# Euclid, books i. & ii., with notes, examples, and explanations, by a late fellow and senior mathematical lecturer

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### Contents

 Section 1 1 Section 2 4 Section 3 5 Section 4 6 Section 5 7 Section 6 11 Section 7 24 Section 8 25
 Section 15 39 Section 16 47 Section 17 48 Section 18 49 Section 19 52 Section 20 60 Section 21 66 Section 22 77

 Section 9 28 Section 10 29 Section 11 31 Section 12 32 Section 13 34 Section 14 38
 Section 23 83 Section 24 100 Section 25 104 Section 26 116 Section 27 118 Section 28

### Popular passages

Page 48 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Page 32 - 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 2 - 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 : 16. And this point is called the centre of the circle. 17. A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Page 109 - If a straight line be bisected, and produced to any point; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line, which is made up of the half and the part produced.
Page 1 - ... angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it. 11. An obtuse angle is that which is greater than a right angle. 12. An acute angle is that which \ is less than a right angle. 13. A term or boundary is the extremity of any thing.
Page 6 - Notions 1. Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. Things which coincide with one another are equal to one another.
Page 77 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Page 3 - An equilateral triangle is that which has three equal sides : 25. An isosceles triangle is that which has two sides equal : 26. A scalene triangle is that which has three unequal sides : 27.
Page 1 - 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 84 - 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.