## First Lessons in Geometry |

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

### Popular passages

Page 48 - 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 iii - 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.

Page iv - 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 iv - 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 54 - ... 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 27 - 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 101 - Suppose your slafe-pencil were straight, so that it would lie flat on the slate, and make a mark as broad as the pencil is long. Then suppose you were to put your pencil across one corner of your slate like a hypotenuse, and slide first one end up to the corner, and then the other, keeping both ends all the time touching the slate frame. You would make a white mark in the corner, of a curved three-cornered shape, like this figure. The curve inside would be a hypocycloid. 8. If you take the corner...

Page iii - Meanwhile, my own children were in most urgent need of a text-book, 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 at comprehending first lessons in Geometry than these of fifteen.

Page 35 - 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.

Page 18 - For as the straight line has but one direction, anil each of the parallel lines may always be considered as going in the same direction as the other, the difference of that direction from the direction of the third straight line must be the same for each of the parallel lines. 88. Corollary. If a straight line is parallel to one of two parallel lines, it is parallel to the other ; if at right angles to one of the two, it is at right angles to the other. 89. Theorem. If a straight line make on the...