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This method of calculation affords the
performing calculations in whole numbers, even when the question is composed of whole fractions, or number and fractions. By an easy process in the statement the frac. tions are rejected, the solution or calculation is performed by the pure proportion of all variation of measure, weight, money, &c., of the whole world, entirely by whole numbers and in an uninterrupted series. It teaches to obtain, by a succession of pure proportion, an answer to any arithmetical proportional question proposed. The rule of three, or the rule of proportion, named also the "golden rule,” has not this power. By this rule we are often compelled to make four, five, and more statements before we are able to obtain the answer required. These proceedings, by the common rule of calculation with fractions, render the process circumstantial and confused to the scholar, and difficult to impress on his memory ; but the rule of pure proportion teaches, in an easy, agreeable, and unavoidable manner, all the rules in general, as rule of three, tare, barter, fellowship, interest, reduction, loss and gain, exchange, and others; and even in the solution and statements of these questions, wherein it is now necessary to employ several of these rules, the rule of pure proportion will suffice; and it also performs the cal. culation always without interruption, and in whole numbers. By this rule all circumstantial calculation of fractional numbers are avoided, and, by the shortness in whole numbers, more agreeable too, than the circumstantial calculation with compound numbers; and it may be said, without hesitation, that the rule of pure proportion affords, in all business of common life, the same easiness as the decimal system does in the science of mathematics. To enlarge this work by a long preface is not the intention of its author. It may speak for itself. It will be found, on examination, to do what it professes, viz., to teach an easy method of calculation, and to afford interesting and necessary knowledge to all men of business.
The pupil, even when he walks out for recreation, will find a subject for his thoughts and an agreeable little companion in this work. The amusing variation will afford to the scholar principles which will enable and animate him to perform questions hitherto unknown in any system of arithmetic; by the knowledge of pure proportion and true judgment, which this system of figures gives of fractions, the young pupil becomes, in the course of his studies, better prepared for the higher branches of mathematics, and the tutors will not have half the trouble to ingraft durable principles of calculation on his memory.
Finally, it may be observed, that the author of this method of calculation has shown a fixed rule, that will not be found in any system of arithmetic—a rule to find the pure proportion of all things. Besides, he has adjusted the necessary pure proportions in a few pages at the end of the work, and placed there also a few sheets of writing paper, for the purpose that new pure proportions, desired and found after this rule, may be neatly traced thereon.
PORTER'S NEW SYSTEM
M A THEM A TICS.
ARITHMETIC is the art or science of computing by numbers, and consists both in Theory and Practice. The Theory considers the nature and quality of numbers, and demonstrates the reason of practical operations. The Practice is that which shows the method of working by nuinbers, so as to be most useful and expeditious for business, and is comprised under five principal or fundamental rules, viz., Notation or Numeration, Addition, Sub. traction, Multiplication, and Division ; the knowledge of which is so necessary, that scarcely anything in life, and nothing in trade, can be done without it.
NUMERATION TEACHETH to express any proposed number by these ten characters : 0, 1, 2, 3, 4, 5, 6, 7, 8, 940 is called a cipher, and the rest figures, or digits; the relative value of which depends upon the place they stand in when joined together, beginning at the right hand, as in the following:
6 Hundreds of Millions.
co Tens of Millions.
Hundreds of Thousands.
a Tens of Thousands.
6 5 4 3 2 1 Though the table consists of only nine places, yet it may be extended to more places at pleasure ; as, after hundreds of millions, read thousands of millions, ten thousands of millions, hundred thousands of millions, billions, trillions, quadrillions, quintillions, sextillions, septillions, octillions, nonillions, decillions, undecillions, &c., as in the following example: Quadrillions. Trillions. Billions. Millions. Units.
707 928 679 437
To write down numbers. Rule. Write down the figures as their values are expressed, and supply any deficiency in the order with ciphers.
Write down the following numbers in order: