Elements of Geometry and Trigonometry: With Notes
J. Ryan, 1830 - Geometry - 316 pages
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ABCD altitude base called centre chord circle circumference circumscribed common cone consequently construction contained cosines cylinder demonstration described determined diameter difference distance divided draw drawn equal equation equivalent evident expressed extremities faces fall figure follows formed formulas four give given gles greater half hence homologous inclination included inscribed intersection join less likewise manner means measure meet multiplied opposite parallel parallelogram pass perpendicular plane polyedron polygon prism PROBLEM proportion proposition pyramid quantities radii radius ratio reason rectangle regular remain respectively right angles Scholium sector sides similar sines solid angle solution sphere spherical triangle square straight line suppose surface taken tang tangent THEOREM third triangle triangle ABC vertex vertices whole
Page 74 - Two similar polygons are composed of the same number of triangles, similar each to each, and similarly situated.
Page 26 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Page 176 - The radius of a sphere is a straight line, drawn from the centre to any point of the surface ; the diameter, or axis, is a line passing through this centre, and terminated on both sides by the surface.
Page 243 - If two angles of one triangle are equal to two angles of another triangle, the third angles are equal, and the triangles are mutually equiangular.
Page 58 - Two triangles of the same altitude are to each other as their bases, and two triangles of the same base are to each other as their altitudes. And triangles generally, are to each other, as the products of their bases and altitudes.
Page ii - District, has deposited in this office the title of a book, the right whereof he claims as proprietor, in the words following, to wit : " THE CHILD'S BOTANY," In conformity to the act of the Congress of the United States, entitled, " An act for the encouragement of learning by securing the copies of maps, charts, and books to the authors and proprietors of such copies, during the times therein mentioned...
Page 280 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Page 126 - If one of two parallel lines is perpendicular to a plane, the other will also be perpendicular to the same plane.
Page 28 - THEOREM. A straight line cannot meet the circumference of a circle in more than two points.
Page 161 - ... bases simply : hence two prisms of the same altitude are to each other as their bases. For a like reason, two prisms of the same base are to each other as their altitudes.