## The Elements of Geometry |

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### Common terms and phrases

altitude angles are equal angles equal arms base bisect called chord circle coincide common CONCLUSION construction contained COROLLARY corresponding describe diagonals divided double draw drawn equal equilateral equivalent EXERCISES exterior angle figure four geometry given given line given point greater half Hence HYPOTHESIS included angle inscribed intercepted interior intersection inverse isosceles triangle Join less locus magnitudes mean meet multiples pair parallel parallelogram pass perigon perimeter perpendicular plane polygon position PROBLEM produced PROOF proved radii radius ratio rectangle regular polygon remainder REQUIRED respectively right angle Rule sect segment sides space sphere spherical square statement straight angle supplemental surface symmetrical taken tangent THEOREM thing third three sides transversal triangle triangles are congruent turning unequal vertex vertices whole

### 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 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.

Page 103 - 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.