Elements of Plane and Spherical Trigonometry: With Its Applications to the Principles of Navigation and Nautical Astronomy. With the Logarithmic and Trigonometrical TablesJ. Souter, 1833 - 264 pages |
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Page i
... negative ; thus the complement CD of the arc BC commences at C where BC terminates , and may be considered as generated by the motion of C , the extremity of the radius AC , in the direction CD ; but the complement C , D of the arc BC1 ...
... negative ; thus the complement CD of the arc BC commences at C where BC terminates , and may be considered as generated by the motion of C , the extremity of the radius AC , in the direction CD ; but the complement C , D of the arc BC1 ...
Page 3
... negative ; thus the complement CD of the arc BC commences at C where BC terminates , and may be considered as generated by the motion of C , the extremity of the radius AC , in the direction CD ; but the complement CD of the arc BC1 ...
... negative ; thus the complement CD of the arc BC commences at C where BC terminates , and may be considered as generated by the motion of C , the extremity of the radius AC , in the direction CD ; but the complement CD of the arc BC1 ...
Page 4
... negative angles , according as they are situated above or below the fixed line AB from which they are measured , as the angles CAB , C , AB ; moreover , an angle may consist of any number of degrees whatever , thus if the revolving line ...
... negative angles , according as they are situated above or below the fixed line AB from which they are measured , as the angles CAB , C , AB ; moreover , an angle may consist of any number of degrees whatever , thus if the revolving line ...
Page 5
... negative ; hence in the first quadrant , the cosines are positive , in the second negative , in the third negative , in the fourth positive , and so on ; the cosine of an arc is equal to the cosine of its supplement , but has a ...
... negative ; hence in the first quadrant , the cosines are positive , in the second negative , in the third negative , in the fourth positive , and so on ; the cosine of an arc is equal to the cosine of its supplement , but has a ...
Page 6
... negative ; in the third the tangent BT , and cotangent Dt , are both positive ; and in the fourth the tangent BT , and cotangent D ̧ are both negative , and so on ; but as we shall soon see , the signs of the tangent and cotangent may ...
... negative ; in the third the tangent BT , and cotangent Dt , are both positive ; and in the fourth the tangent BT , and cotangent D ̧ are both negative , and so on ; but as we shall soon see , the signs of the tangent and cotangent may ...
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Common terms and phrases
a+b+c ABC are given arc BC arith Asin celestial centre circle circumference colatitude comp complement computation cos.² cos.c cosec cosine cotangent coversed sine declination deduced determine diameter diff difference of latitude distance equal equations EXAMPLES expression find the angle formula Geom Geometry given side hence horizon hypotenuse included angle logarithmic longitude measured meridian miles multiplying negative object observed opposite angle parallax parallel sailing perpendicular plane sailing plane triangle polar triangle pole PROBLEM quadrant quantities radius right ascension right-angled triangle rule sailing secant semidiameter ship side opposite sin.² sin.c sine and cosine solution sphere spherical angle spherical excess Spherical Geometry spherical triangle spherical trigonometry subtracted surface tabular line tangent theorem third side three angles three sides triangle ABC Trigono trigonometrical lines true altitude values
Popular passages
Page 6 - 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 140 - If the zenith distance and declination be of the same name, that is, both north or both south, their sum will be the latitude ; but, if of different names, their difference will be the latitude, of the same name as the greater.
Page 145 - PS' ; the coaltitudes zs, zs', and the hour angle SPS', which measures the interval between the observations ; and the quantity sought is the colatitude ZP. Now, in the triangle PSS , we have given two sides and the included angle to find the third side ss', and one of the remaining angles, say the angle PSS'. In the triangle zss...
Page 51 - The sum of the three sides of a spherical triangle is less than the circumference of a great circle. Let ABC be any spherical triangle ; produce the sides AB, AC, till they meet again in D. The arcs ABD, ACD, will be semicircumferenc.es, since (Prop.
Page 144 - It should also be observed here, that in the preceding examples the celestial object is supposed to be on the meridian above the pole ; that is, to be higher than the elevated pole. But, if a meridian altitude be taken below the pole, which may be done if the object is circumpolar, or so near to the elevated pole as to perform its apparent daily revolution about it without passing below the horizon, then the latitude of the place will be equal to the sum of the true altitude, and the codeclination...
Page 53 - ... that the two angles A and D lie on the same side of BC, the two B and E on the same side of AC, and the two C and F on the same side of AB.
Page 115 - ... the surface of the celestial sphere. The Zenith of an observer is that pole of his horizon which is exactly above his head. Vertical Circles are great circles passing through the zenith of an observer, and perpendicular to his horizon.