## The Elements of Geometry |

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### Common terms and phrases

ABCD alternate angles angles are equal angles equal angles opposite base bisect called chord circumcenter coincide common commutative law CONCLUSION construction COROLLARY diagonal diameter divided draw end point equal are congruent equal sects equiangular equilateral equivalent exterior angle figure given line given point given sect greater greatest common divisor hypothenuse HYPOTHESIS included angle inscribed inscribed angle intercepted interior isosceles triangle less line perpendicular magnitudes meet multiples number of sides pair parallelogram pass perigon perimeter perpendicular bisector plane MN PROOF proportional quadrilateral radii radius ratio rectangle rectangle contained regular polygon respectively equal right angle Rule of Inversion sect joining segment sphere spherical polygon spherical triangle square straight angle subtended surface symmetrical tangent tetrahedron THEOREM THEOREM VII transversal triangles are congruent vertex vertices

### Popular passages

Page 44 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.

Page 112 - 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 24 - A right-angled triangle is one which has a right angle. The side opposite the right angle is called the hypothenuse.

Page 190 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Page 270 - BC with the same radius. Then a line through A touching this arc will be the required parallel. Or, use a straight edge and triangle.

Page 101 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.

Page 266 - If two triangles have two sides and the included angle of one equal respectively to two sides and the included angle of the other, the triangles are equal.

Page 104 - 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...

Page 107 - In an obtuse-angled triangle the square on the side opposite the obtuse angle is greater than the sum of the squares on the other two sides by twice the rectangle contained by either side and the projection on it of the other side.