## 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 equally distant equivalent Exercise extremities faces fall figure follows formed four frustum given line given point given straight line greater 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 plane pole polyedron polygon prism problem proportional Proposition VII prove pyramid radii radius ratio rectangle regular polygon right angles Scholium segment sides similar sphere spherical square Suggestion surface tangent Theorem third triangle triangle ABC unit vertex vertices volume

### Popular passages

Page 200 - 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 133 - The area of a rectangle is equal to the product of its base and altitude.

Page 137 - 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 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 214 - The acute angle which a straight line makes with its own projection upon a plane is the least angle which it makes with any line of that plane.

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 184 - If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side.

Page 128 - Find the locus of a point the sum of whose distances from two given straight lines is equal to a given constant, k.

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.