## Elements of Geometry Containing Books I. to VI. and Portions of Books XI. and XII. of Euclid, with Exercises and Notes |

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### Common terms and phrases

ABCD alternate base bisected Book called centre chord circle circumference coincide common construction described diagonals diameter difference distance divided double draw drawn equal equilateral equimultiples Eucl Euclid exterior angle extremities fall figure four given point given straight line greater half Hence inscribed intersect isosceles triangle join length less Let ABC magnitudes measure meet method multiple NOTE opposite sides parallel parallelogram pass perpendicular PROBLEM produced proof Prop PROPOSITION prove Q. E. D. Ex quadrilateral ratio rect respects right angles segment shew shewn sides Similarly square suppose Take taken tangent THEOREM third touch triangle triangle ABC twice vertex vertical whole

### Popular passages

Page 23 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it. Let AB be the given straight line, which may be produced to any length both ways, and let c be a point without it. It is required to draw a straight line perpendicular to AB from the point c. Take any point D upon the other side of AB, and from the centre c, at the distance CD, describe (Post.

Page 82 - If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.

Page 40 - 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 161 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.

Page 91 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle, Let ABC be any triangle, and the angle at B one of its acute angles, and upon BC, one of the sides containing it, let fall the perpendicular AD from the opposite angle.

Page 5 - 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.

Page 5 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.

Page 35 - ... shall be equal to three given straight lines, but any two whatever of these must be greater than the third.

Page 90 - ... the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse...

Page 265 - EQUAL parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles...