# First Lessons in Geometry: In Two Parts

Ivison, Blakeman, Taylor & Company, 1875

### Contents

 PART I 9 ANGLES 17 KINDS OF ANGLES 23 INTERIOR ANGLES 30 PROBLEMS RELATING TO ANGLES 38 TRIANGLES 44
 PROBLEMS RELATING TO TRIANGLES 53 PARALLELOGRAMS 59 MEASUREMENT OF SURFACES 66 THE CIRCLE AND ITS LINES 73 PARTS OF THE CIRCLE 82 THEOREMS ILLUSTRATED 88

### Popular passages

Page 25 - Then it is called an acute angle. An acute angle is one which is less than a right angle.
Page 134 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.
Page 152 - PROPOSITION XXII. THEOREM. DEMONSTRATION. We wish to prove that The angle formed by a tangent and a chord meeting at the point of contact is measured by half the intercepted arc. Let the tangent CAB and the chord AD meet at the point of contact A ; then will the angle BAD be measured by half the intercepted arc A D. For draw the diameter AE F. Because AB is a tangent, and AE a radius at the point of contact, the angle BAF is a right angle, and is measured by the semicircle AD F.
Page 138 - If two triangles have two angles and the included side of the one, equal to two angles and the included side of the other, each to each, the two triangles will be equal.
Page 74 - A circle is a plane figure bounded by a curved line, all points of which are equally distant from the centre. The curved line is called a "circumference.
Page 147 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 156 - But D c F is an angle at the circumference, and is therefore measured by half the arc F D. Then the equal angle DEB must be measured by half of the arc FD, or its equal BD, plus A c.
Page 83 - A. semicircle is half a circle. Read four segments each larger than a semicircle. The part of the circle between the two radii of, oi, and the arc/ i, is called a " sector." Read four sectors each less than one-fourth of a circle.* A sector is a part of a circle bounded by two radii and an arc. What part of the whole circle is the sector/ oh? It is called a
Page 88 - Things which are double of the same thing, are equal to each other. 7. Things which are halves of the same thing, are equal to each other. 8. The whole is greater than any of its parts. 9. The whole is equal to the sum of all its parts. 10. All right angles are equal to each other. II. From one point to another, only one straight line can be drawn.