An Introduction to the Theory and Practice of Plain and Spherical Trigonometry: And the Stereographic Projection of the Sphere : Including the Theory of Navigation ...Longman, Rees, Orme, Brown, and Green, 1826 - 442 pages |
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Page ix
... examples adapted to that work , until the first edition of the following treatise ; wherein the author , with great labour and attention , suited all his examples to the year 1796 , and corrected the situations of all the stars to the ...
... examples adapted to that work , until the first edition of the following treatise ; wherein the author , with great labour and attention , suited all his examples to the year 1796 , and corrected the situations of all the stars to the ...
Page xvii
... examples . By these means the students will readily learn the use of the Nautical Almanac , and in a school where several are studying the same subject , their pro- gress will not be retarded by waiting for the Almanac . The examples ...
... examples . By these means the students will readily learn the use of the Nautical Almanac , and in a school where several are studying the same subject , their pro- gress will not be retarded by waiting for the Almanac . The examples ...
Page 57
... example : only AB , being shorter than BC , cuts Ac in two points on the same side of BC , hence the angle A may be ... EXAMPLES . I. In the plane triangle ABC , AC 104 Given BC = 70 B = 44 ° .12 ′ Required the other parts . 2. In the ...
... example : only AB , being shorter than BC , cuts Ac in two points on the same side of BC , hence the angle A may be ... EXAMPLES . I. In the plane triangle ABC , AC 104 Given BC = 70 B = 44 ° .12 ′ Required the other parts . 2. In the ...
Page 62
... EXAMPLE 1 . Being on one side of a river , and wanting to know the distance of a fort , or other object , on the other side , suppose I measured 500 yards along the side of the river in a straight line AB and found the two angles be ...
... EXAMPLE 1 . Being on one side of a river , and wanting to know the distance of a fort , or other object , on the other side , suppose I measured 500 yards along the side of the river in a straight line AB and found the two angles be ...
Page 63
... examples are referred to the foregoing figure , and serve to exercise the above observations . EXAMPLE II . An engineer wanted to know the breadth of a river ( over which the general intended to pass the whole army ) , in order to ...
... examples are referred to the foregoing figure , and serve to exercise the above observations . EXAMPLE II . An engineer wanted to know the breadth of a river ( over which the general intended to pass the whole army ) , in order to ...
Common terms and phrases
acute angle CAB Answer apparent altitude azimuth base centre circle co-tangent compasses complement construction cosec cosine degrees diff difference of latitude difference of longitude draw ecliptic equator Euclid find the angle formulæ given side greater Greenwich Hence horizon horizontal parallax hypoth hypothenuse less line of numbers line of sines log sine measured meridian miles moon's N.sine N.cos natural number Naut Nautical Almanac noon North oblique observed obtuse opposite angle parallax parallel perpendicular plane sailing Plate pole prime vertical PROPOSITION quadrant Rad x sine rad2 radius rhumb line right angles right ascension right-angled spherical triangle RULE scale of chords SCHOLIUM secant side AC sine A sine sine BC Sine Co-sine sphere spherical angle spherical triangle ABC Spherical Trigonometry star star's subtract sun's declination supplement tables tang tangent of half three angles three sides Trigonometry true altitude versed sine
Popular passages
Page 21 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Page 2 - And if the given number be a proper vulgar fraction ; subtract the logarithm of the denominator from the logarithm of the numerator, and the remainder will be the logarithm sought ; which, being that of a decimal fraction, must always have a negative index.
Page 28 - The CO-SINE of an arc is the sine of the complement of that arc as L.
Page 107 - C' (89) (90) (91) (92) (93) 112. 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.
Page 31 - An angle at the circumference of a circle is measured by half the arc that subtends it. Let BAC be an angle at the circumference : it has for its measure half the arc "BC, which subtends it.
Page 136 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 258 - The HORIZON is a great circle which separates the visible half of the heavens from the invisible ; the earth being considered as a point in the centre of the sphere of the fixed stars.
Page 28 - The SECANT of an arc, is a straight line drawn from the center, through one end of the arc, and extended to the tangent which is drawn from the other end.
Page 27 - The sine, or right sine, of an arc, is the line drawn from one extremity of the arc, perpendicular to the diameter passing through the other extremity. Thus, BF is the sine of the arc AB, or of the arc BDE.