I have carefully inspected the "Juvenile Arithmetick and Schollar's Guide," by Dr. Ruter, and am of the opinion, it is well calculated and arranged, to conduct the pupil by an easy gradation to a perspicuous conception of the science of numbers. I therefore recommend it to the publick use, particularly in common schools. September 2, 1827. SAMUEL BURR, Professor of Mathematicks. A cursory examination of Dr. Ruter's Arithmetick, has convinced me, that the simple and familiar manner in which the learned author unfolds the principles of this science, and adapts them to the understanding of the young learner, can not fail to give his work a decided preference, for practical purposes, over those arithmeticks in common use. In my opinion, teachers who adopt it, as well as pupils who study it, will realize satisfactory and highly beneficial results. S. KIRKHAM, Author of Grammar in Familiar Lectures. Pittsburgh, April 2, 1828. I have examined the system of Arithmetick compiled by Dr. Ruter, and am of opinion that it is well calculated for conveying to youth, a general knowledge of that science in a shorter time, than any I have seen. G. GARDNER, March 29, 1828. Teacher of Mathematicks, Mill-Creek Township. Having examined the Juvenile Arithmetick, I have no hesitation in pronouncing it an excellent elementary School Book, The rules are judiciously arranged, and peculiarly well adapted to juvenile comprehension: The work contains multum in parvo, and I think its publication will be conducive to publick utility. Hoping its merits will be duly appreciated, I take great pleasure in recommending it to the publick patronage. Yours respectfully, RICHARD MORECRAFT. Cincinnati, January 2, 1828. Teacher. From my acquaintance with Ruter's Arithmetick, I am convinced that it is well calculated to encourage the student, improve his mind, and prepare him for business. JOHN LOCKE, May 16, 1828. Principal of Cincinnati Female Academy. Gentlemen-I have examined with some attention the Juvenile Arithmetick, &c. by the Rev. Dr. Ruter, and am decidely of opinion, that it is admirably calculated for conveying to youth with great facility a general knowledge of that important science. The ingenious manner in which the compiler has given an elucidation of Vulgar Fractions, together with an exclusion of all extraneous matter, renders it in my estimation a treatise of peculiar merit. Your obedient servant, JOHN WINRIGHT. Cincinnati, September 2, 1827. Teacher. PREFACE. THIS ARITHMETICK has been compiled with a view to facilitate the progress of pupils, and lessen the labour of teachers. The questions preceding and following the rules, are designed to lead young learners into habits of thinking and calculating; and thus, to prepare them for practical operations. Experience has demonstrated, that, in the instruction of children in any science, it is necessary to excite their entire attention to the subject before them. The latent energies of their minds must be roused up, and called forth into action. When this can be effectually done, success is rendered certain.To accomplish this important object, the best method has been found in the frequent use of well selected questions. Though it is a successful course in all juvenile studies, it is particularly so in the science of numbers; and the progress of pupils must be slow with out it. The questions in the following pages are thought to be sufficiently numerous for the purposes intended; the rules have been arranged according to the plan of some of the best authors on this subject, ard the work is offered to the publick with the hope that it will be useful in the schools of our country. 1* M. R. Signifies plus, or addition. ::: Signifies proportion, Denotes equality. Thus, 4+7 denotes that 7 is to be added to 4. 5-3, Denotes that 3 is to be taken from 5. 8X2, Signifies that 8 is to be multiplied by 2. 93, That 9 is to be divided by 3. 3:2: :6:4, Shows that 3 is to 2 as 6 is to 4. 7+9-16, Shows that the sum of 7 and 9 is equal to 16. Vor Denotes the Square Root. Denotes the Cube Root. Denotes the Biquadrate Root. This mark, called a Vinculum, shows that the several figures over which it is drawn are to to be taken together as a simple quantity. ARITHMETICK. ARITHMETICK is the science which treats of the nature and properties of numbers: and its operations are conducted chiefly by five principal rules. These are, Numeration, Addition, Subtraction, Multiplication, and Division. Numbers in Arithmetick are expressed by the following ten digits or characters, namely: 1 one, 2 two, 3 three, 4 four, 5 five, 6 six, 7 seven, 8 eight, 9 nine, 0 cypher. An Integer signifies a whole number, or certain quan tity of units, as one, three, ten. A Fraction is a broken number, or part of a number, as one half, two-thirds, one-fourth, three-fourths, five-eigths, &c. Numeration teaches the different value of figures by their different places, and to express any proposed numbers either by words or characters; or to read and write any sum or number. NUMERATION TABLE. 653267-S293 1 2 543 4237 Units. Tens. 76543 3456 Hundreds. Thousands. Tens of thousands. 37285 Tens of millions. Ten thousands of millions. Hundred thousands of millions. Here any figure in the place of units, reckoning from right to left, denotes only its simple value; but that in the second place denotes ten times its simple value; and that in the third place, one hundred times its simple value; and so on, the value of any figure in each successive place, being always ten times its former value. Thus in the number 6543, the 3 in the first place denotes only three; but 4 in the second place signifies four tens or 40; 5 in the third place, five hundred; and six in the fourth place, six thousand; which makes the whole number read thus-six thousand five hundred and fortythree. The cypher stands for nothing when alone, or when on the left hand side of an integer; but being joined on the right hand side of other figures, it increases their value in the same ten fold proportion: thus, 50 denotes five tens; and 500 is read five hundred. Though the preceding numeration table contains only twelve places, which render it sufficiently large for young students, yet it may be extended to more places at pleasure. EXAMPLE. Quatrillions. Trillions. Billions. Millions. Units. 987,654; 321,234; 567,898; 765,432; 123,456 Here note, that Billions is substituted for millions of millions: Trillions, for millions of millions of millions Quatrillions, for millions of millions of millions of millions. From millions, to billions, trillions, quatrillions, and other degrees of numeration, the same intermediate denominations, of tens, hundreds, thousands, &c. are ised, as from units to millions. And thus, in ascertaining the amount of very high numbers, we proceed from Millions to Billions, Trillions, Quatrillions, Quintillions, Sextillions, Septillions, Octillions, Nonillions, Decillions, Undecillions, Duodecillions, Tredecillions, Quatuordecillions, Quindecillions, Sexdecillions, Septendecillions, Octodecillions, Novemdecillions, Vigintillions, &c. all of which answer to millions so often repeated, as their indices respectively require, according to the above proportion. |
