## Plane and Solid Geometry |

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### Common terms and phrases

ABCD adjacent altitude angles are equal base bisect bisector called centre chord circle circumference circumscribed coincide common cone construct cylinder diagonals diameter diedral angles difference distance divided draw drawn edges equal equally distant equiangular equilateral equivalent EXERCISES faces fall figure formed four frustum given greater hence homologous included inscribed interior angles intersection isosceles join known lateral less Likewise limit mean measured meet number of sides oblique one-half opposite parallel parallelogram parallelopiped passes perimeter perpendicular plane polyedron polygon portion prism PROBLEM proportional PROPOSITION prove pyramid quantity radii radius ratio rectangle regular polygon respectively right angles right triangle segments Show sides similar sphere spherical square straight line SUGGESTION surface tangent THEOREM third triangle triangle ABC vertex vertices volume

### Popular passages

Page 46 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the centre.

Page 105 - ... any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V. THEOREM. 403. The area of a triangle is equal to half the product of its base by its altitude.

Page 82 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.

Page 192 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.

Page 108 - 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 146 - A STRAIGHT line is perpendicular to a plane, when it is perpendicular to every straight line which it meets in that plane.

Page 30 - In an isosceles triangle, the angles opposite the equal sides are equal.

Page 80 - In any proportion the terms are in proportion by Composition ; that is, the sum of the first two terms is to the first term as the sum of the last two terms is to the third term.

Page 79 - If the product of two quantities is equal to the product of two others, one pair may be made the extremes, and the other pair the means, of a proportion. Let ad = ос.

Page 148 - Equal oblique lines from a point to a plane meet the plane at equal distances from the foot of the perpendicular ; and of two unequal oblique lines the greater meets the plane at the greater distance from the foot of the perpendicular.