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ABCD adjacent altitude base called centre chord circle circumference common cone consequently construct contained corresponding Cosine Cotang cylinder described determine diagonal diameter difference distance divided draw drawn edge equal equivalent EXAMPLES faces feet figure formed four frustum given gles greater half hence hypothenuse inches included inscribed join length less logarithm magnitudes manner means measured meet middle multiplied opposite parallel parallelogram parallelopipedon pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid radius ratio rectangle regular remain right angles right-angled triangle rods Scholium segment sides similar sine solidity solve sphere spherical triangle square straight line taken Tang tangent THEOREM third triangle triangle A B C values vertex VIII whole yards
Página 28 - 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.
Página 79 - Two rectangles having equal altitudes are to each other as their bases.
Página 251 - The convex surface of the cylinder is equal to the circumference of its base multiplied by its altitude (Prop.
Página 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.
Página 35 - If any side of a triangle be produced, the exterior angle is equal to the sum of the two interior and opposite angles.
Página 168 - 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.
Página 303 - Equal triangles upon the same base, and upon the same side of it, are between the same parallels.
Página 4 - 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. 9) M=a*, then, raising both sides to the wth power, we have Mm = (a")m = a"" . Therefore, log (M m) = xm = (log M) X »»12.