Elements of Geometry and Trigonometry: With Notes
J. Ryan, 1828 - Geometry - 316 pages
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ABCD altitude base called centre chord circ 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 sine solid angle sphere spherical triangle square straight line suppose surface taken tang tangent THEOREM third triangle triangle ABC vertex vertices whole
Page 257 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Page iii - 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 187 - For, if the arc AD be drawn from the vertex A to the middle point D of the base, the two triangles ABD, ACD, will have all the sides of the one respectively equal to the corresponding sides of the other...
Page 3 - A right-angled triangle is one which has a right angle. The side opposite the right angle is called the hypothenuse.
Page 27 - 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 11 - If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side.
Page 73 - If two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar. In the two polygons ABCDE and A'B'C'D'E', let the triangles AEB, EEC, CED be similar, respectively, to the triangles A'E'B', B'E'C', C'E'D'; and similarly placed.
Page 157 - Any two rectangular parallelopipedons are to each other as the products of their bases by their altitudes ; that is to say, as the products of their three dimensions.
Page 107 - ... of the regular inscribed and circumscribed polygons having double the number of sides. Let AB be a side of the given inscribed polygon ; EF, parallel to AB, a side of the circumscribed polygon ; C the centre of the circle. If the chord AM and the tangents AP, BQ, be drawn, AM...
Page 59 - 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.