A Treatise of Plane and Spherical Trigonometry: In Theory and Practice ; Adapted to the Use of Students ; Extracted Mostly from Similar Works of Ludlam, Playfair, Vince, and Bonnycastle |
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Page 44
... station , the height of the instru- ment being five feet . See fig . prob . 4 . The height of the object above the ground is found to be 104-17 yards , as in prob . 2 . R or sine C 90 ° : cos . B 58 ° :: AB : BC . Log . cos . 58 ° Log ...
... station , the height of the instru- ment being five feet . See fig . prob . 4 . The height of the object above the ground is found to be 104-17 yards , as in prob . 2 . R or sine C 90 ° : cos . B 58 ° :: AB : BC . Log . cos . 58 ° Log ...
Page 47
... station . ( See the last fig . ) Answer . The distances are found as in the first an- alogy of the last problem , and are AB 306-19 yards , and AC = 296.54 . 11. To find the distance between two places A , B , which are not accessible ...
... station . ( See the last fig . ) Answer . The distances are found as in the first an- alogy of the last problem , and are AB 306-19 yards , and AC = 296.54 . 11. To find the distance between two places A , B , which are not accessible ...
Page 49
... station O , in the base AB ; otherwise the figure or plan of the survey may appear correct , when it is not so ; and there will be no means of discovering whether the angles have been justly taken . G 92. To carry on a Measurement by a ...
... station O , in the base AB ; otherwise the figure or plan of the survey may appear correct , when it is not so ; and there will be no means of discovering whether the angles have been justly taken . G 92. To carry on a Measurement by a ...
Page 50
... stations A , B. If the angles CAB , CBA , DAB , DBA , be taken with a theodolite , or other instrument , we can find ... station and the last may be also determined . For the two sides AB , BD , and the in- cluded angle ABD being known ...
... stations A , B. If the angles CAB , CBA , DAB , DBA , be taken with a theodolite , or other instrument , we can find ... station and the last may be also determined . For the two sides AB , BD , and the in- cluded angle ABD being known ...
Page 52
... station , MAm the meridian , Ċ the fort , AC its di- rection on bearing , B my second station , BC the bearing of the fort = angle m DC . Angle ACB = m DC - DAC = 56 ° 15 ′ - 22 ° 30 ′ = 33 ° 45 ' . Angle BAC = CAD + DAB = 22 ° 30 ′ + ...
... station , MAm the meridian , Ċ the fort , AC its di- rection on bearing , B my second station , BC the bearing of the fort = angle m DC . Angle ACB = m DC - DAC = 56 ° 15 ′ - 22 ° 30 ′ = 33 ° 45 ' . Angle BAC = CAD + DAB = 22 ° 30 ′ + ...
Common terms and phrases
90 degrees adjacent angle AHDL algebra analogy angle ABC angle ACB Answer arc or angle base centre chord circle comp complement cosecant cosine cotangent Euclid's Elements find the angles find the rest geometry Given the side greater than 90 half the sum half their difference height Hence hypothenuse AC included angle less than 90 logarithmic sines mathematics measured mechanical philosophy negative opposite angle perp perpendicular plane triangle plane trigonometry PROP propositions quadrant AH quantity right-angled spherical triangle right-angled triangle Scholium secant side AB side AC sides and angles sine a sine sine and cosine sine² sines and tangents solution spherical angle spherical triangle ABC spherical trigonometry supplement tables tangent of half theorems third side three angles three sides triangle are given trigono versed sine yards
Popular passages
Page 12 - 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 ix - 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 23 - Then multiply the second and third terms together, and divide the product by the first term: the quotient will be the fourth term, or answer.
Page 13 - In any triangle, twice the rectangle contained by any two sides is to the difference between the sum of the squares of those sides, and the square of the base, as the radius to the cosine of the angle included by the two sides. Let ABC be any triangle, 2AB.BC is to the difference between AB2+BC2 and AC2 as radius to cos.
Page 87 - The cosine of half the sum of two sides of a spherical triangle is to the cosine of half their difference as the cotangent of half the included angle is to the tangent of half the sum of the other two angles. The sine of half the sum of two sides of a spherical...
Page 74 - The sum of any two sides is greater than the third side, and their difference is less than the third side.