# First Lessons in Geometry ...

Swan, Brewer & Tileston, 1861 - Geom - 144 pages

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### Contents

 Similarity and Isoperimetrt 26 Different Kinds of Triangle 33 Quadrangles 39 Parallelograms 40 Rectangles and Squares 43 Triangles and Rectangles 46 Circles 52 Chords 62 XV11 More about Circles 65
 More about the Rolling Wheel 95 Wheels Rolling round a Wheel 98 Wheel Rolling in a Hoop 101 Hanging Chain 105 Path of a Stone in the Air 109 XXXIH The Shadow of a Ball 112 The Shadow of a Reel 115 The Cows Foot in a Cup of Milk 120 XXXVI Cures 125 About Cones 129

### Popular passages

Page 46 - Triangle the right angle) is called the hypotenuse, and the other sides are sometimes called legs. An acute-angled triangle is one that has all of its angles acute, Fig.
Page ii - Arithmetic, is sadly out of place in the hands of a child whose powers of observation and conception have, as yet, received no training whatever. I have, therefore, avoided reasoning, and simply given interesting geometrical facts, fitted, I hope, to arouse a child to the observation of phenomena, and to the perception of forms as real...
Page i - I have long been seeking a Geometry for beginners, suited to my taste, and to my convictions of what is a proper foundation for scientific education. Finding that Mr. Josiah Holbrook agreed most cordially with me in my estimate of this study, I had hoped that his treatise would satisfy me, but, although the best I had seen, it did not satisfy my needs.
Page 52 - ... or periphery. A portion of the circular line is called an arc, eg abc (fig. 39). The size of an arc with reference to the whole circumference is measured by degrees. Every circle is divided into 360 equal parts, which are called degrees ; each degree contains 60 minutes, and each minute 60 seconds.
Page 25 - It is obvious that if the three angles of one triangle are equal to the three angles of another, the triangles are not necessarily equal.
Page i - I have tried to present them in simple and attractive dress. I have addressed the child's imagination, rather than his reason, because I wished to teach him to conceive of forms. The child's powers of sensation are developed, before his powers of conception, and these before his reasoning powers. This is, therefore, the true order of education; and a powerful logical drill, like Colburn's admirable first lessons in Arithmetic, is sadly out of place in the hands of a child whose powers of observation...
Page 110 - Ans. 428.4+ rods. 8. A certain room is 24 feet long, 18 feet wide, and 12 feet high ; required the distance from one of the lower corners to an opposite upper corner.
Page 95 - ... shaped hill of the same height and the same breadth at the bottom. 6. The second curious thing about sliding on the inside of a cycloid is. that it takes always exactly the same time to slide to the bottom, however high up or low down you start. If A, in the last figure, is the top of such a hill, and c the lowest point, it will take a sled exactly as long to go from B to c, as to go from A to c. But this, you must remember, is only when we imagine the hill and the runners of the sleds to be,...
Page i - Meanwhile, my own children were in most urgent need of a textbook, and the sense of their want has driven me to take the time necessary for writing these pages. Two children, one of five, the other of seven and a half, were before my mind's eye all the time of my writing; and it will be found that children of this age are quicker of comprehending first lessons in Geometry than those of fifteen.
Page 33 - If one of the angles of a triangle is a right angle, the triangle is a right triangle. In a right triangle the side opposite the right angle is called the hypotenuse and is the longest side.