## Chauvenet's Treatise on Elementary Geometry |

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### Common terms and phrases

ABCD adjacent altitude 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 edges equal equivalent Exercise extremities faces fall feet figure follows formed four given circle given line given point given straight line greater half Hence hypotenuse increased indefinitely inscribed intersection joining lateral length less limit locus measure meet middle point number of sides one-half parallel parallelogram pass perimeter perpendicular placed plane plane MN polygon prism problem Proposition XIV prove pyramid radii radius ratio rectangle regular regular inscribed regular polygon respectively right angles right triangle Scholium segments sides similar sphere spherical square Suggestion surface tangent Theorem third triangle triangle ABC unit vertex vertices volume

### Popular passages

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

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

Page 249 - 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 282 - The area of a lune is to the surface of the sphere as the angle of the lune is to four right angles, or as the arc which measures that angle is to the circumference.

Page 214 - The acute angle which a straight line makes with its projection upon a plane is the least angle which it makes with any line of the plane.

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...

Page 79 - An angle formed by a tangent and a chord is measured by one-half the intercepted arc.

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.