Elements of Plane and Spherical Trigonometry: With Practical Applications

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R. S. Davis, 1862 - Geometry - 490 pages
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Page 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.
Page 37 - 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 79 - Two rectangles having equal altitudes are to each other as their bases.
Page 251 - The convex surface of the cylinder is equal to the circumference of its base multiplied by its altitude (Prop.
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 35 - If any side of a triangle be produced, the exterior angle is equal to the sum of the two interior and opposite angles.
Page 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.
Page 303 - Equal triangles upon the same base, and upon the same side of it, are between the same parallels.
Page 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.
Page 102 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing.

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