Elements of Plane and Spherical Trigonometry: With Practical Applications |
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Page 16
... perpendicular to A C. Then , since the triangles AB C , A B ' C ' are similar , their sides have to one another the ... perpendicular to OA , and B D ' perpendicular to OA ' . Then , by the old definitions , the lines of the figure are ...
... perpendicular to A C. Then , since the triangles AB C , A B ' C ' are similar , their sides have to one another the ... perpendicular to OA , and B D ' perpendicular to OA ' . Then , by the old definitions , the lines of the figure are ...
Page 17
... perpendicular let fall from one extremity of the arc , upon the di- ameter passing through the other extremity . The COSINE is the distance from the centre to the foot of the sine . The trigonometric TANGENT is that part of the tangent ...
... perpendicular let fall from one extremity of the arc , upon the di- ameter passing through the other extremity . The COSINE is the distance from the centre to the foot of the sine . The trigonometric TANGENT is that part of the tangent ...
Page 20
... perpendicular to OC , and ED perpendicular to O D. Draw D G perpendicular to EF , and DC perpendicular to OC . The trian- gles GED and COD have their sides perpendicular , hence they are similar ( Geom . , Prop . XXV . Bk . IV . ) , and ...
... perpendicular to OC , and ED perpendicular to O D. Draw D G perpendicular to EF , and DC perpendicular to OC . The trian- gles GED and COD have their sides perpendicular , hence they are similar ( Geom . , Prop . XXV . Bk . IV . ) , and ...
Page 21
... perpendicular to OF , and ED perpendicular to OD . Draw DG per- pendicular to FE produced , and DC perpendicular to OF . The triangles GED and COD have their sides perpendicular , hence they are similar ( Geom . , Prop . XXV . Bk . IV ...
... perpendicular to OF , and ED perpendicular to OD . Draw DG per- pendicular to FE produced , and DC perpendicular to OF . The triangles GED and COD have their sides perpendicular , hence they are similar ( Geom . , Prop . XXV . Bk . IV ...
Page 26
... perpendicular to AC , then the angle ABD is equal to ABC , A D is equal to DC , and AD BC = AB . B Therefore , A D C AD sin ABD AB = A B A B or , since 30 ° and 60 ° are complements the one of the other , sin 30 ° cos 60 ° - whence by ...
... perpendicular to AC , then the angle ABD is equal to ABC , A D is equal to DC , and AD BC = AB . B Therefore , A D C AD sin ABD AB = A B A B or , since 30 ° and 60 ° are complements the one of the other , sin 30 ° cos 60 ° - whence by ...
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Common terms and phrases
A B C A+ log acute angle adjacent sides Algebra angle equal angle of elevation angle opposite angle or arc ar.co.log Arithme column headed cos² cosec Cotang decimal denoted divided Elementary Algebra 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 log cos log cot log sin logarithmic cosine logarithmic sine logarithmic tangent 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 cos sin A sin sin a+b sin² sine and cosine Solution solve the triangle spherical triangle ABC SPHERICAL TRIGONOMETRY subtract sun's declination suvers suversed sine Tang tangent of half 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.