LIGHTNING CALCULATOR, AND Accountant's Assistant. THE SHORTEST, SIMPLEST, AND MOST RAPID METHOD OF COMPUTING WITHIN THE COMPREHENSION OF EVERY ONE HAVING N. B.-Any infringement upon the copyright of this book will be PHILADELPHIA: COLLINS, PRINTER, 705 JAYNE STREET. QA III 07 Educ dept. Entered according to Act of Congress, in the year 1866, by In the Clerk's Office of the District Court of the United States EDUCATION DEPT. 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 calculation or Mathematics. M29804 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 Conic 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 Differential, or that branch of Mathematics which investigates the nature of a continued variable cause that has produced a known effect. PREFACE. MATHEMATICAL LAWS are the acknowledged basis of all science. Ever since the streets of Athens resounded with that historical cry of "Eureka," emanating from one of antiquity's greatest mathematicians, the science has been steadily progressing. It is not our purpose, in this small work, to introduce any of the higher branches of mathematics, viz.: Algebra, Conic Sections, Calculus, etc. Our object is merely to present to the public a system of calculation that is practical to every business man. It consists of the addition of numbers on a principle entirely different from the one ordinarily used. In the practical application of this new principle of addition, scarcely any mental labor is required, compared with the principle of addition set forth in standard works. The superiority we claim for this principle above all others, is this, that it requires no great mental exertion, affording the |