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THE SHORTEST, SIMPLEST, AND MOST RAPID METHOD OF COMPUTING
THE SLIGHTEST KNOWLEDGE OF FIGURBS.
HOY D. ORTON.
ENTIRELY NEW EDITION,
WITH EXTENSIVE MODIFICATIONS AND IMPROVEMENTS.
N. B.-Any Infringement upon the copyright of this book will be
prosecated to the fullest extent of the law.
H. D. ORTON & CO.,
38 SOUTH SEVENTH STREET,
Edica T 118.71.620
Entered according to Act of Congress, in the year 1871, by
HOY D. ORTON,
N. B.-It gives me pleasure to state that, in the revision of this book, I have been deeply indebted to S. J. DONALDSON, Jr., of Baltimore, a gentleman favorably known as the author of " Lyrics, and Other Poems."
Arithmetic means reckoning by numbers, calculating.
numbers. All numbers are represented by the ten following figures: (Written) C. 1. 2. 3. 4. 5. 6. % 8.9.
Cipher. one, two, three. four. five. six. seven. eight. nine. (Printed) 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. These figures, except the cipher, are often called Digits. Digit means the measure of a finger's breadth. Figures were called digits from counting the fingers in
reckoning. The character 0 is called a cipher, from the Arabic word tsphara, which signifies a blank or void. The uses of this character in numeration are so important, that its name, cipher, has been extended to the whole art of Arithmetic, which has been called to cipher, meaning to work with figures.
INTRODUCTION. QUANTITY is that which can be increased or diminished by augments or abatements of hoinogeneous parts. Quantities are of two essential kinds, Geometrical and Physical.
1. Geometrical quantities are those which occupy space; as lines, surfaces, solids, liquids, gases, etc.
2. Physical quantities are those which exist in the time, but occupy no space; they are known by their character and action upon geometrical quantities, as attraction, light, heat, electricity and mag netism, colors, force, power, etc.
To obtain the magnitude of a quantity we compare it with a part of the same; this part is imprinted in our mind as a unit, by which the whole is measured and conceived. No quantity can be measured by a quantity of another kind, but any quantity can be compared with any other quantity, and by such comparison arises what we call culculation or Mathematics.
MATHEMATICS. NATHEMATICS is a science by which the comparative value of quantities are investigated; it is divided into :
1. ARITHMETIC, that branch of Mathematics which treats of the nature and property of numbers; it is subdivided into Addition, Subtraction, Multiplication, Division, Involution, Evolution and Logarithms.
2. ALGEBRA, that branch of Matheunatics which employs letters to represent quantities, and by that means performs solutions without knowing or noticing the value of the quantities. The subdivisions of Algebra are the same as in Arithmetic.
3. GEOMETRY, that branch of Mathematics which investigates the relative property of quantities that occupies space; its subdivisions are Longemetry, Planemetry, Stereometry, Trigonometry and Conio Sections.
4. DIFFERENTIAL-CALCULS, that branch of Mathematics which ascertains the mean effect produced by group of continued variable causes.
5. INTEGRAL-CALCULS, the contrary of Di Kereutial, or that branch of Mathematics which inrestigates the nature of a continued variable cau: e that bus produced a known effect.