## Chauvenet's Treatise on Elementary Geometry |

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### Common terms and phrases

ABCD adjacent angles altitude angles are equal apothem bisects centre chord coincide common cone construct convex Corollary cylinder Definition diagonal diameter dicular diedral angle distance divided draw equal circles equally distant equilateral equivalent Exercise find the locus frustum given circle given line given point given straight line greater Hence hypotenuse included angle inscribed angle intercepted arcs isosceles triangle lateral area lateral edges mean proportional middle point number of sides parallel lines parallelogram parallelopiped pass a plane pendicular perimeter perpen perpendicular plane angle plane MN plane passed polyedral angle Proposition VI PROPOSITION VII quadrilateral radii radius ratio rectangle rectangular parallelopiped regular inscribed regular polygon respectively equal right angles right triangle Scholium secant segment similar slant height sphere spherical polygon spherical triangle square surface tangent tetraedron THEOREM triangle ABC triangles are equal triangular prism triedral upper base vertex volume

### Popular passages

Page 139 - Two triangles having 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.

Page 135 - The area of a rectangle is equal to the product of its base and altitude.

Page 119 - The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.

Page 29 - The perpendicular is the shortest line that can be drawn from a point to a straight line.

Page 251 - A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism, and whose vertices are the three vertices of the inclined section. Let ABC-DEF be a truncated triangular prism whose base is ABC and inclined section DEF.

Page 280 - Each side of a spherical triangle is less than the sum of the other two sides.

Page 52 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.

Page 270 - Any line or plane tangent to a sphere is perpendicular to the radius drawn to the point of contact.

Page 202 - If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of those lines.

Page 81 - An angle formed by a tangent and a chord is measured by one-half the intercepted arc.