Elements of Plane and Spherical Trigonometry: With Practical Applications |
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Page 15
... opposite side to the hypothenuse . B Thus , in any right - angled triangle , A B C , if the sides be denoted by p , b , h , we shall have , h P A b C b sin A sin B = h ' ( 1 ) 48. The TANGENT of an angle is the ratio of the opposite ...
... opposite side to the hypothenuse . B Thus , in any right - angled triangle , A B C , if the sides be denoted by p , b , h , we shall have , h P A b C b sin A sin B = h ' ( 1 ) 48. The TANGENT of an angle is the ratio of the opposite ...
Page 41
... side , in order to solve a plane triangle . The solution of plane triangles depends upon the following FUNDAMENTAL PROPOSITIONS . 109. In a right - angled triangle , the side opposite to an acute angle is equal to the product of the ...
... side , in order to solve a plane triangle . The solution of plane triangles depends upon the following FUNDAMENTAL PROPOSITIONS . 109. In a right - angled triangle , the side opposite to an acute angle is equal to the product of the ...
Page 42
... sides are proportional to the sines of the opposite angles . B C a P Let ABC ... opposite the angles A , B , C , re- spectively , are denoted by a , b , and c . From one of the angles , as B , draw BD perpendicular to the opposite side ...
... sides are proportional to the sines of the opposite angles . B C a P Let ABC ... opposite the angles A , B , C , re- spectively , are denoted by a , b , and c . From one of the angles , as B , draw BD perpendicular to the opposite side ...
Page 43
... opposite angles is to the tangent of half their difference . For , by ( 90 ) , whence ( Geom . , Prop . XII . Bk ... side is equal to the sum of the squares of the two other sides , diminished by twice the rectangle of these sides multiplied ...
... opposite angles is to the tangent of half their difference . For , by ( 90 ) , whence ( Geom . , Prop . XII . Bk ... side is equal to the sum of the squares of the two other sides , diminished by twice the rectangle of these sides multiplied ...
Page 44
... sides , diminished by the square of the opposite side , and whose denominator is twice the product of the containing sides . For , by ( 96 ) , a2 = b + c2 whence , cos A = - 2 be cos A , b2 + c2 - a2 2 bc ( 99 ) cos C a2 + b2 - c2 2 ab ...
... sides , diminished by the square of the opposite side , and whose denominator is twice the product of the containing sides . For , by ( 96 ) , a2 = b + c2 whence , cos A = - 2 be cos A , b2 + c2 - a2 2 bc ( 99 ) cos C a2 + b2 - c2 2 ab ...
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Common terms and phrases
A B C acute angle adjacent sides Algebra angle equal angle of elevation angle opposite angle or arc ar.co.log Arithme Blog column headed cos(A+B cos² cosec Cotang coth coversed sine decimal denoted divided Elementary Algebra equal to 90 equation Equations Art EXAMPLES feet find the SINE formulæ Geom Geometry given number Given the hypothenuse Greenleaf's New Series half the sum Hence included angle Let ABC log cos log cot log sin logarithmic cosine logarithmic sine logarithmic tangent logh M.
M. Sine minus the logarithmic Napier's rules negative oblique oblique-angled spherical triangle Parker's Exercises perpendicular plane triangle Prop right-angled spherical triangle right-angled triangle equal rods School secant side b equal side opposite sin A sin sin² sines and cosines Solution solve the triangle spherical triangle ABC SPHERICAL TRIGONOMETRY subtract sun's declination suvers Tang tangent of half three sides trigonometric functions values whence yards
Popular passages
Page 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 7 - This process, like its converse (Art. 23), is based upon the supposition that the differences of logarithms are proportional to the differences of their corresponding numbers.
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 74 - Spherical Triangle the cosine of any side is equal to the product of the cosines of the other two sides, plus the product of the sines of those sides into the cosine of their included angle ; that is, (1) cos a = cos b...
Page 43 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Page 39 - ... be at the head of the column, take the degrees at the top of the table, and the minutes on the left ; but if the name be at the foot of the column, take the degrees at the bottom, and the minutes on the right.
Page 46 - The cosine of half of any angle of a plane triangle is equal to the square root of half the sum of the three sides, into half the sum less the side opposite the angle, divided by the rectangle of the two adjacent sides.