To learn one thing at a time-to learn that thing thoroughly and to learn its connections with other things are the golden steps that lead to the temple of knowledge. It will be seen, in Lessons XVI. and XVII., Section VII., that UNITY has been employed to denote any number entering into an arithmetical question. This use of unity affords a powerful means of solving most questions which otherwise present great difficulties; and is, it is believed, a link of closer connection between the subjects of arithmetic and algebra, than has before been used. It has been the author's aim, in the present work, to treat the subject of number in accordance with these principles, and to give to the whole a scientific form, and logical development. That he might not fail in so difficult and delicate an undertaking, he has defined all the terms, and given a full analysis of every process employed. The work is complete in itself. It is a mental analysis of the science of numbers, designed to be accessible to the youngest pupils because of its simple gradations, and useful to the advanced pupil because of its scientific arrangement, its logical connections and its higher analysis of the properties and relations of numbers. In the preparation of this work, many valuable suggestions and methods have been furnished by practical teachers. They were cheerfully offered and thankfully adopted. FISHKILL LANDING, February, 1854. SUGGESTIONS.-There is but one simple idea in Arithmetic-it is the idea of the unit ONE. Any collection of units is a number. Hence, every number is derived from one, and consequently has one for a base. Counting is merely naming numbers. In this lesson, the names of numbers are written opposite the collection. How many units in four? In six apples, what is the unit! What is the unit in seven pears? How many units in twelve peaches? What is the unit that is counted in the lesson? How many stars in the 4th line? How many in the 14th? From what are all numbers derived? What is the base of Every number? Which figure stands for two? Which figure stands for four? Which figure stands for nine? Which stands for eight? What stands for ten? What stands for twelve? What stands for fourteen? What stands for sixteen? What stands for eighteen? What stands for twenty? What stands for seventeen? What stands for fifteen ? What stands for nineteen? What stands for thirteen? SUGGESTIONS-This lesson is intended to teach that number may be expressed by figures, as well as by words. The teacher should explain to the pupil that the figure 2 and the word two, have the same meaning, and similarly for every figure and its corresponding word. Either the figure or the word, denotes as many units as its name points out. LESSON III. Figures from One to One Hundred. 0 Thirty-four. 34 Sixty-eight. 68 1 Thirty-five . 4 35 Sixty-nine . 69 .70 2 Thirty-six 3 Thirty-seven 37 Seventy-one. 71 Thirty-eight. 38 Seventy-two. 72 5 Thirty-nine 39 Seventy-three 73 6 Forty.. . 40 Seventy-four 74 7 Forty-one 41 Seventy-five. 75 8 Forty-two. 42 Seventy-six. 76 9 Forty-three. 43 Seventy-seven 77 . 10 Forty-four. 44 Seventy-eight 78 11 Forty-five. 45 Seventy-nine 79 . 12 Forty-six. . 46 Eighty .80 13 Forty-seven. 47 Eighty-one . 81 . 14 Forty-eight. 48 Eighty-two. 82 Fifteen . 15 Forty-nine 49 Eighty-three 83 50 Eighty-four . 84 . 51 Eighty-five . 85 52 Eighty-six . 86 53 Eighty-seven 87 54 Eighty-eight 88 55 Eighty-nine . 89 .56 Ninety .90 57 Ninety-one. 91 58 Ninety-two . 92 59 Ninety-three 93 . 60 Ninety-four. 94 61 Ninety-five. 95 62 Ninety-six .96 Twenty-nine 29 Sixty-three. 63 Ninety-seven 97 Thirty . 30 Sixty-four Thirty-three. 33 Sixty-seven. 67 Two hundred 200 SUGGESTION. This lesson is intended to teach that the words and the figures are simply two forms of language. This table is read, one I, one; two I's, two; three I's, three; IV, four, &c. What stands for two? What stands for five? What stands for ten? What stands for thirty? What stands for fifty? What stands for seventy? What stands for ninety? dred? What stands for one thousand ? What stands for four? What stands for eight? What stands for twenty? What stands for forty? What stands for sixty? What stands for eighty? What stands for one hun five hundred? What for SUGGESTION. This lesson is intended to teach that numbere may be expressed by the Roman characters, as well as by worde and by figures. Hence, there are three ways of expressing numbers, viz.: by words, by figures, and by letters. |