## Chauvenet's Treatise on Elementary Geometry |

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### Common terms and phrases

ABCD adjacent altitude angles are equal base bisects BOOK called centre chord circle circumference circumscribed coincide common cone consequently construct contains Corollary cylinder Definition describe diagonal diameter diedral angle difference distance divided draw drawn equal equivalent Exercise extremities faces fall figure follows formed four frustum given line given point given straight line greater half Hence included angle increased indefinitely inscribed intersection isosceles joining length less limit locus mean measure meet middle point number of sides one-half opposite parallel parallelogram parallelopiped pass perimeter perpendicular placed plane pole polyedron polygon prism problem proportional Proposition VII prove pyramid radii radius ratio rectangle regular polygon respectively right angles Scholium segment sides similar sphere spherical square Suggestion surface tangent Theorem third triangle triangle ABC unit vertex vertices 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.