-SONS IN FRENCH. 



1M9 



actual performing of tho operation. But the purpoaea of division 

 may 1: answered by these fractional expression*; 



for aa tlu-y uro of tho, aame nature with other vulgar fractious, 



.i.tractod, multiplied, or divided. 

 ilxAMPLEB. (1.) Divide xy by a. 



. / 



Here, <ry -r a = . 

 a 



(2.) Divide (d x) by h. 



, d IT x d 



) -. ft = r = r 



tit n 



And hero it may bo observed that if tho signs of all tho 

 terms of a fraction bo changed both in the numerator and de- 



be + be 



nominator, its valuo will not bo altered ; for 



be 



be 



6 



103. If some of tho letters in tho divisor are in each term of 

 the dividend, tho fractional expression may be rendered more 

 simple, by rejecting equal factors from the numerator and 

 denominator. 



EXAMPLE. Divide ab by ac. 



Aiis. 

 c 



These reductions are made upon the principle that a given 

 divisor is contained in a given dividend, just as many times as 

 double the divisor is contained in double the dividend ; triple the 

 divisor in triple tho dividend, and so on. 



104. If the divisor is in some of the terms of the dividend, 

 but not in all, those which contain the divisor may bo divided 

 as in Art. 93, and the others set down in tho form of a 

 fraction. 



EXAMPLE. Divide ab + d by a. 



105. The quotient of any quantity divided by itself or its 



equal, is evidently unity or 1. Thus -= 1, -= 1, -p- = 1, etc. 



a x abc 



106. If the dividend is greater than the divisor, the quotient 

 must be greater than a unit : but if the dividend is less than the 

 divisor, the quotient must be less than a unit. 



EXERCISE 7. 

 Perform tho following exercises in division. 



LESSONS IN FRENCH. XLV. 



SECTION XCIX. [ 130, 131.]- PRACTICAL SUMMARY OF THE 

 RULES OP THB PAST PAKTICIM., 



THE participle paat ia VABIABLK under any of the following 

 conditions : 



1. When employed an an adjective; in which COM it agrees 

 in gender and number with the noon which it qualifies, alter 

 which it is always placed* : 



Dei livrea imprimeu. Printed book*. 



Cos femmes pai&iaaent blen Thou women appear very dejeeUd. 

 abattuei. 



2. When used in the formation of the teases of passive verbs ; 

 when it always agrees with the subject : 



Kilos Bont bien revues de tout lo 

 moude. 



Thty art well revived by ntrybody. 



3. When employed in forming the compound tenses of neater 

 verbs having dtre as an auxiliary ; in which instance, as in the 

 preceding case, it agrees with the subject : 



Votre sceur est partie ce matin. Four titter vent away thit morning. 



4. When employed in forming the tenses of active verbs 

 having avoir as an auxiliary ; in which connection it agrees not 

 with the subject, but with the direct object, provided that object 

 precedes the auxiliary : 



Los maisons qua nous avons The house* which ire Jiare bought. 

 achetees. 



5. When used along with etre in the formation of the com- 

 pound tenses of pronominal reflective verbs, wherein the reflec- 

 tive pronoun is the direct object ; in which position it agrees 

 with that pronoun or direct object : 



Ces dames se sont flatties. 



Those lodiea have flattered themtelvm. 



6. When used along with 6tre (aa in Eule 5) in tho forma- 

 tion of the compound tenses of reciprocal and reflective verbs, 

 in which the reflective pronoun is not the direct, but the in- 

 direct object ; in which event it agrees with the direct object, 

 provided (as in Bnle 4) that object precedes the auxiliary : 



Les histoires qu'ils se sont racon- The stone* which thy related to each 

 txSes. other. 



