## Elements of Plane and Solid Geometry |

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### Common terms and phrases

AABC ABē ABC and DEF ACē altitude angle formed angles are equal angles equal apothem bisector bisects chord circum circumference cone Construct a triangle COROLLARY cylinder DEFINITION diagonals diameter dihedral angles divided Draw EFGH equally distant equiangular polygon equilateral triangle equivalent EXERCISE exterior angles Find frustum given circle given line given point hypotenuse inscribed angle isosceles triangle joining the middle lateral area Let ABC Let To Prove line joining medians meet middle points number of sides opposite sides parallel parallelogram parallelopiped perimeter perpendicular point of intersection polyhedron prism prolonged PROPOSITION Prove ABCD pyramid quadrilateral radii radius rectangle regular inscribed regular polygon rhombus right angles right-angled triangle SCHOLIUM secants segments Show similar polygons slant height sphere spherical square straight line surface tangent tetrahedron THEOREM trapezoid triangle ABC trihedral unequal vertex vertical angle volume Whence

### Popular passages

Page 167 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.

Page 139 - A line parallel to one side of a triangle divides the other two sides proportionally.

Page 187 - Any two rectangles are to each other as the products of their bases by their altitudes.

Page 202 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.

Page 180 - In an inscribed quadrilateral, the product of the diagonals is equal to the sum of the products of the opposite sides.

Page 90 - In the same circle, or in equal circles, equal chords are equally distant from the center; and, conversely, chords equally distant from the center are equal.

Page 195 - Since similar triangles are to each other as the squares of their homologous sides, ABC : DBE : : AB' : BD3 ; whence BD = AB J ^5| ~ AB A/— ^ — . j A150 f in -f- n The construction of Fig.

Page 129 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D ; and read, A is to B as C to D.

Page 15 - If two triangles have two sides and the included angle of one equal respectively to two sides and the included angle of the other, the triangles are equal.

Page 17 - If two triangles have two angles and the included side of one equal respectively to two angles and the included side of the other, the triangles are congruent.