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angle is measured arch ball blackboard called catenary caustic centre chain CHAPTER chord circle circumfer circumference compasses conic sections cube curve cycloid diagonal directrix divide draw a figure drawn edge ellipse epicycloid equal angles equilateral triangle evolute exactly fancy feet foot four geometrical name Geometry half as large hang hoop hyperbola hypocycloid hypotenuse inches in diameter inscribed isoperimetrical isosceles lamp larger largest last figure Let the teacher little triangles mark measured by half middle move opposite parabola parallel lines parallelogram pencil piece pins plane polygon proportion Pythagorean quadrangle quarter radius of curvature rectangle regular polygon right angle right cone right triangle rolling round shadow shape slate sphere spool square corner square inches stake stick straight lines cross string Suppose tangent tell things thread three angles vertex vertices wheel yard
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.