# Elementary mathematical analysis: a text book for first year college students

McGraw-Hill book company, inc., 1914 - 490 pāgines

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Pāgina 303 - 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.
Pāgina 124 - At a point 200 feet from, and on a level with the base of a tower, the angle of elevation of the top of the tower is observed to be 60° : what is the height of the tower?
Pāgina 301 - 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.
Pāgina 372 - Hence the quotient of two complex numbers is a complex number whose modulus is the quotient of the moduli, and whose amplitude is the difference of the amplitudes of the two complex numbers.
Pāgina 227 - The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers.
Pāgina 302 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other...
Pāgina 406 - 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.
Pāgina 10 - ... 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.
Pāgina 411 - Parabola is the locus of a point whose distance from a fixed point is always equal to its distance from a fixed straight line.
Pāgina 125 - From the top of a vertical cliff, the angle of depression of a point on the shore 150 feet from the base of the cliff, is observed to be 30° : find the height of the cliff.