LESSONS IN ALOKHKA. 



IM 



/or some one, by moans of that vrhioh U ex- 

 pressed by tbo w-. ' <l wild it ; a, erbitmt, to got, or 

 .rot, by botftfintf. H tinds its oxaot opposite in er, which 



from some ono'n int. 



; as, o;rbiitcii, to bog off, to decline. The force aii'l u > - 

 of these particles are bo.st illustrated by example* : 



mitten, to find. (Srnntcn. to find out for one's 



self, invent. 



2M<cn. to stand. (Srrtcb.cn, to ariao, originate. 



-.I'.uicii. to build. (Srb.-.ucii, to erect, to produce. 



ptelcn, to play. SBtrfvitlen, to play away, to lose 



by gambling. 

 Butyrcn, to carry, or lead. SJcrfiiljrtn, to load away, to so- 



duco. 



i.il;cn, to salt. 33faljen, to ovorsa.lt, spoil in 



salting. 



(4.) Or and ccr arc also both employed in converting nouns 

 i'-etives into verbs expressive of transition from ono state 

 or condition into another ; thus 



Grfalteii, (fait, cold) to got cold. ! 35crebe(n, (ctef, noble) to ennoble, 

 (irfubnen, (fiifyn, bold) to become ' SStraottetn, (ott, God) to deify. 



bold, dare. 



Gfrlabmeii. (labm, lame) to be- 

 come lame. 



QJrralten, (alt. old) to grow old 

 or obsolete. 



In some instances, moreover, ec and vet are only euphonic or 

 intensive. 



93. -PREFIXES SEPARABLE AND INSEPARABLE. 



(1.) The prefixes of this class, when separable, are always 

 under the full accent ; whon inseparable, the accent falls upon 

 the radical. 



(2.) Their effect, to/ten separable, is, in union with radicals, to 

 produce certain intransitive compounds, in which each of the 

 parts (prefix and radical) has its own peculiar and natural signi- 

 fication. 



There are, however, some compounds of turcty and urn in 

 which, though these particles are separable, the verbs are, never- 

 theless, transitive. Still, it will be found that in such cases the 

 signification of the compound is figurative ; as, umbcingen, to 

 bring about (one's death), i.e., to kill. 



(3.) Their effect, when inseparable, is, in connection with the 

 radicals, to form certain transitive componnds ; which, for the 

 most part, are used in a figurative or metaphorical sense. 



(4.) Wo subjoin a list of the prefixes of this class, illustrating 

 each by a couple of examples ; the first being one in which the 

 prefix is separable, the second one in which it is inseparable : 



urc$, through ; 



inter, behind ; 

 Utber, over; 

 Urn, around ; 

 SBicter, again ; back ; 



iJurc^'ttingen, to press or force through. 



S)UH$trin'a.en, to penetrate. 



&inter / get)en, to go behind. 



ijtnterge'^en, to deceive. 



lU'berfefcen, to set or put over. 



Ueberff&'en, to translate. 



llm'geljen, to go around. 



Umgeb/cn, to evade. 



SBie'ter&olen, to fetch or bring back. 



2Bi;lcr&i/len, to repeat. 



99. VERBS COMPOUNDED WITH NOUNS AND 



ADJECTIVES. 



(1.) A variety of compounds is produced by the union of verbs 

 with nouns and adjectives. These follow the same general laws 

 which govern those produced by means of prefixes. Some of 

 them, accordingly, are separable ; as 



3ef)lfcblagen, to miscarry ; from feb,l and fc$lagen. 



8retfpre$en, to acquit ; fret foremen, 



(eictytominen, to equal ; a.lei<$ lommen. 



8creten, to tear away ; lo reiiien. 



istattftntcn, to take place; fiatt finten. 



(2.) Some are inseparable ; as 



'jautb.abcn, to handle ; from bant and babcn. 



Siebaugeln, to ogle ; ,, lieb augcln. 



aJiiitbmapen, to suspect; mutb mapcn. 



v iU'll^cftcn, to perform ; coll jieljcn. 



2Billfab,ren, to gratify ; null fabren. 



SBeiffajen, to foretell ; \ot\t fagcn. 



(3.) Those verb* Uko the augment syllable a < in the perfect 

 participle ; except wUutbnt. which ha* cU|ogcn. In some c*ses, 

 however, verbs compounded with cell, also, take tilt aogmmt ; 

 as, ooUgtgoffcn, from voUajef tn, to poor full. 



KEY TO EXERCISES IN LESSONS I2T GERMAN. 



EXERCISE 180 (Vol. III., page 370). 



1. I wish you a good morning. 2. I have the honour to wish 700 

 a good morning. 3. I remember my frieud* with wuoero affoctiou. 

 4. In times of prosperity he did not think of him. but la th boon of 

 auxiety and distress ho remembered him. 5. I intend to go on a 

 journey. 6. I intend to return soon. 7. We intend to go on a journey. 

 8. You intended to do me mischief. 9. The father intends to agree to 

 it. 10. I did not intend to go there. 11. I am packing my trunk. 

 because I intend in a few days to go on a journey. 12. I am on the 

 point of departing. 13. I am on the point of going oat. 14. They 

 conduct the criminal to the place of execution. 15. The duke's son 

 led the troops to the assault himself. 18. He led them to the attack. 

 17. Russia waged war with Poland. 18. The merchant brings goods to 

 the market. 19. A little child was leading the blind man. 30. Alaric 

 was buried by the Goths iu the Busento, after they had first turned off 

 the current. 21. He guides every one according to his counsel. 22. 

 He who does not submit to be guided by reason, runs the risk of being 

 led by his passions to r lin. 23. The diligent scholar overtook his 

 comrades in learning the English language, although they bad begun 

 to learn it about four weeks sooner. 24. We overtook the friends on 

 their journey, although they weut away half an hour earner. 25. 

 Mon do not attain to so great an age now-a-days as in former times. 

 26. At the present day one hears of nothing else than war. 27. At 

 the present day one hears much complaining of bod times. 



LESSONS IN ALGEBRA. XXXIX. 



GEOMETRICAL PROPORTION AND PROGRESSION (continued). 

 CASE IV. ADDITION AND SUBTBACTION OF EQUAL RATIOS. 



If to or from two analogous or two homologous terms of a pro- 

 portion, two otJier quantities having the same ratio be added or 

 subtracted, the proportion will be preserved. (Euclid V. 2.) 



For a ratio is not altered by adding to it, or subtracting from 

 it, the terms of another equal ratio. 



If a : b : : c : d, and a : b : : m : n, 



Then, by adding to, or subtracting from, a and b, the terms 

 of the equal ratio m : n, we have, 



a + m : 6 + 11 : : c . d, and a-m-.b-n: : c : d. 

 And by adding and subtracting m and n to and from c and d, 

 we have, 



a:6::c + m:d + n, and a . b : c - m : d - n. 

 Here the addition and subtraction are to and from analogous 

 terms. But by alternation these terms will become homologous, 

 and we shall have, 



a + m: c : : b + n : cl, and a m-.c : : 6 n: d. 

 Cor. 1. This addition may evidently be extended to any 

 number of equal ratios. (Euclid V. 2, Cor.) 

 c:d) 



7i : I f then a:6::c + h + m + z:d + J 

 m: n f + n + y. 

 x:y ) 



a : b : : C : d \ then O+W:6::C-l-n:d. 

 (Euclid V. 24.) 



( a + m : c + n : : 6 -. d. 



And ro : n::&:dj ut ce j or a + m : 6 : : c + ti : d. 



Hence, if two analogous or homologous terms be added to or 

 subtracted from Hie two others, the proportion will be preserved. 

 Thus, if a : 6 : : c : d, and 12 : 4 : : 6 : 2, then, 



1. Adding the last two terms to thejirsi two, 



+ C:0 + d::a:6 12 + 6: 4 + 2:: 12:4 



or a + c:a::6 + d:6 12 + 6:12::4+2:4 



anda + c:c::6+d:d 12+6: 6::4-r 2:2 



2. Adding the two antecedents to the two consequents. 

 a + b:b::c + d:d 12 + 4: 4::6 + 2:2 

 a + 6 : a : : c + d : c, etc. 12 + 4 : 12 : : 6 + 2 : 6, 



This is called composition. (Euclid V. 18.) 



3. Subtracting the first two terms from the last two, 



C -a : a : :d-b:b,OT C a : C : :d-fc:d, etc. 



Thus, if a :b : : 



Cor. 2. If 



And m : b : : n : d ) 

 For by alternation a : c : : b . d 



