LIGHTNING CALCULATOR, AND Accountant's Assistant. THE SHORTEST, SIMPLEST, AND MOST RAPID METHOD OF COMPUTING WITHIN THE COMPREHENSION OF EVERY ONE HAVING THE SLIGHTEST KNOWLEDGE OF FIGURES. BY HOY D. ORTON. ENTIRELY NEW EDITION, WITH EXTENSIVE MODIFICATIONS AND IMPROVEMENTS. N. B.-Any infringement upon the copyright of this book will be H. D. ORTON & CO., 38 SOUTH SEVENTH STREET, PHILADELPHIA, PA. Edice T 18.71.620 ARVARD COLLEGE Acht 21, 192 Frank H. Blanchard Entered according to Act of Congress, in the year 1871, by in the Office of the Librarian of Congress, at Washington. 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." INTRODUCTION. Arithmetic means reckoning by numbers, calculating. Notation means writing numbers. Numeration means reading numbers. Number is one or more things or units, as one, two, &c. Unit or one is a single thing. Numbers are represented by figures. Figures are characters used in Arithmetic to represent numbers. All numbers are represented by the ten following figures: (Written) O. 1. 2. 3. 4. 5. 6. 7. 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. iii INTRODUCTION. QUANTITY is that which can be increased or diminished by augments or abatements of homogeneous 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 cuiculation or Mathematics. iv MATHEMATICS. MATHEMATICS 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 Mathematics 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 Differeutial, or that branch of Mathematics which investigates the nature of a continued variable cause that has produced a known effect. |