# Marks' First Lessons in Geometry: In Two Parts : Objectively Presented and Designed for the Use of Primary Classes in Grammar Schools, Academies, Etc

Ivison, Blakeman, Taylor,, 1871 - Geometry - 157 pages

### 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 74 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the center.
Page 24 - An ACUTE ANGLE is one which is less than a right angle ; as the angle DEF.
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 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.
Page 25 - Then it is called an acute angle. An acute angle is one which is less than a right angle.
Page 83 - A segment bounded by a diameter and a semicircumference is a "semicircle." 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/z, is called a
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.