect. 



THREE MOODS. 

 1. The Indicative. 2. Tbe SubjutictiiM. 3. The Imperative. 



FOUR OTHER FORMS. 

 1. The Infinitive. 2. The Participle. 3. The Gerund. 4. The Supine. 



In all, fifteen varieties of expression enter into the Latin verb. 

 Ton are not to suppose from this that every verb has all these 

 forms. Even when the Latin was a living language, many 

 verbs were defective, that is, lacked some of the ordinary 

 forms. We, however, are bound to write the language as we 

 find it written in the remains of Roman literature, and so are 

 restricted to forma which actually occur in extant Latin writings ; 

 and as poetry has its licences, so are we obliged, in order to be 

 correct, to confine ourselves to the usages of the best prose 

 writers. In general, the Latin of Cicero is the model to be 

 followed. 



Verbs which have been above described as active, may also 

 be called transitive ; that is, active in voice, and transitive in 

 import ; thus, laudo puerum, I praise the boy, is a transitive 

 verb, because the action of the verb passes over (trans, across, 

 over, and eo, I go) to the object, puerum. As some verbs are 

 transitive, others are intransitive or not transitive. Such is 

 dormio, I sleep, in which no action passes over to an object. 

 Intransitives are sometimes called neuters; that is, neither 

 active nor passive. When they have a passive form, they bear 

 the name of neuter passives ; as, ausus sum, I have ventured ; 

 gavisns sum, I have rejoiced. Sometimes a verb, in the passive 

 form, has a reflective force, and may be Englished by a neuter 

 or intransitive verb ; as, moveor, / move myself, or simply, / 

 move. A few active forms have a passive signification; as, 

 vapulo, I am beaten ; veneo, I am sold. Somewhat similar is 

 fio (factus sum, fieri), I become, I pass from one state into another; 

 I am made. 



The tenses may be divided into three classes ; thus : 



I. PRESEKT TIME 



II. PAST TIKE. 



III. FUTURE TIME 



the action incomplete Present, 



the action complete Perfect. 



the action incomplete Imperfect. 



the action complete Pluperfect. 



the action incomplete First Future, 



the action complete Second Future. 



INCOMPLETE 



COMPLETE 



You thus see that there are three forms of complete action, and 

 three of incomplete : 



ing PRESENT. 



row writing IMPERFECT. 

 1 shall be writing FUTURE. 

 PERFECT. 

 PLUPERFECT. 



shall have written SECOND (or 



PERFECT) FUTURE. 



The natural sequence of our ideas requires a corresponding se- 

 quence of tenses. We do not in thought suddenly pass from 

 the present to the past in the same sentence, or in the same 

 member of a sentence. Consequently, we must avoid doing so 

 ui the employment of the tenses. The tenses may be divided 

 into pairs namely, similar and dissimilar ; for example : 



(I Bcripsi, I lutve written 

 J. 2 ecripseram, I had written 

 (3 scripsero, I shall have icrit 



SIMILAR TENSES. 



Present Present. 

 Present Perfect present. 

 Imperfect Imperfect. 

 Imperfect Pluperfect. 



DISSIMILAR TENSES. 



Present Imperfect. 



Perfect present Imperfect 

 Pluperfect Perfect present. 



Now similar tenses should folloiv each other, and not dissimilar 

 ones. That is, if yon use one present, use another ; if you use 

 a present, do not let an imperfect immediately follow. 



Observe, however, that the present infinitive may come after 

 a finite verb in the imperfect tense, as solebat scribere, he was ' 

 wont to write. The rule I have now given relates to what is ! 

 called the consecutio tempornm, or "sequence of tenses. Compare 

 Exercise 75 (Latin-English), in the next lesson. 



KEY TO EXERCISES IN LESSONS IN LATIN.-XTILL 

 ExEttCisE 69. LATIN-ENGLISH. 



1. There is no firm friendship among the ted. 2. I h**ten to death. 

 3. The Gauls dwell beyoud the Uhine. 4. We have no weapon* again** 

 death. 5. A generous man is mild toward th oooqnarad. 6. Comet* 

 an admirable on account of their rarity and beauty. 7. Slave* obey 

 on account of fear, the good from a regard to duty. 8. Sailing along 

 the shore U often dangeroui. 0. No one is happy before dear 

 On what account dost thou laugh ? 11. Below the moon all thing* 

 are perishable. 12. Thou dwellest many year* among barbarian*, U. 

 The kingdom of Pluto i* placed under the earth. 14. The government 

 of nation* is in the power of king*. 15. Fi*h die out of water. 10. 

 The thing happened contrary to expectation. 17. Tbe camel bean 

 hatred to hone*. 18. Painted garment* are mentioned with (in) 

 Homer. 19. Many animal* congregate and fight against other animal*, 

 20. Tbe hippopotamus feed* on the corn-field* around the Nile. 



EXERCISE 70. ENGLISH-LATIN. 



1. Inter maloa nulla eat firma societas. 2. Contra mortem nulla 

 habet homo arma. 3. Ultra mortem est vita. 4. Ad Bhenntn pro- 

 peramus. 5. Ante domum sunt auiici. 6. Apud me aunt filii mei. 

 7. Apud to suntne filii vestri ? 8. Mitis erga victos est rex. 9. Poet 

 mortem boni sunt felices. 10. Quid est infra ten-am ? 11. Deu* eat 

 super omuia et per omnia. 12. Infra nubes habitant homines. 13. 

 Penes me mei sunt liberi. 14. Apud Ciceronem sunt multa pulcbra 

 dicta. 15. Bus propter te amo. 16. Intra muros sunt milites. 



EXERCISE 71. LATIN-ENGLISH. 



1. Poison is for (acts as) a remedy sometimes. 2. An infant ha* no 

 power without another's aid. 3. Eagles do not build in tree*. 4. 

 The cuckoo lays in the nests of other birds. 5. By old age our sense* 

 grow dull. 6. Some men are born with teeth. 7. Xerxes fled from 

 Greece with very few soldiers. 8. Metellus leads elephants in triumph. 

 9. The traveller sings in presence of the robber. 10. The stars move 

 from the east (rising of the sun) to the west (setting of the son). 11. 

 Britain was discovered by the Phoenicians. 12. Bees cannot exist 

 without a queen. 13. It is sweet to die for one's country. 

 EXERCISE 72. ENGLISH-LATIN. 



1. Estne aliquando veuenum pro remedio? 2. In Grsecia pugnat 

 Xerxes. 3. In senectute visus et auditus hebescunt. 4. Pa'ritne in 

 alieno nido coccyx ? 5. Soror tua coram multis cantat. 6. Ab ortu 

 solis ad occasum properant. 7. Grsecia proficiscens exercitus in Italia in 

 properat. 8. Metellus cum multis militibus est in Britannia. 9. 

 Filius meus sine dentibus est natus. 10. Estne exercitus sine ele- 

 phantis ? 11. Elephanti in triumpho a duce ducuntur. 12. Dulcene 

 est pro patria inori ? 13. Quid sine Dei ope sunt mortales ? 14. 

 Omnesne aves in arboribus iiidificant ? 15. Clam patre est puer in 

 domo. 16. Infantes in gremio matris felices est dulce videre. 17. 

 Tecumne est soror tua ? 18. Sine patre nihil potest puer. 19. Mecum 

 est filia mea. 20. Quot liberi tecum sunt ? 21. Quot homines sunt 

 in Britannia ? 



LESSONS IN GEOMETRY. XIX. 



THE following method of constructing a regular pentagon 

 involves the use of the circumscribing circle, on the circumference 

 of which the angular points of the pentagon may be marked. 

 We have added this to the modes of construction given in the 

 last lesson to show the student that there are many ways of 

 constructing each of the regular polygons, and to urge him to 

 exercise his ingenuity in finding out other methods for the con- 

 struction of the hexagon, heptagon, etc., than those we are 

 about to give him in this and the following lessons. 



PROBLEM L. To construct a pentagon on a given straight 

 line (another way). 

 Let A B (Fig. 68) 

 be the given straight 

 line on which the re- 

 quired regular pen- 

 tagon is to be de- 

 scribed. At the point 

 A, in the straight 

 line A B, draw A c, 

 of indefinite length, 

 perpendicular to A B, 

 and produce A B inde- 

 finitely both ways to- 

 wards x and Y. Bisect 



Fig. 68. 



A B in D, and along A c set off A E, equal to A D. Join B E, and 

 produce it indefinitely to F, and set off E G along X r, equal to E A 

 or A D. Then from A as centre with the distance A G, describe the 

 semicircle x o H, and from B as centre, with a distance equal to 

 A G, describe the semicircle K L T, and let the semicircles x o H, 



