## 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 angles 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 regular inscribed regular polygon respectively equal right angles right triangle Scholium secant secant line 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 22 - In an isosceles triangle the angles opposite the equal sides are equal.

Page 133 - The area of a rectangle is equal to the product of its base and altitude.

Page 247 - 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.

Page 117 - 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 267 - A spherical angle is measured by the arc of a great circle described from its vertex as a pole and included between its sides (produced if necessary). Let AB, AC be arcs of great circles intersecting at A; AB...

Page 113 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.

Page 38 - The sum of the three angles of any triangle is equal to two right angles.

Page 210 - If two intersecting planes are each perpendicular to a third plane, their intersection is also perpendicular to that plane. Let the planes BD and BC intersecting in the line AB be perpendicular to the plane PQ.

Page 54 - Every point in the bisector of an angle is equally distant from the sides of the angle ; and every point not in the bisector is unequally distant from the sides of the angle...