## Euclid, Book 1 |

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### Common terms and phrases

ABCD AC is equal adjacent Algebra alternate angle ABC angle ACB angle AGH angle BAC Axiom base base BC bisect called centre circle Constr Construct depend describe diagonals difference divided double draw draw a line drawn Education equal equal to twice Euclid example EXERCISES exterior angle fall figure four given point given straight line greater half inches intersect isosceles triangle join length less locus measure meet method middle point NOTES opposite sides parallel parallelogram perpendicular Problem produced proof Prop Proposition prove radius rectangle AQ rectangle contained respects rider right angles sides equal square on AC Stage student Take taken Theorems third triangle ABC Tutorial twice the rectangle unequal University vertex whole

### Popular passages

Page 45 - 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 126 - 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 on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.

Page 31 - 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 138 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part.

Page 2 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.

Page 66 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Page 130 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.

Page 99 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.

Page 26 - To draw a straight line at right angles to a given straight line, from a given point in the same.

Page 63 - Through a given point to draw a straight line parallel to a given straight line, Let A be the given point, and BC the given straight line : it is required to draw through the point A a straight line parallel to BC.