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

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### Common terms and phrases

acute adjacent altitude base bisecting Book called centre chord circle circumference circumscribed coincide common cone constant contained Conversely Corollary DEFINITIONS described diagonals diameter diedral angles difference direction distance divided draw drawn edges equal equally distant equilateral equivalent extremities feet figure formed four frustum given angle given line given point greater half hence homologous lines included inscribed intersection isosceles triangle less locus manner mean measure meet number of sides opposite opposite sides parallel parallelogram parallelopiped pass perimeter perpendicular plane plane M N polygon prism PROBLEM produced proportion proposition proved pyramid quantity radius ratio rectangle regular polygon respectively right angles right triangle segments sides similar sphere spherical triangle square straight line tangent THEOREM third triangle A B C triangular triedral vertex vertices volume

### 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.