READINGS IN GERMAN. 



L'l 



16. A numeral figure is often prefixed to a letter. This is 

 called a coefficient. It shows how often the quantity expressed 

 by the letter is to be taken. Thus 26 signifies twice b ; and 9b, 

 '.) timoH b, or 9 multiplied ii. 



The co-efficient may bo either a whole number or fraction. 

 Tim - \b is two-thirds of b. When the co-efficient is not ox- 

 pressed, 1 is always to be understood. Thus a is the same as 

 to say, once a, or one times. 



17. The co-efficient may also be a letter, as well M a figure. 

 In the quantity mb, m may be considered the co-efficient of b ; 

 because b is to be token as many times as there are units in m. 

 If m stands for 6, then mb is six times b. In 3oic, 3 may be con- 



1 as the co-efficient of abc ; 3a the co-efficient of be ; or 

 in' coefficient of c. 



18. A simple quantity is either a single letter or number, 

 or several letters connected together wMiout the signs + or 

 . Thus a, ab, aid, and 8b, are each of them simple quan- 



19. A compound quantity consists of a number of simple 

 quantities connected by the sign -f- or . Thus a + b, d y, 

 b - d + 37i, are each compound quantities. The members of 

 which each is composed are called terms. 



20. A simple term is called a monomial ; thus, a, b, c are 



ials. If there are two terms in a compound quantity, it 

 id called a binomial : thus a -f- b and a b are binomials. 

 The latter term (a b) is also called a residual quantity, 

 M it expresses the difference of two quantities, or the 

 remainder after one is taken from the other. A compound 

 quantity, consisting of three terms, is sometimes called a tri- 

 nomial; one of four terms, a guadrinomial. A quantity consist- 

 ing of several terms is, however, generally called a polynomial. 



21. When the several members of a compound quantity 

 are to be subjected to the same operation, they are connected 



by a line called a vinculum ( ), or by a parenthesis ( ). Thus 



a b + c, or a (b 4- c), shows that the sum of b and c is to be 

 subtracted from a. But a b + c signifies that b is to be sub- 

 tracted from a, and c is to be added to the result. 



22. A single letter, or a number of letters, representing any 

 quantities with their relations, is called an algebraic expression 

 or formula. Thus a + b + 3d is an algebraic expression. 



23. Multiplication is usually denoted by two oblique lines 

 crossing each other, thus X : hence, a x b is a multiplied into 

 b ; and 6 x 3 is 6 times 3, or C multiplied into 3. Sometimes 

 a point is used to indicate multiplication : thus, a . b is the same 

 as a X b. But the sign of multiplication is more commonly 

 omitted between simple quantities, and the letters are con- 

 nected together in the form of a word or syllable : thus, ab is 

 the same as a . b or a X b ; and bcde is the same as b X c X 

 d X e. When a compound quantity is to be multiplied, a 

 vinculum or parenthesis is used, as in the case of subtraction. 

 Thrm the sum of a and b multiplied into the sum of c and d, is 

 a + b X c-f d", or (a + b) x (c + d). And (6 -f 2) X 5 is 8 X 5, 

 or 40. But 6 + (2 X 5) is 6 + 10, or 16. When the marks of 

 parenthesis are used, the sign of multiplication is frequently 

 omitted. Thus (x -f y} (x-y) is (x -f y) X (x y). 



24. When two or more quantities are multiplied together, 

 each of them is called a factor. In the product ab, a is a factor, 

 and so is b. In the product x X (a -f- m), x is one of the factors, 

 and (a + m) the other. Hence every co-efficient may be con- 

 sidered as a factor (Art. 17). In the product 3i/, 3 is a factor 

 as well as y. 



25. A quantity is said to be resolved into factors, when any 

 factors are taken which, being multiplied together, will pro- 

 duce the given quantity. Thus Sab may be resolved into the 

 two factors 3a and b, because 3a x b is Sab. And 5amn may 

 be resolved into the three factors 5a, and m, and n. And 48 

 may be resolved into the two factors 2 X 24, or 3 X 16, or 

 4 X 12, or 6 X 8 ; or into the three factors 2x3x8, or 4x6 

 X 2, etc. 



26. Division is expressed in two ways : (1.) By an horizontal 

 lino between two dots -h, which shows that the quantity pre- 

 ceding it is to be divided by that which follows. Thus a -r c, 

 is a divided by c. 



(2.) Division is more commonly expressed in the form of a 

 fraction, putting the dividend in the place of the numerator, 



and the divisor in that of the denominator. Thus- is a 

 divided by b. b 



READINGS IN GERMAN. I. 



I RODUCTION. 



THE object of learning a modern language u not simply, M in 

 the case of one that is no longer spoken, to be able to read and 

 write, but also to speak it. For this pnrpose it is obriooaly 

 necessary to acquire a knowledge of the pronunciation M well 

 as the meaning of the word*. Hence we are not surprised at 

 having received many applications from the readers of our les- 

 sons in German for some instruction on this subject ; and it U 

 our intention to publish in the pages of the POPULAR EDUCATOR 

 a series of German Beading Lessons expressly prepared with a 

 view to teach the proper pronunciation of the language. These- 

 lessons will be found much better adapted to answer the pur- 

 pose than any mere collection of rules, however carefully drawn 

 up, and however clearly expressed. In no case is the principle, 

 that example is better than precept, more applicable than in 

 that of pronunciation, a knowledge of which can only be acquired 

 by frequent exemplification. Wo have no hesitation in saying. 

 that the study of our lessons will enable the reader to pronounce 

 German, if not with absolute perfection, at least so as to be 

 easily understood by a native, which is, after all, the only prac- 

 tical object in view. 



It is proper to observe, that whilst the lessons are especially 

 intended to teach pronunciation, they are also calculated to bo- 

 very useful to our readers as exercises in translation, being easy, 

 in construction, simple in style, rich in words, and adapted in 

 substance to persons of all ages. A vocabulary will be appended 

 to each lesson, containing an explanation of the meaning of 

 every word in it which has not been previously explained. A* 

 few words will be explained more than once in the whole coarser 

 of the vocabularies, it will be necessary for the learner to study 

 each with great core on its first occurrence, that he may avoid 

 the inconvenience of having to look through preceding pages 

 for the meaning. 



DIRECTIONS FOR THE USE OF THE INTERLINEAR 

 PRONUNCIATION. 



Pronounce every syllable as in English. 



To make a vowel long which otherwise would be short, or 

 might be either short or long, an apostrophe has been placed 

 immediately after that vowel. Thus rol will rhyme with doll, 

 but vo'l will rhyme with whole. 



To make a vowel short which otherwise would be long, or 

 might be either long or short, the short sign or breve has been 

 placed over that vowel. Thus mild will rhyme with wild, but 

 mild will rhyme with build. Boot will rhyme with root, but bJdf 

 will rhyme with put. 



ah is long, and sounded as in father ; a is short, and sounded 

 as in castle. 



ey is to be pronounced as in obey. 



ai, representing the short sound of t, t when unaccented and 

 terminating a syllable, should be pronounced like cy in the 

 noun sur'-vey. The letters ey could not well be used for this 

 sound, as they have generally the sound of ee when unac- 

 cented. 



D has no corresponding sound in English ; place the organs as 

 if to pronounce o long ; keep them exactly in this position, 

 and then try to pronounce the German or English a. For 

 the short sound of this vowel place the organs again as if 

 to pronounce o, and without changing, try to pronounce ef, 

 el, eck, em, en, ep, er, ess, et, and you will utter the sound 

 required. The sound which comes nearest to it is the c in 

 her. 



11 has no parallel in English. Pronounce oo in ootf, firmly 

 maintain this position, and try to pronounce long e in eel ; 

 the sound uttered will be the one required. For the short 

 sound, place the organs in a similar position, and without 

 changing it try to say if, ii, ick, im, in, ip, r, in, it. 

 For those who have studied French it may be well to re- 

 mark that the German u has the same sound as the 

 French u. 



ou is always to be sounded as in out, our.' 

 gh before e and i must be pronounced like g in get, gimlet. 

 6) has different sounds, according to its position in the worA 

 In the interlinear pronunciation we shall denote it by 

 ct>, when it is pronounced like an aspirated fc, or like the 



