116 



THE POPULAR EDUCATOR. 



brother is dead ? 4. I had been told that lie was dangerously sick. 5. 

 Did you not generally go to bed as soou as you had finished your lessons ? 

 6. As soon as I had finished them, I used to go to the play. 7. As 

 soon as you had finished your lessons last evening, what did you do ? 

 8. As soon as I had finished them, I went to the ball. 9. Had uot 

 that little girl a wish to sleep ? 10. Sho had more wish to sleep than 

 to study. 11. What had you done witii your hook when I asked you 

 (or it? 12. I had mislaid it. 13. I had forgotten it in the garden. 

 14. Why was your watch stopped ? 15 Because I hud forgotten to 

 wind it up. 16. Had not the watchmaker wound it up ? 17. He had 

 forgotten to do it. 18. Had you not lost your purse ? 19. I had lost 

 it, but I have found it again. 20. Had your cousin left ? 21. He had 

 not left yet. 22. Was he out ? 23. He was out with my mother. 24. 

 Whither was he gone ? 25. He was gone to my brother's, who had 

 invited him to dinner. 



EXERCISE 106 (Vol. I., page 405). 



1. N'aviez-vous pas eu 1'intention de parler a moil frere ? 2. J'avais 

 eu 1'iuteution de lui parler, inais il 6ta.it parti. 3. M lle votre soeur so 

 coucha-t-elle, hier au soir, aussitot qu'elle eut lu son livre ? 4. Elle 

 se coucha aussitot qu'elle 1'eut lu. 5. Vous avait-on dit que votre 

 eo3ur e'tait malade ? 6. On m'avait dit qu'elle avait 6t6 dangereuse- 

 ment malade. 7. Saviez-vous ce que vous aviez fait de votre plume ? 



8. Je savais que je 1'avais e'gare'e. 9. Combien de vos livres avez-vous 

 e'gare's ? 10. J'en avais egare cinq, mais niou frere les a retrouve's. 11. 

 Oil les aviez-vous laisses ? 12. Je les avais laisses dans lejardin. 13. 

 La montre de votre frure e'tait-elle arrete'e ? 11. Elle e'tait arrete'e. 15. 

 Pourquoi e'tait-elle arrcte"e ? 16. II avait oublid do la reinouter. 

 17. N'avait-il pas perdu sa clef ? 18. II ne 1'avait pas perdue. 19. Le 

 teinturier e'tait-il parti ? 20. II n" e'tait pas encore parti, il avait 1'iu- 

 tentioa de partir a cinq heures. 21. Lui aviez-vous parld, quautl 

 j'arrivai hier ? 22. Je lui avais parle 1 . 23. Lui aviez-vous dit que rna 

 sosur est ici ? 24 Je le lui avais dit. 25. Est-il encore ici ? 26. NOD, 

 Monsieur, il est parti ; il a parti ce matin a six heures. 



EXERCISE 107 (Vol. I., page 405). 



1. Where were your relations last year? 2. They were in England. 

 3. Where did the gentlemen remain who accompanied you this 

 morning? 4. They remained at the house of their partners. 5. 

 What were your friends reading when you left them ? 6. They were 

 reading the news which they had just received. 7. What does your 

 father say ? 8. He says nothing. 9. How old is that gentleman ? 



10. He is nearly fifty years old. 11. How old are your children ? 

 12. The eldest is ten years old, and the youngest six. 13. Have you 

 asked that gentleman for your gold chain ? 14. I have asked him for 

 it. 15. Have you returned to the clerk the money which he had lent 

 you? 16. I have returned it to him. 17. Had you a wish to send 

 the locksmith your keys? 18. I had a wish to send them to him, for 

 they are broken. 19. Was it worth tho while to send those bottles 

 to the inukeeper ? 20. It was worth the while to send them to him, 

 for he had none. 21. Have you asked your father for napkiud ? 22. 

 I would not ask him for any. 



EXERCISE 108 (Vol. I., page 405). 



1. Que vous disait le serrurier ? 2. II me disait qu'il a apporte 

 ma clef. 3. Combien de lettres avez-vous porte'es a la poste ? 4. 

 J'en ai ports sept : trois pour vous, et quatre pour mon pere. 5. Oil 

 est le monsieur qui a apportd cette lettre ? 6. II demeure chez mon 

 pure; voulez-vous lui parler? 7. Je voulais lui envoyer une lettre 

 que j'ai apporte'e d'Angleterre. 8. Avez-vous rendu a cet homme 

 1'argent qu'il vous avait prete' ? 9. Je le lui ai rendu. 10. Aviez- 

 vous envie d' envoyer a M. votre frere la clef de votre chambre ? 



11. J'avais envie de la lui envoyer. 12. Cela valait-il la peine de 

 donuer ce livre a M. votre frere ? 13. Cela valait la peine de le 

 lui donner, car il en avait hesoin. 14. Cela valait-il la peine d'en- 

 voyer ces bouteilles au pharmacien ? 15. Cela valait la peine de 

 les lui envoyer. 16. Ou est le proprie'taire ? 17. II est en Angle- 

 terre. 18. Combien d'enfants a le serrurier ? 19. II en a dix. 20. 

 Combien de livres a le me'decin? 21. II a cinq cents volumes. 22. 

 Avez-vous donne" cette lettre au monsieur ? 23. J'ai oubli de la lui 

 douner. 



EXERCISE 109 (Vol. I., page 406). 



1. How long has Mr. L. lived in Paris? 2. He has been living 

 there ten years. 3. Has he not lived in Lyons ? 4. He lived there 

 formerly. 5. Can you tell me where the captain's son is ? 6. He has 

 been in England one year. 7. Do you know where Mr. B. lives ? 8. 

 He lived formerly in Eouen ; I do not know where he lives now. 



9. Have you been here long? 10. We have been here more than two 

 months. 11. How long have you had this orchard ? 12. We have 

 had it a year. 13. Do you know how far it is from Paris to Vienna ? 

 14. It is three hundred and six leagues from Paris to Vienna, and two 

 hundred leagues from Vienna to Copenhagen. 15. Has the company 

 been here long ? 16. It has been here more than two hours. 17. Is 

 it long since you read this bill ? 18. It is more than three hours ago 

 that I read it. 19. Has not your sister been reading more than half 

 an hour ? 20. She has been reading so long, that she is tired of it. 

 21. Have you been waiting long for this piece of music ? 22. I have 

 been waiting for it more than a year. 



LESSONS IN ALGEBRA. IV. 



SUBTRACTION. 



56. SUBTRACTION is the finding of the difference between any two 

 quantities or collections of quantities. 



EXAMPLES. (1.) Charles has 5a pears, and James has 3a 

 pears. How many more pears has Charles than James ? 



In this example, we wish to take 3a pears from 5a pears. 

 But subtraction is denoted by the sign . Hence the expres- 

 sion 5a 3a pears represents the answer. But 5a 3a = 2a 

 pears ; which is the answer. 



(2.) A gentleman owns a house valued at ,4,500, but he is in 

 debt <800. How much is he worth ? 



Hero wo have .4,500 <800 = .3,700. Ans. 



57. Let us now attend to the principle upon which these 

 operations are performed. Let us suppose that you open a 

 book account with your neighbour, and that when cast up, the 

 debtor side, which is considered positive, is <500, and the credit 

 side, which is considered negative, is .300. On balancing the 

 account, you find that he owes you .500 .300 = 200. Now, 

 if you take <50 from the positive or debtor side, it will have the 

 same effect on the balance, as if you added .50 to the negative 

 or credit side ; and on the other hand, if you take <50 from 

 the negative or credit side, it mil have the same effect on 

 the balance, as if you added .50 to the positive or debtor 

 side. 



58. In like manner, if, in the expression 12a 5a, you take 

 Sa from 12a, it will have the same effect on the expression, as 

 if you added 3a to 5a, and retained the negative sign in the sum ; 

 thus, 9a 5a is the same as l2a 8a. Again, if in the expres- 

 sion 12a 5a, you take Sa from 5a, and retain the negative sign 

 in the difference, it will have the same effect on the expression, 

 as if you added 3o, to 12a ; thus, 12o. 2a, is the same as 

 15a 5a. 



59. Hence universally, talcing away a positive quantity from an 

 algebraic expression is the same in effect as adding an equal 

 negative quantity; and taking away a negative quantity is the 

 same as adding an equal positive one. 



60. Upon this principle is founded the following 



GENERAL RULE FOR SUBTRACTION. 



Change the signs of all the quantities to be subtracted, i.e., of 

 the subtrahend, or suppose them to be changed from + to , and 

 from to + ; then if the quantities are ALIKE, unite the terms 

 as in addition (Arts. 49, 50) ; but if the quantities are UNLIKE, 

 write the terms of tlie subtrahend after those of the minuend. 

 (Art. 54). 



Otherwise. Put the quantity to be subtracted in brackets, 

 and write it after the quantity from which it is to be subtracted, 

 with the sign between them; then apply the Eules of 



Addition. 



EXAMPLES. 



(1.) Prom 6a + 96, take 3a + 46. 



Here, change the signs of the subtrahend, but not those of the 

 minuend, thus : 



Q a + 9J> 3a 46. Next reduce these terms, by Art. 52, 

 and you 1 have the answer, 3a + 5b. 



(2.) From 166 (3.) 14da (4.) 28 (5.) 166 (6.) Uda 

 Take 126 6da 16 126 6da 



8da 



46 



Answer, 46 8da 12 



(7.) 166 (8.) 126 (9.) 6da (10.) 16 (11.) 126 (12.) Gda 

 286 166 Uda 28 166 14da 



126 46 



8da 



+ 12 



+ 46 + 8da 



(13.) + 166 (14.) + 14da (15.) 28 (16.) 166 (17.) Uda 

 _ 126 Gda +16 + 126 + 6da 



+ 286 + 20da 44 286 



(18.) From 8a6, take 6xy. Ans. Sab 6an/. 

 (19.) From 6aay (20.) Waaxx 



Take IT ay 



2Qax 



Answer, 6aay \1ay IGaaxx 20a 



(21.) 6dd + 3d 4>ddd 

 Wdc + 2dddd + 4>dy 



6dd + 3d 4(M<2 lOdc 2dcWt! 



