# Mathematical Monthly Volume 1

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## Description

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1859 edition. Excerpt: ...Hill proposes to carry the idea still further by making the study of Geometry precede Arithmetic, and to this end has prepared the little work before us. He says " geometrical facts and conceptions are easier to a child than those of arithmetic, but arithmetical reasoning is easier than geometrical." This suggests the order of these studies as a discipline of the reasoning powers. Arithmetical reasoning first, and geometrical afterwards. We most sincerely commend this little volume and the whole subject to the attention of teachers and all in any way interested in the Bubject of education, and add the following chapters to show how clear and vivid an idea of even the higher curves can be obtained by description alone, and how decidedly this habit of conceiving of a curve in kind must assist the student afterwards to apply his analysis and compute it in magnitude. Chapter XXVII. About a Wheel Rolling.--1. When a wagon is going upon a straight and level road, look at the head cf a spike in the tire of one of the wheels, and you will see that it moves in beautiful curves, making a row of arches that is called a cycloid. 2. That is to say, a cycloid is the path of a point in the circumference of a circle rolling on a straight line. You can draw part of a cycloid by putting the point of your pencil into a little notch in the edge of a spool, and tying it fast, so that the point of the pencil shall be kept just at the edge of the spool; and then rolling the spool carefully and slowly against the inside of the frame of the slate. 8. You will see, I think, that each arch in the cycloid must be just as high from c to D as the diameter of the circle that makes it; and just as wide at the bottom, from A to B, as the whole circumference of...