## Plane and Solid Geometry |

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### Common terms and phrases

AABC ABCD altitude angles are equal apothem bisector bisects called chord circular cone circumference circumscribed coincide cone of revolution congruent conic surface construct COROLLARY cube diagonal diameter dihedral angles distance draw equidistant equilateral triangle equivalent EXERCISE face angles figure Find the area Find the locus Find the volume frustum given circle given line given point greater hypotenuse inscribed intersection isosceles triangle lateral area lateral edges lateral faces lune measured by arc mid-point number of sides oblique parallel lines parallelogram perimeter perpendicular plane geometry plane MN polyhedral angle polyhedron Proof proportional prove quadrilateral radii radius ratio rectangle rectangular parallelepiped regular polygon regular pyramid right angle right prism right section right triangle segments slant height sphere spherical polygon spherical triangle square straight angle straight line surface symmetric tangent tetrahedron THEOREM triangle ABC trihedral vertex vertices

### Popular passages

Page 67 - The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side.

Page 360 - Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases.

Page 190 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.

Page 152 - If the product of two quantities is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means.

Page 54 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.

Page 31 - In an isosceles triangle the angles opposite the equal sides are equal.

Page 77 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Given A ABC and A'B'C...

Page 51 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.

Page 22 - The following are the most important axioms used in geometry: 1. If equals are added to equals the sums are equal. 2. If equals are subtracted from equals the remainders are equal. 3. If equals are multiplied by equals the products are equal. 4. If equals are divided by equals the quotients are equal.

Page 213 - The square constructed upon the sum of two lines is equivalent to the sum of the squares constructed upon these two lines, increased by twice the rectangle of these lines.