## An Elementary Geometry: Plane, Solid, and Spherical : with Numerous Exercises Illustrative of the Principles of Each Book |

### From inside the book

Page 60

...

...

**the squares of the other two sides plus twice the product of one of**these sides and the distance from the vertex of the obtuse angle to the foot of the perpendicular let fall upon this side from the vertex of the opposite angle . If A ...### Other editions - View all

### Common terms and phrases

A B D ABCD adjacent angles altitude apothem arcs A B centre chord circumference circumscribed polygon construct the triangle convex surface Corollary diagonals diameter dicular diedral angles distance divided draw edges equal angles equally distant equivalent bases face angles feet frustum given angle given line given point given side hence homologous lines hypothenuse intersection isosceles triangle line joining line parallel lines A B lines drawn locus middle points mutually equiangular number of sides opposite sides parallelogram parallelopiped perimeter perpen perpendicular plane M N polar triangle polyedral angle polyedrons produced proposition pyramid quadrilateral radii radius ratio rectangle regular polygon respectively equal right triangle Scholium segments similar sphere spherical angle spherical polygon spherical triangle square tangent tetraedron THEOREM triangle A B C triangle is equal triangular prism triedral vertex vertices

### Popular passages

Page 129 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.

Page 164 - Any two rectangles are to each other as the products of their bases by their altitudes.

Page 123 - To construct a square equivalent to the sum of two given squares.

Page 118 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.

Page 20 - If two triangles have two sides of one respectively equal to two sides of the other, and the angles contained by those sides supplementary, the triangles are equal in area.

Page 75 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.

Page 218 - If one angle of a triangle is equal to the sum of the other two, the triangle can be divided into two isosceles triangles.

Page 201 - In an isosceles spherical triangle, the angles opposite the equal sides are equal.

Page 114 - Through a given point to draw a line parallel to a given straight line. Let C be the given point, and AB the given line. From C draw a line CD to AB; at C in the line DC make an angle DCE equal to CDA (5); CE is parallel to AB (I.

Page 134 - A straight line is perpendicular to a plane, when it is perpendicular to every straight line of the plane which it meets.