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Page 323 - In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By Theorem II. we have a : b : : sin. A : sin. B.
Page 321 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides by the projection of the other upon that side.
Page 374 - Hence the product of two complex numbers is a complex number whose modulus is the product of the moduli and whose amplitude is the sum of the amplitudes of the two complex numbers.
Page 248 - The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers.
Page 321 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other...
Page 461 - A term may be transposed from one member of an equation to the other by changing its sign.
Page 408 - A conic is the locus of a point whose distance from a fixed point called the focus is in a constant ratio to its distance from a fixed line called a directrix.
Page 12 - ... function. A magnitude so related to another magnitude that for any value of one there is a corresponding value of the other. For instance, the area of a circle is a function of its radius. The radius is also a function of the area. functional reserves. The ability of the body to accomplish additional muscular or other activity and useful work beyond the normal level of activity of an individual.