## Elementary Geometry, Plane and Solid: For Use in High Schools and Academies |

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### Other editions - View all

Elementary Geometry Plane and Solid: For Use in High Schools and Academies Thomas F. Holgate No preview available - 2015 |

Elementary Geometry, Plane and Solid; For Use in High Schools and Academies Thomas F 1859-1945 Holgate No preview available - 2015 |

### Common terms and phrases

ABCD adjacent altitude base bisector bisects boundaries called centre chord circle circular circumscribed coincide common cone construct contains COROLLARY cylinder DEFINITION described diagonals diameter difference dihedral angle distance divided draw drawn edges equidistant equilateral EXERCISES face angles faces figure Find fixed formed four geometrical given line-segment given plane given point greater half Hence identically equal inscribed intersect isosceles joining length less lies limit line-segment lying magnitudes mean measure meet mid-point opposite sides pair parallel parallel planes parallelogram pass perimeter perpendicular placed plane polygon polyhedron position prism Proof Prop proportional PROPOSITION pyramid quadrilateral radii radius ratio rectangle regular polygon required to prove respectively right angles segment Show sides similar Similarly sphere square straight line subtended Suppose surface tangent theorem third triangle unequal unit vertex vertices volume

### Popular passages

Page 187 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Page 207 - The formula states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the base and altitude.

Page 78 - The line which joins the mid-points of two sides of a triangle is parallel to the third side and equal to one half of it.

Page 45 - Prove that, if two sides of a triangle are unequal, the angle opposite the greater side is greater than the angle opposite the less.

Page 231 - A polygon of three sides is called a triangle ; one of four sides, a quadrilateral; one of five sides, a, pentagon; one of six sides, a hexagon ; one of seven sides, a heptagon ; one of eight sides, an octagon ; one of ten sides, a decagon ; one of twelve sides, a dodecagon.

Page 95 - 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 200 - The area of a triangle is equal to half the product of its base by its altitude.

Page 161 - ... 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 201 - Two parallelograms are similar when they have an angle of the one equal to an angle of the other, and the including sides proportional.

Page 29 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.