294 



THE POPULAR EDUCATOR. 



4. Find the number of solutions, and the values of x, y, z and n, in 

 the equations 



tx + y + z + 2n = 100. 

 h(to + 5g + 2z + n = 100. 



5. Bought 100 animals for 100 : there were cows at 5, sheep at 1, 

 and rahbits at Is. How many solutions will this question admit of? 

 and what was the price of each ? 



6. A person had a bag of nuts containing (he said) less than 500, and 

 if he counted them by twos, threes, fours, fives or sixes, there was 

 .dways an odd one ; but when he counted them by sevens, there was 

 aone left. How many nuts did he have ? 



7. I retired to rest one evening at m minutes to n o'clock ; and on 

 rising 6 hours 55 minutes after, it wanted n minutes to m o'clock. Find 

 the times of retiring to rest and getting up. 



8. Find a sum consisting of P shillings and S pounds, the double of 

 i*-hich is P pounds and S shillings ? 



9. What is the value of x, when x and 18 shillings are twice the value 

 of 18 and x shillings ? 



10. Divide 1591 into two parts, respectively divisible the one by 23 

 and the other by 34, and state the number of solutions. 



11. Divide ff into two other fractions, whose denominators shall be 7 

 and 11. 



12. Find two whole numbers whose sum and product together = 139, 

 and how many solutions. 



13. Divide 30 into 3 such parts that the 1st x 7, 2nd x 19, and 3rd x 38, 

 the sum of products = 745. What are the parts ? 



14. Into what two parts must 4890 be divided that the 1st -H 37 may 

 leave the remainder 3, and the 2nd 4- 54 may leave the remainder 6 ? 



15. I have a quantity of malt, weighing 39 Ibs. per bushel, and if I had 

 5 Ibs. more it would measure an exact number of bushels ; or if I had 

 5 Ibs. less it would weigh an exact number of cwts. What is the smallest 

 quantity I can have to satisfy these conditions ? 



16. If I take out the nuts from a bag in successive quantities thus, 

 1 the first draw, 2 the second, 4 the third, 8 the fourth, etc., I find that 

 on taking out the last term of this progression no nuts will remain ; I 

 also find that if I had drawn them out in lo'os of 17 each, there would 

 have been none left after a certain number of draws. Kequired the 

 uumber of nuts. 



KEY TO EXERCISES IN LESSONS IN ALGEBEA. XL. 



1. n = 4, a = 4,s = 256; 

 fr^m which r = 4, 

 i.aa the series = 

 4, AG, 64, 256. 



1. 2, 4 and 8. 



2. 2, 10 and 50. 



EXERCISE 71. 



2. r = 3, and the series 



=1, -J-, 1, 3, 9. 



3. s = ijj, z = T ij. 



4. 1093. 



EXERCISE 72. 



3. 5, 10, 20 and 40. 



4. 120, 60 and 30. 6. 1, 3, 9 and 27. 



5- 2 = Tffsts. s = 2 l^a If- 



6. z = 8192, s = 16382. 



7. z= 531411, s=797160. 

 8.965114681693 13s.4d. 



5. 5, 10 and 20. 



LESSONS IN GERMAN. LXXIII. - 



121. THE NOUN. 



Rule. A noun or pronoun which, is the subject of a sentence 

 must be in the nominative case ; as, >er SDicnfcb benft, ctt lenft, 

 man devises, God disposes. 



OBSERVATIONS. The subject or nominative in German is 

 seldom omitted, except in the case of the pronouns agreeing 

 with verbs in the second person (singular and plaral) of the 

 imperative ; as, SieS (bu), read! e^t unb fagt (3fyr) tfym, go and 

 tell him. See, however, 136 (2). 



122. EULE. 



A noun or pronoun which is the predicate of the sentence 

 must be in the nominative case ; as, er tuar etn grcper .Rcnig, lie 

 was a great king ; btefcr .ftnabe tft Jtaufmann getwrbcn, this boy 

 ! as become a merchant. 



123. EULE. 



A noun used to limit the application of another noun signify- 

 ing a different thing, is put in the genitive ; as, ber 8auf ber 

 ?>onne, the course of the sun ; bte Crrjteljung ber .Ktnber, the educa- 

 tion of the children. 



OBSERVATIONS. (1.) If, however, the limiting noun (unless 

 restricted itself by an adjective or some other qualifying word) 

 signify measure, number, weight, or quantity, it is then put in 

 the same case with that which it limits ; as, fecfyg $funb Slice 

 (not 3,fjee8), six pounds (of) tea ; but (with a restrictive term), 

 f$ qjfunb btefeS $b,eeg. 



(2.) It should be observed that the two nouns under this 



rule must be of different significations ; for two nouns standing 

 for the same thing would be in the same case, forming an in- 

 stance of apposition. 



(3.) The noun in the genitive, that is, the limiting noun, is 1 

 commonly said to be governed by the other one. 



(4.) It seems hardly necessary to observe that under this rule 

 come all words which perform the office of nouns ; as, pronouns, 

 adjectives used substantively, etc. ; thus, bte @nabe ber rojjen, 

 the favour of the great. 



(5.) We say often in English, he is a friend to, or an enemy 

 to, or a nephew to any one ; where, were these phrases put into 

 German, we might expect the dative to be used. But in such 

 cases the German always employs the genitive ; thus, er tft eitt 

 Setnb fetneg SSaterlanbcS, he is an enemy of his native country. 



(6.) We say in English, the month of August, the city of 

 London, and the like, where the common and the proper name 

 of the same thing are connected by the preposition of. The 

 Germans put the two nouns in apposition. (See 133. 06s.) 



(7.) So, too, in English, we say, the fifth of August ; but in 

 German the numeral is put in direct agreement with the name 

 of the month ; as, ber fitnftc 2lugufi, the fifth (of) August, or 

 August the fifth. 



(8.) In place of the genitive, the preposition son, followed by 

 the dative, is, in the following instances, generally used : 



(a) When succeeded by nouns signifying quality, rank, mea- 

 sure, weight, age, distance, and the like ; as, etn Warm con tyoljem 

 Stanbe, a man of high standing ; cin Sob iff von jtcet Ijmntevt Sonneu, 

 a ship of two hundred tons ; cin 2)fcmn on acbtjtg Safyren, a man 

 of eighty years ; eine 9lctfe son bret 3Jiei(cn, a journey of three 

 miles, etc. 



(o) When followed by nouns denoting the material or sub- 

 stance of which anything is made ; as, cin Secret Bon tlber, a 

 cup of silver, i.e., a silver cup ; eine lltjr son 0fb, a gold watch, 

 etc. 



(c) When followed by nouns whose cases are not indicated 

 by the terminations of declension nor by the presence of the 

 article ; as, ein >ater ton fccb. 3 JJtnbern, a father of six children ; 

 tie Jtonigin con Sngfanb, the queen of England ; tie rcn$en son 

 3canfrcicf>, the boundaries of France. 



(d) When followed by a word indicating the whole, of which 

 the word preceding expresses but a, part ; as, cincr vcm-mctnen 23e* 

 fanntcn, one of my acquaintances ; roelcb. er on betten ? which of 

 the two ? 



124. EULE. 



A noun limiting the application of an adjective, where in 

 English the relation would be expressed by such words as of or 

 from, is put in the genitive ; as, bte mctflen SScrlujle finb etncg @r= 

 fa$c fabtg, most losses are capable of reparation ; bte (Jrbe tft oU 

 ber ute bcS -crrn, the earth is full of the goodness of the Lord. 



OBSERVATIONS. (1.) The adjectives comprehended under 

 this rule are, among others, the following : 



Sebitrftig, in want, needing. 

 23ewufjt, conscious. 

 giSfytg, capable, susceptible. 

 8rof;, glad. 

 @en)at;r, aware. 



eaiarttg, waiting, in expecta- 

 tion, 

 eimfi, sure, certain. 



c!BoI;nt, used to, in the habit. 

 Jtunbig, having a knowledge, 



skilled. 



Sebtg, empty, void. 

 2)Jufce, tired, weary. 

 Scfyulfctg, guilty, indebted. 

 Sfjeilfjcift, partaking. 

 SBcrti), worth, worthy. 



(2.) After gcroaljv, gctootynt, leS, mube, fatt, ofl, and ftertlj, the 

 accusative is often used ; as, er n>arb fetnen Sritber geroatyr, he was 

 aware of (the presence of) his brother, i.e., he observed his 

 brother. 



125. EULE. 



A noun limiting the application of any of the verbs following, 

 is put in the genitive : 



: Barren, to wait. 



Sadden, to laugh. 



j Spflegcn, to foster. 



j @ct)onen, to spare. 



gotten, to mock. 



2ldbtcn, to mind, or regard 

 33ebuxfen, to want. 

 SBcgefyren, to desire. 

 23rauc$en, to use. 

 ntbe^ren, to need. 



rmangetn, to want, or be with- j iCerfe^len, to miss, or fail. 



out. 



, to mention. 

 eben!cn, to think, or ponder, 

 entcpen, to enjoy, 

 eomfcren, to observe. 



SScrcieffen, to forget. 



SSM'ren, to guard. 



SE'.'.fyritefymen, to observe. 



SOSaften, to manage. 



SCBarten, to attend to. or mind. 



