## Euclid's Elements of geometry, books i. ii. iii. iv |

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ABCD angle ABC angle BAC angle BCD angle equal assumed base base BC BC is equal bisected BOOK centre circle ABC circumference coincide common Conclusion Conclusion.—Therefore const Construction Construction.-1 Demonstration Demonstration.-1 describe diameter distance divided double draw drawn equal exterior angle extremities fall figure four given circle given point given straight line greater half Hypothesis Hypothesis.—Let impossible inscribed join less manner meet opposite angles parallel parallelogram pass perpendicular produced proved Q. E. D. PROPOSITION reason rectangle contained rectilineal figure References-Prop right angles segment semicircle Sequence.—The shown sides square on AC straight line AC Take third touches the circle triangle ABC twice the rectangle whole

### Popular passages

Page 25 - 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.

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.

Page 99 - 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 4 - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...

Page 66 - ... 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 65 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.

Page 32 - F, which is the common vertex of the triangles ; that is, together with four right angles. Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Page 58 - 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...

Page 88 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...

Page 33 - The straight lines which join the extremities of two equal and parallel straight lines towards the same parts, are also themselves equal and parallel.