The Logic and Utility of Mathematics; With the Best Methods of Instruction Explained and Illustrated (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1850 Excerpt: ...which of the figures, change, at all, their signification. Selecting any two of the figures, as 3 and 5, Examples. or example, we see at once that there are but three ways of writing them, that will at all change their signification. Fust: First, write them by the side of each 3 5, other ) 5 3. Second: Second, write them, the one over i f, the other ) f. Third. Third, place a decimal point before.3, each ).5. Now, each manner of writing gives a different signification to both the figures. Use, howLcsmthe ever, has established that signification, and we language by ltnow it sotm we nave learnetJ tJie lan. guage. We have thus explained what we mean by the arithmetical language. Its grammar emits grammar: braces the names of its elementary signs, or Alphabet--Alphabet, --the formation and number of its their uses, words, --and the laws by which figures are connected for the purpose of expressing ideas. We feel that there is simplicity and beauty in this system, and hope it may be useful. NECESSITY OF EXACT DEFINITIONS AND TERMS. 200. The principles of every science are Principles of a collection of mental processes, having estab-8Ciencolished connections with each other. In every branch of mathematics, the Definitions and Definitions and terms: Terms give form to, and are the signs of, certain elementary ideas, which are the basis of the science. Between any term and the idea which it is employed to express, the connection should be so intimate, that the one will always suggest the other. These definitions and terms, when their sig-when once.--, 1 fixed must nifications are once fixed, must always be used always be in the same sense. The necessity of this is most "M"'1"'""' urgent. For, "in the whole range of arithmetical sci...