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ABCD adjacent altitude base called chord circle circumference common cone consequently construct contained corresponding Cosine Cotang described diagonal diameter difference distance divided draw drawn edge equal equal Prop equivalent EXAMPLES extremities feet figure formed four given gles greater half height hence homologous hypothenuse inches included inscribed join length less line A B logarithm magnitudes manner means measured meet middle multiplied opposite parallel parallelogram pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid radius ratio rectangle regular remain right angles right-angled triangle Scholium segment side A B sides similar sine solidity sphere spherical triangle square straight line surface taken tangent THEOREM third triangle triangle A B C vertex whole
Page 59 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 120 - At a point in a given straight line to make an angle equal to a given angle.
Page 52 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
Page 19 - In an isosceles triangle, the angles opposite the equal sides are equal.
Page 199 - 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 121 - Through a given point to draw a straight line parallel to a given straight line, Let A be the given point, and BC the given straight line : it is required to draw through the point A a straight line parallel to BC.
Page 103 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Page 2 - The logarithm of any POWER of a number is equal to the product of the logarithm of the number by the exponent of the power. For let m be any number, and take the equation (Art.