246 



THE POPULAB EDUCATOR. 



11. I could when I was young. 12. He bade [bat] me go thither, 

 that he might speak to me about it. 



SECTION XXVIII. SEPARABLE PARTICLES (continued). 



2Bo, ta, Ijin, etc., besides being compounded one with another 

 (Sect.' XXVII.) are also united with prepositions ; thus pro- 

 ducing a separate class of adverbs, as : 2Bocn fpredjen k ? Of 

 what (whereof are you speaking ? 3cf; frred;e con meinen ud>ern ; 

 njollen ie tins taon fyaben ? I am speaking of my books; will you 

 have one of them ? (one thereof ?) 3d; bin auf bent 3)aci>e ; fom 

 men ie tyerauf ! I am on the roof ; come up ! 3d; fann nid;t 

 I)inauf geb,en ; fommen ie tyerab '. I cannot go up ; you come 

 down ! 



inab, Ijtnauf, f;mau, Ijerab, etc., when used with nouns, are 

 translated by prepositions ; and the adverb, unlike its English 

 equivalent, is placed after the noun, as: 3d; geb,e ten JBerg 

 Ijinauf, I go up the mountain, tfommen ie ten Serg Ijerab, 

 come down the mountain. 



1. The verb fommen frequently answers to our " get," as: 

 2Bie tfl er in tiefen arten gefomnten? How did he "get" into this 

 garden? r tocijj nicfyt, nrie er tyerauS fommen felt, he does not 

 know how to "get " out. 3d; font me mit tiefem Oftanne fetyr gut 

 fort, I "get" along with this man very well. 



VOCABULARY. 



RESUME OP EXAMPLES. 



@ie fe^en $ind>' in baS toUbe 2Jleer. 

 JDa giejjt unenb'lidjcr SKegen Ijerab'. 

 >ie tfnaben etlten ben SSerg fjtnaitf'. 



Der 33ergmann fletgt fjeraitf an8 



ber Siefe be cf;aci)te8. 

 3petru ging ^tnauJ' unb toeinte Bit'* 



terticl). 

 llnb fytnctn' mtt bebddj'ttgem cfjrttt 



etn 5n>e trttt. 

 Sc icirft ftc^ in kte brau'fenbe Slutf . 



!Cer 9{tc$ter rief ten SSauet ^erein'. 

 SaS Sekn te 3Menfcf;eP. fcljwanft, 



ttne etn iJladfjen, ^tnfl'bec unb 



Ijeru'fcer. 

 Jtet iJac^'beier fiet om ftaufe 



^erun'ter. 



They look down into the wild 

 sea. 



There pours down interminable 

 rain. 



The boys hastened up the 

 mountain. 



The miner comes up out of the 

 depth of the shaft. 



Peter went out and wept bit- 

 terly. 



And thither (therein) with con- 

 siderate step a lion strides. 



He throws himself into the 

 roaring flood. 



The judge called the peasant in. 



The life of man, like a skiff, 

 fluctuates hither and thither. 



The tiler fell down from 

 house. 



the 



EXERCISE 48. 



1. abcn ie meinen Sreunb gefefyen ? 2. 3a, er tfl tie traf e I;tnab 

 gegangen. 3. 2BoUen ie in tie Sajute Ijtneingefyen ? 4. Sftein, id; gefye 

 in taS 3n)ifcf)entecf tyinunter. 5. gafyren ie tyeute mit ( 112. 7) tent 

 JDampfboote nad; dftahtj Ijinuber ? 6. 3a, unt tiefen Slbenb hjerte id; mit 

 fctr Gnfenbafc,n tiber bie neue cbiffSbriicfe tnteter tyeruber fommen. 7. -Sin* 



6, I)tnauf geljt unfer Sauf. 8. 2Da Clef; fprang ben S3crg tytnab, rofifjrenb 

 c a|~e ten ugel fymauflief. 9. 2>te olbaten fiutten au bee Saferne 

 ]jevau, at ter geinb in tie @tatt ^ineinflitrmte. 10. &(8 tie S'iactjtrDac^e 

 in tag auS trat, eilte ter erfcfyrorfene 3)ieb tie 3;rewe ^erunter. 11. 3d) 

 fann nidjt auS ten Jvreu$tt>egcn tiefeS arten3 I;tnaugfomnten. 12. SBiffen 

 @te nid)t, line tiefer 3>ogel ^eteingefommen iftV 13. 3a, acer er toetp 

 ntcfjt, ruo er njteter r;inauSfommen fann. 14. S)er junge djiDetjev fcf;aute 

 tyinuber nac^ ten blauen SBergen fetne3 35atertante. 15. fommen @te 

 petite nid;t ^erunter ? 16. 3a, roenn ter O^etm ^erauffommt, tuetbe t<^ 

 ^ina6gel;en. 17. ^aben @ie tiefen iKann fdjon gefe^cn? 18. 3a, er fam 

 iire tyeretn, atS id) Ijtnaugging. 19. 2)er Sreunt fu^r in etner tunte 

 ben 8tup ^inuber unb 6,eriiber. 20. S)er trom ftiirjt mtt grofem eraufd; 

 ben gelfen tycrab. 



EXEKCISE 49. 



1. The son hastened down to receive his father. 2. His 

 speech lasted over two hours. 3. The roe sprang out from his 

 hiding place. 4. Will you go over to Frankfort to-day by the 

 steamboat ? 5. No, I shall go over by the railroad and return 

 by the steamboat. 6. Do not go beyond the crossway. 7. I 

 saw your friend come in as your uncle went out. 8. These men 

 who go over that bridge are in danger of their lives. 9. Will 

 you go out to-day with your friend ? 10. From this hill we can 

 look over our country. 11. How did the thief get into your 

 house ? 12. Edward precipitated himself from the rock. 13. I 

 shall pass your house this morning, and shall come in, without 

 your asking me to do so. 



LESSONS IN ARITHMETIC. XVI. 



DECIMALS (continued). 



15. Terminating and Circulating Decimals. Reducing Fractions 

 to Decimals. 



It is evident, from what has been said, that vulgar fractious 

 can be reduced to decimals by the process of the division of 

 decimals. For we have only to write down the dividend with a 

 decimal point, followed by a series of ciphers, and then divide 

 by the divisor, according to the rule already given for the division 

 of decimals. Thus, ^ may be reduced to a decimal as follows : 



40 ) 7-000 ( -175 

 40 



300 

 280 



200 

 200 



Therefore / a = '175 



Decimals which, after continuing the division of the fractions 

 from which they arise far enough, at last give a result without a 

 remainder, are called terminating decimals. 



16. To determine wJiether a Fraction will produce a Terminat- 

 ing Decimal or not. 



Since a decimal is a fraction with 10 or power of 10 for its 

 denominator, it is evident that if a given fraction will produce a 

 terminating decimal, it must be capable of being expressed in 

 the form of an equivalent fraction, which shall have a power of 10 

 for its denominator. 



Now 10 is composed of the prime factors 2 and 5. Hence, if 

 the denominator of the given fraction, when in its lowest terms, 

 contains any factor besides 2 and 5, it cannot produce a ter- 

 minating decimal. But if the denominator contains only 2's and 

 5's as its factors, then, by multiplying numerator and denomi- 

 nator of the fraction by a factor, we can always transform 

 the fraction into an equivalent one, having a power of 10 for its 

 denominator that is, into a terminating decimal. 



For example : 



||g will produce a terminating decimal, because 250 is com- 

 posed only of factors 2 and 5. 



250 = 5x5x5x2. 



Hence, if we multiply this by 2 X 2, i.e., 4, we shall make 

 250, the denominator, a power of 10. 



Therefore $& = 



= '868. 



Similarly, f gives a terminating decimal, for 8 is 2 X 2 X 2, 



