## Chauvenet's Treatise on Elementary Geometry |

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### Common terms and phrases

ABCD adjacent altitude angle BAC angles are equal base bisect called centre chord circle circumference coincide common consequently construct contain Conversely Corollary corresponding Definition describe diagonals diameter difference direction distance divided draw drawn edges equal equally distant expressed exterior extremities faces fall figure follows formed four geometry given point greater hence homologous included indefinite inscribed intersection join less limit line drawn mean measure meet middle point oblique one-half opposite sides parallel parallelogram pass perimeter perpendicular placed plane polygon portion position preceding prism problem produced proportion PROPOSITION quadrilateral quantities radii radius ratio rectangle regular respectively revolving right angles Scholium secant segment sides similar square straight line suppose surface symmetrical tangent theorem third triangle ABC unit vertex vertices

### Popular passages

Page 201 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...

Page 31 - The perpendicular is the shortest line that can be drawn from a point to a straight line. Let PC be the perpendicular, and PD any oblique line, from the point P to the line AB. Then PC < PD. For, produce PC to P', making CP

Page 201 - Words, Facts, and Phrases : A Dictionary of Curious, Quaint, and Out-of-the-Way Matters. By ELIEZER EDWARDS.

Page 120 - Any side of a spherical triangle is less than the sum of the other two.

Page 81 - 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 92 - Every point in the bisector of an angle is equally distant from the sides of the angle...

Page 58 - An angle formed by a tangent and a chord is measured by one-half the intercepted arc.