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acute angle Almagest altitude angle of depression angle of elevation apothem chord circle colog cologarithm computed cos2 cosecant cosine cot2 cotangent Cotg diagonal esc2 examples Exercise figure Find antilog Find log find the angle Find the area Find the distance Find the height Find the numerical Find the side find the value five-place tables formula four-place tables geometry given angle given number given sides Hence Hipparchus history of trigonometry horizontal plane hypotenuse isosceles triangle law of sines Law of Tangents Let the pupil log cot loga logarithms mantissa method negative number of radians numerical value oblique triangles obtained parallelogram Plane Trigonometry polygon Prove radians radius Regiomontanus regular polygon right triangle sec2 secant sexagesimal Similarly sin2 solution spherical spherical trigonometry subtends Subtract tan2 Tang tangent tower triangle ABC trigono trigonometric functions
Pàgina 14 - To Divide One Number by Another, Subtract the logarithm of the divisor from the logarithm of the dividend, and obtain the antilogarithm of the difference.
Pàgina 167 - The circumference of a circle is supposed to be divided into 360 equal parts, called degrees; each degree into 60 minutes, and each minute into 60 seconds. Degrees, minutes, and seconds are designated by the characters °, ', ". Thus 23° 14' 35" is read 23 degrees, 14 minutes, and 35 seconds.
Pàgina 111 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.
Pàgina 133 - AB may be comFIG. 74. puted (How?). 93. V. To find the Distance of an Inaccessible Object. Let A (Fig. 75) be the position of the observer and let it be required to determine the distance from A to B. Let the pupil determine what measurements and computations are necessary in accordance with the figure. FIG. 75. 94. VI. To find the Distance between two Objects separated by an Impassable Barrier (and possibly invisible to each other).
Pàgina 107 - B are both acute. In Fig. 56 the angle A is acute, and angle ABC obtuse. Let CD, denoted by p, be the altitude in each triangle. In Fig. 55, in the rt.
Pàgina 21 - What is the side of a square whose area is equal to that of a circle 452 feet in diameter ? Ans. ^(452)
Pàgina 108 - 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.
Pàgina 10 - Hence, the characteristic of an integral or mixed number is one less than the number of figures to the left of the decimal point. 5. Characteristic of a Decimal Fraction. 1 = 10°.