## Plane and Solid Geometry (Google eBook) |

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### Common terms and phrases

ABCD acute angle adjacent adjacent angles altitude angle formed angles are equal apothem arc BC base and altitude bisect bisector called centre chord circumference cone construct a square cylinder diagonals diameter diedral angles distance divided draw equally distant equilateral equivalent face-angles faces four right angles frustum given point given straight line hence homologous sides hypotenuse inscribed polygon interior angles intersection isosceles triangle join lateral area lateral edges Let ABC lune mean proportional measured by one-half middle point mutually equiangular number of sides oblique lines parallelogram perimeter perpendicular plane MN polyedral angle polyedron Proposition VIII prove q.e.d. EXERCISES q.e.d. Proposition quadrilateral radii radius ratio rectangle rectangular parallelopiped regular polygon rhombus right triangle Scholium segments semiperimeter sphere spherical angle spherical polygon spherical triangle surface tangent Theorem triangle ABC triangles are equal triangular prism V-ABC vertex vertical angle 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.