## An Elementary Treatise on Plane and Solid Geometry |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

### Common terms and phrases

adjacent altitude applied base called centre chord circle circumference coincide common cone construct contained convex surface Corollary cylinder Definitions denote described diameter difference divided draw drawn equal equal distances equiangular equilateral equivalent extremities faces fall figure formed frustum give given given circle given polygon given square greater half the product Hence homologous sides hypothenuse included infinitely small inscribed isosceles Join less measure meet middle number of sides opposite parallel parallel lines parallelogram parallelopipeds passes perimeter perpendicular plane polyedron preceding prism Problem Proof prove pyramid radii radius ratio rectangles regular polygon remainder respectively right angles right triangle Scholium sector segment side BC similar similar polygons Solution sphere spherical triangle square straight line Suppose surface Take tangent Theorem third triangles ABC vertex vertices whence

### Popular passages

Page 68 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.

Page 127 - Every section of a sphere, made by a plane, is a circle, Let AMB be a section, made by a plane, in the sphere whose centre is C.

Page 71 - Rectangles of the same altitude are to each other as their bases, and rectangles of the same base are to each other as their altitudes. 245.

Page 20 - The sum of the three angles of any triangle is equal to two right angles.

Page xv - The first term of a ratio is called the antecedent, and the second term the consequent.

Page 83 - ... we suppose the error A to be of any magnitude whatever. 286. Definition. Similar sectors and similar segments are such as correspond to similar arcs. 287. Theorem. Similar sectors are to each other as the squares of their radii. Proof. The similar sectors AOB, A'OB ' (fig. 136) are, by the same reasoning as in t5 97, the same parts of their respective circles, which the angle O= O...

Page 31 - Theorem. In the same circle, or in equal circles, equal arcs are subtended by equal chords.

Page 87 - To construct a parallelogram equivalent to a given square, and having the sum of its base and altitude equal to a given line.

Page 99 - B, from the plane. 320. Theorem. Oblique lines drawn from a point to a plane at equal distances from the perpendicular are equal; and of two oblique lines unequally distant the more remote is the greater.

Page 78 - Similar triangles are to each other as the squares of their homologous sides. Proof. In the similar .triangles ABC, A'B'C