The Diameter of a Circle being given, to find the Circumference, The Circumference of a Circle being given, to find the Diameter, To find the Solid Contents of a Globe, To find the Solid Contents of a Cylinder, To find the Solid Contents of a Pyramid, SUGGESTIONS TO TEACHERS ON THE METHOD OF USING THIS WORK. FOR a course of mental arithmetic, adapted to the capacities of very young pupils, they may take the mental exercises in each rule, as far as the first example for the slate. This course is not meant to include any of the exercises styled "Questions on the foregoing." This course embraces the whole of the first 20 pages, together with the arithmetical tables, extending to the Appendix. The necessity of impressing these tables on the minds of pupils at an early age is sufficiently obvious. When the pupil is perfect master of this course, as will, most probably, be the case after one or two reviews, the teacher will find no difficulty in making him understand the operations by slate. He may then take the whole in course. In every school, it would be well to institute classes; and as there are seldom any answers given to the mental questions, the pupils may be allowed to read in their turns the questions from the book; thus giving the teacher no further trouble than occasional corrections. By this, the reader will perceive, that the work may be used to advantage in monitorial schools, as the former editions have been. In large schools these corrections may be made by an advanced scholar, instead of the teacher. Whenever an advanced scholar takes up tho book with a view of profiting from it, he should omit nothing as he pro gresses, but make it his practice to qualify himself to answer any question, in the mental exercises, rules, or respecting the reason of the operations. Teachers will find it to be a useful occupation for their scholars, to assign them a morning lesson, to be recited as soon as they come into school. With little exertion on the part of teachers, pupils in this way may be made assiduous and ambitious, very much to their advantage, and to the credit of their teachers. The mental questions, under the head of "Questions on the foregoing," will, intelligently answered, furnish to committees an admirable test of the pupil's knowledge of this subject. The Appendix is designed for those who have time and opportunity to devote to the study of the more abstruse parts of mathematics. Note. Lest some may mistake the object of the figures in the parentheses, it may here be remarked, that these figures are separate answers, left without assigning any value to them, reserving this particular for the discretion of the pupil, which he must necessarily exercise, in order to obtain the answer which follows, that being the aggregate of the whole. The above directions are those which seem the best to the author; but as every intelligent teacher has a way of his own, which, though not intrinsically the best, is, perhaps, the best for him, the subject is respectfully submitted to his own choice, TI.* 1. How many little fingers have you on your righ hand? How many on your left? How many on both? 2. How many eyes have you? 3. If you have two apples in one hand, and one in the other, how many have you in both? How many are two and one, then, put together? 4. How many do your ears and eyes make, counted together? 5. If you have two nuts in one hand, and two in the other, how many have you in both? How many do two and two make, put together? 6. If you have three pins in one hand, and James puts another in, how many will you have in your hand? How many are three and one then? 7. If you have three pins in one hand, and James puts two more in, how many will you have in your hand? How many are three and two then? 8. If you have four apples in one pocket, and two in the other, how many will you have in both? How many are four and two then? 9. Thomas has four cents, and William has three; how many have they both together? How many are four and three then? 10. You have five pins in one hand, and three in the other; how many have you in both? How many are five and three then? 11. You have four nuts in one hand, and four in the other ; how many have you in both? How many are four and four then? *The questions in ¶ I and ¶ II are intended for very young children. Older pupils may omit these. But the two remaining sections, and the four tables, will claim an attentive perusal. 12. If you count the fingers and thumb on one hand, and only the fingers on the other, how many will they make? How many are five and four then? 13. How many fingers and thumbs have you on both hands? 14. James has five marbles, and Thomas five; how many have they both? How many are five and five then? 15. How many cents would it take to buy two whistles, if one cost six cents, and the other four? How many are six and four then? 16. If you have eight pins on one sleeve, and two on the other, how many will you have on both? How many are eight and two then? 17. How many legs have two cats and a bird? 18. If I should give you six cents, and you should find five, how many would you have then? How many are six and five then? 19. If you count all your fingers, thumbs, and nose, how many will they make? 20. If you buy a picture-book for ten cents, and a pear for two cents, how many cents will pay for both? How many are ten and two then? 21. How much money would you have, if your father should give you seven cents, and your brother six? How many are seven and six then? 22. If you have seven pins in one hand, and seven in the other, how many will you have in both? How many are seven and seven then? 23. A man bought a chair for three dollars, and a lookingglass for twelve; how much did he give for both? How many are three and twelve then? 24. You give thirteen cents for a spelling-book, and three for an inkstand; how much do they come to? How many are thirteen and three? 25. Count one hundred. .14 .2 Fifteen. ...... ..15 .3 Sixteen... ..16 .4 .5 Eighteen Note. The pupil is to recite the above, with the written numbers covered ofer. The answers to the following questions are to be given by writing them down on the slate at recitation, to test the pupil's knowledge of numbers from one to one hundred. 26. Write down in proper figures, Four; Seven; Eight; Twelve; Eighteen; Twenty-two; Thirty-two; Forty-five; Forty-nine; Fifty-six; Fifty-nine; Sixty-three; Seventy-five; Eighty-seven; Ninety-two; Ninety-seven; Ninety-nine. 27. James has seventy-eight cents, and Rufus eighty-seven cents; which has the most? 28. Thomas has fifty-nine dollars, and William sixty-nine; which has the most? Which is the most, eighty-nine, or ninety-nine? Forty-seven, or seventy-four? 29. Repeat the |