# The First Book of Euclid's Elements, Simplified, Explained, and Illustrated for the Use of Beginners. ... By W. Trollope

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### Contents

 Section 1 6 Section 2 10 Section 3 11 Section 4 20 Section 5 23 Section 6 27 Section 7 28 Section 8 29
 Section 19 69 Section 20 71 Section 21 81 Section 22 84 Section 23 86 Section 24 90 Section 25 93 Section 26 94

 Section 9 30 Section 10 35 Section 11 41 Section 12 45 Section 13 46 Section 14 56 Section 15 57 Section 16 58 Section 17 61 Section 18 65
 Section 27 95 Section 28 99 Section 29 100 Section 30 101 Section 31 103 Section 32 108 Section 33 111 Section 34 112 Section 35 115

### Popular passages

Page 58 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Page 24 - Upon the same base, and on the same side of it, there cannot be two triangles, that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity, equal to one another.
Page 34 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Page 6 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.
Page 109 - If the square described upon one of the sides of a triangle, be equal to the squares described upon the other two sides of it; the angle contained by these two sides is a right angle.
Page 9 - Parallel straight lines are such as are in the same plane, and which being produced ever so far both ways, do not meet.
Page 99 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Page 49 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle. Let...
Page 104 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Page 6 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.