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A B C ABCD adjacent altitude base called centre chord circle circumference circumscribed common cone consequently construct contained corresponding Cosine Cotang described diagonal diameter difference distance divided draw drawn edges equal equivalent EXAMPLES extremities faces feet figure formed four frustum given gles greater half height hence hypothenuse inches included inscribed intersection join length less logarithm manner means measured meet middle multiplied opposite parallel parallelogram parallelopipedon pass perpendicular plane pole polygon prism PROBLEM Prop proportional PROPOSITION pyramid quadrantal radii radius ratio rectangle regular remain right angles rods Scholium segment shown sides similar Sine solidity sphere spherical triangle square straight line surface Tang tangent THEOREM third triangle triangle ABC vertex vertices whole
Page 35 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 117 - 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 50 - If any number of magnitudes 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; then will A : B : : A + C + E : B + D + F.
Page 77 - Two rectangles having equal altitudes are to each other as their bases.
Page 158 - If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of those lines.
Page 313 - FRACTION is a negative number, and is one more tftan the number of ciphers between the decimal point and the first significant figure.
Page 314 - 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.
Page 100 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.