## Solid Geometry, Volumes 6-9 |

### From inside the book

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**have an angle of the one equal to an angle of the other**, and the including sides proportional , they are similar . 358. If two triangles have their sides respectively propor- tional xiv REFERENCES TO PLANE GEOMETRY . Page 250

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**have 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 . 412. The areas of two similar polygons are to each other as the squares of any two homologous sides ...### Other editions - View all

### Common terms and phrases

ABCDE altitude auxiliary circle bisects called centre chord circumference circumscribed coincide convex cube curve diameter dihedral angles directrix distance Draw drawn ellipse equidistant equivalent face angles feet Find the volume focal radii foci frustum given plane given point Hence homologous hyperbola inches inscribed intersection lateral area lateral edges lateral faces latus rectum limit lune parabola parallel planes pass a plane perimeter perpendicular plane MN plane parallel plane passing PMē polyhedral angle polyhedron prismatoid Proof prove Q. E. D. PROPOSITION radius rectangular parallelopiped regular polygon regular pyramid respectively right circular cone right circular cylinder right prism right section S-ABC segment similar slant height sphere spherical angle spherical polygon spherical triangle square straight line symmetrical tangent tetrahedron THEOREM total surface triangular prism trihedral upper base vertex vertices Wentworth's

### Popular passages

Page 274 - If two planes are perpendicular to each other, a straight line drawn in one of them, perpendicular to their intersection, is perpendicular to the other.

Page 360 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.

Page 383 - The arc of a great circle drawn from the vertex of an isosceles spherical triangle to the middle of the base bisects the vertical angle, is perpendicular to the base, and divides the triangle into two symmetrical triangles.

Page 250 - The areas of two triangles which have 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. To prove that Proof. A Let the triangles ABC and ADE have the common angle A. A ABC -AB X AC Now and A ADE AD X AE Draw BE.

Page 246 - 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 245 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.

Page 370 - A spherical angle is measured by the arc of the great circle described from its vertex as a pole and ) included between its sides (produced if necessary). Let AB, AC be arcs of great circles intersecting at A; AB...

Page 366 - A plane perpendicular to a radius at its extremity is tangent to the sphere. Let...

Page 295 - An oblique prism is equivalent to a right prism whose base is equal to a right section of the oblique prism, and whose altitude is equal to a lateral edge of the oblique prism. r Let FI be a right section of the oblique prism AD', and FI' a right prism whose lateral edges are equal to the lateral edges of AD'.

Page 395 - The area of a lune is to the area of the surface of the sphere as the angle of the lune is to four right angles.