## Elements of Plane Geometry |

### Other editions - View all

### Common terms and phrases

AB² AC² altitude angle formed angles are equal base BC² bisector bisects central angle chord circumcenter circumference circumscribed circle decagon diagonals diameter Draw drawn equal circles equiangular equiangular polygon equilateral triangle equivalent exterior Find the area geometry given circle given line given point Given the line Hence homologous sides hypotenuse inscribed circle inscribed polygon inscribed regular intercepted arc interior angles intersecting isosceles triangle legs limit measured by arc median nine-point circle number of sides orthocenter parallel parallelogram perigon perimeter perpendicular points equidistant prove Proof Q. E. D. Ex Q. E. D. PROPOSITION quadrilateral radii radius ratio rectangle regular inscribed regular polygon respectively rhombus right angle right triangle secant segments similar polygons square straight angle straight line tangent THEOREM third side trapezoid triangle ABC triangle is equal vertex vertical angle

### Popular passages

Page 41 - 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 42 - ... if two triangles have two sides of one equal, respectively, to two sides of the other...

Page 179 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.

Page 5 - Axioms. 1. Things which are equal to the same thing are equal to each other. 2. If equals are added to equals, the wholes are equal. 3. If equals are taken from equals, the remainders are equal.

Page 135 - Conversely, if the product of two quantities is equal to the product of two other quantities, the first two may be made the extremes, and the other two the means of a proportion.

Page 67 - A Polygon of three sides is called a triangle ; one of four sides, a quadrilateral; one of five sides, a pentagon; one of six sides, a hexagon; one of seven sides, a heptagon; one of eight sides, an octagon ; one of ten sides, a decagon ; one of twelve sides, a dodecagon, &c.

Page 176 - The sum of the squares of two sides of a triangle is equal to twice the square of half the third side increased by twice the square of the median upon that side.

Page 173 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides by the projection of the other upon that side.

Page 17 - In a right triangle, the side opposite the right angle is called the hypotenuse, and the other two sides the legs.

Page 202 - Assuming that the areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles...