LESSON'S IN FKKNCii. 



117 



sum of its digits is equal to 26 j but if 198 be added to it, the 

 digits w tod. What is the number ? 



Let th- .U/iN be equal to x- y, x, and x + y, respectively. 

 Th.-n th- number = 100 (x - y) + 10* + (* +y) = 111* - 99y, 

 oto. This example will give '-he result = 234. 



EXERCISE 69. 



1. The sum of three numbers in arithmetical progression is 9, and 

 the sum of their cubes is 153. What are the numbers ? 



10 sum of three numbers in arithmetical progression is 15, and 

 the sum f the squares of the two extremes is 58. What are the 

 numbers ? 



'if sum of the squares of the extremes of four numbers in 

 arithmetical progression is 200, and the sum of the squares of the 

 means is 130. What are the numbers ? 



4. There are four numbers in arithmetical progression ; the sum of 

 the squares of the first two is 34, and the sum of the squares of the 

 last two 130. What are the numbers ? 



5. There are four numbers in arithmetical progression whose sum is 

 28, and their continued product is 585. What are the numbers ? 



KEY TO EXERCISES IN LESSONS IN ALGEBRA. XXXVI. 



EXERCISE 67. 

 1. The ratio of 44 : 35 | 4. 126. 



is the greater ; for 5. 42a* + 6a : 105by 

 i = 11'}, and 11 : 9 - 70b. 



6. x 1 - y': bh. 



7. 10* 1 + 3U + 28 : 2r* 



2. 2a -r 7 : J-i. 



3. 5. 



+ 9* - 18 is a 



ratio of greater 

 inequality. 



8. Ratio of equality, 

 or 1. 



9. 3024: 3240 or 14:15. 

 10. 21*': 21y* or **: j/' 



LESSONS IN FRENCH. LXXXIV. 



128. VBEBS REQUIRING THE PREPOSITION de BBFORB 

 AN INFINITIVE (continue i). 



Futrm (se), to ./latter one's self. 



I'retnir, to shudder. 



Gurder (se), to take tare. 



Gemir, to lament. 



Glorifier (se), to pride one's self. 



Hasardsr (se), ( venture. 



Hater (ee), to hasten. 



Impnter, te impute. 



Indigner ('), to be indignant. 



Ingerer ('), to take into one's head. 



luspirer, ( inspire. 



Jurer, to swear. 



Manquer, to /til. 



Mfditer, to think, to intend 



Meier (se), to meddle. 



Menaeer, to threaten. 



Veriter, to deserrd. 



Moqtier (se), to laugh at. 



Mourir (figu.), to long. 



'NfSgliger, to neglect. 



Uier, to deny. 



Pardonner, to excuse. 



Parler, to speak. 



Passer (se), to do irithout. 



Permettre, to permit. 



Persuader, to pcrsua lr. 



Piquer (se), to take pride in. 



Plnindre, to pity. 



Plain. Ire (se), to complain. 



Prendre garde, to tofc; care, heed, 



Prendre soin, to take care. 



Prescrire, to prescribe. 



Presser, to urge. 



n rant mieux hasarder de 

 aauvcr tin coupable qe de COn- 

 damnor uu innocent. VOLTAIRE. 



Le monde se vante de faire des 

 heuroux. MASSILLON. 



Presser (se), to hasten. 

 Pre'sumer, to presume. 

 Prier, to desire. 

 Promettre, to promise.' 

 Proposer, to propose. 

 Proposer (se), to intend. 

 Protester, to protest. 

 Puuir, to punish. 

 Rebuter (se), to be weary. 

 Recommander, to recommend. 

 Refuser, to refuse. 

 Regretter, to regret. 

 R^jouir (se), to rejoice. 

 Remercier, to thank. 

 Repentir (se), to repent. 

 Reprendre, to censure. 

 Reprocher (se), to reproach one's 

 K.-.soudre, to revolt'-. [wl/. 



RessouTenir (se), to remember. 

 Rire, to I*ujh. 

 Rougir, to blush. 

 Scandaliser (se), to take offence. 

 Seoir (imp.), to become, siut. 

 Sommer, to summon. 

 Soupyonner, to suspect. 

 Souvenir (se), to remember. 

 Sufflre (imp.), to suffice. 

 Sugg^rer, to suggest. 

 Supplier, to beseech. 

 Tdtnoigner, t shoic. 

 Tenter, to attempt. 

 Trembler, to tremble. 

 Vanter (se), to boost. 



It i* better to run the risk of 

 sparing a guilty person, than to con- 

 demn an innocent one. 



The world boasts thai it can render 

 men happy. 



129- RULE ON THE CONSTRUCTION OF VERBS REQUIRING 



DIFFERENT PREPOSITIONS. 



(1.) Two or more verbs may govern the same object, pro- 

 vMed they are all transitive, or require all the same preposi- 

 tion .- 



Nous almoas. nous instrui 

 sons, et nous iouons nos en- 

 tants. 



We love, we instruct, and we prai 

 our children. 



Je pen** et j'tfcrte souvent ft I I often think of, *nd writ* to my 



mes amis. | frundt. 



Those sentences are correct, because aimer, insfcrulre, and 

 louer, being all transitive verbs, admit of a direct object ; and 

 penser and ecrire require both the same preposition, viz., 4. 



(2.) But when the verbs require different kinds of objects, or 

 different prepositions, they cannot govern one and the sane 

 noun ; and therefore another form must be given to the sentence. 

 We could not say in French, Un grand nombre de vaisseauz 

 entrent et sortent de ce port tous les xnois, A great number of 

 vessel* enter and <jo out of thi$ port every month, or J'aime et 

 j'6cris a mes enfants, I lave and write to my children, because 

 entrer requires the preposition dans ; sortir, the preposition 

 de ; aimer, no preposition ; and ecrire, the preposition i. We 

 should say : 



Un grand nombre de vaisseaux 

 entrent dans ce port et en sortent 

 tous les raois. 



J'aime mes enfants, ct jo leur 

 e'cris. 



A large number of vessels eUr 

 this port and leave it every month. 



I \>ne my children and writ* to 

 them. 



See 89, (1.), (2.), also note, and 136. 



130. THE PARTICIPLE PAST. 



(1.) We have seen [ 67, (3.)] that the participle past, not 

 accompanied by an auxiliary, assumes the gender and number 

 of the noun which it qualifies : 



Les inanities sourdes et Quiet and e*nee+ltd enmity it 



cachees sout plus a craiudre que more to be /eared than open and 



les haines OUVertes et declarers, declared hatred. 

 NolL. 



(2.) The participle past, accompanied by the auxiliary etre, 

 agrees in gender and number with the subject of the verb, 

 whether the subject be placed before or after it, and whether 

 the verb is passive or intransitive. (See 131, (1.)] : 



Le fer est emoussg ; les buchers * The ie#rd ie Htsosed ; the jnUs art 

 sont e~teints. VOLTAIRH. j etrimgvished. 



La rertu obscure eat souvent j 

 meprisee. MASSILLON. 



Ma mere est sortie 



Mes tantes sont arriV^OS. 



Leurs fils sont devenus grand's. 



Hnrofcle rirtne ie tftev. despised. 



Ify m*ther ie JIM tut. 

 My tn( h*w rrived. 

 Their sns hove beeome tmU. 

 Hit jrnd/e>thr eUed yesterday. 

 When he perceived the n in 



Son grand-pore est mort bier, i 



Quant il vit 1'urue oil ataient | 

 renfermees lea cendres d'Hippias, ' which were enclosed the ashtt of 

 il versa un torrent de larmes. ', Hippie*, he shed a torrent of tears. 



FBNELON. i 



(3.) The participle paat, having avoir as its auxiliary, never 

 agrees with the subject : 



Vous rioz P Ecrirez qu'elle ft 

 ri. RACINX. 



Mes amis ont parle ; leurs 

 cceurs sont attendris. VOLTAIRB. 



Mes cousiues ont lu. 



BESCHEBELLK. 



(4.) The participle past, having avoir for an auxiliary, 

 agrees with its direct object, when the latter precedes the 

 auxiliary : 



You laugh r Put dtnen that sht 

 laughed. 



My friends tare sfokm ; their 

 hearts are moved. 



Ify cousins have read. 



La lettre quo vous avez 6crite. 



Pedro, qu'as-tu fait de nos 

 monturcs ? Seigneur, je les ai 

 attaches a la grille. LB SACK. 



Les meilleures harangues sout 

 celles que le coeur a dictees. 



MARUONTXL. 



Je les ai cherches dans tons 

 les coins, et je no les ai pas 

 trouv6s. MME. DK GKXLIS. 



The letter which von have written. 



Pedro, what haet thoii elone with 

 our horse* 7 Vy tord, I hare 

 fastened them to the grf.lt. 



The beet addressee are tteei which 

 the heart has dictated, 



7 have sought them M every e*nur, 

 but have not found them. 



(5.) But, if the direct object is placed after the participle, 

 this participle remains invariable : 

 J'ai recu votre lettre. 



C'est la Yt?rito elle-mdme qni Iui 



a dicte" cos belles paroles. 



Bossurr. 



Les dieux ont attach6 preeque 

 autant de malheurs a la liberto, 



qu'a la servitude. 



I hare received your letter. 

 It is truth itself which has dic- 

 tated to him thoee JM words. 



The gods have att 



s 



many misfortunes to liberty as to 

 servitude. 



