The Elements of Geometry |
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Common terms and phrases
altitude angles equal apothem base and altitude bisector bisects chord circumference circumscribed Conc concur congruent Const construct convex surface cube diagonals diameter dihedral distance divided Draw drawn edge equals the sum equilateral triangle exterior figure Find frustum geometry given circle given line given point homologous sides hypotenuse inscribed interior angles intersect isoangular isosceles triangle join line-segment locus median mid-join mid-perpendicular n-gon number of sides parallel parallelogram pass perimeter perpendicular perpendicular to plane plane MQ polyhedral polyhedron prism PROB proof Prove pyramid radii radius ratio rectangle rectangular parallelepiped regular hexagon regular polygon right angles right circular right triangle segments Show Similarly slant height sphere spherical spherical polygon square straight line SUMMARY OF PROPOSITIONS supplemental tangent theorem total surface trapezoid triangle equals trihedral vertex angle vertices volume
Popular passages
Page 234 - The projection of a point on a plane is the foot of the perpendicular from the point to the plane. The projection of a figure upon a plane is the locus of the projections of all the points of the figure upon the plane. Thus, A'B' represents the projection of AB upon plane MN.
Page 110 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Page 113 - The circumference of every circle is supposed to be divided into 360 equal parts called degrees, and each degree into 60 equal parts called minutes, and each minute into 60 equal parts called seconds, and these into thirds, fourths, &c.
Page 282 - A cylinder is a solid bounded by a cylindrical surface and two parallel planes intersecting this surface.
Page 110 - In any proportion, the product of the means equals the product of the extremes.
Page 179 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.
Page 210 - The center of a regular polygon is the common center of the circumscribed and inscribed circles of the polygon.
Page 50 - Through a given point to draw a line parallel to a given straight line.
Page 233 - A PLANE is a surface, such, that if any two of its points be joined by a straight line, such.
Page 59 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, they are equal in all their parts.