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 BonnycastleF. Nichols, 1811 - 128 σελίδες |
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Σελίδα 30
... directions given for the construction of each . To save expense , the actual construction of the figures is omitted in this work ; but the rules for constructing them will be sufficiently illustrated by inspecting the triangles in page ...
... directions given for the construction of each . To save expense , the actual construction of the figures is omitted in this work ; but the rules for constructing them will be sufficiently illustrated by inspecting the triangles in page ...
Σελίδα 42
... directions , and is best learned from some person who is acquainted with their use . Practical Examples . 1. Having measured a distance of 200 feet from the bottom of a steeple , in a direct horizontal line , I then took the angle of ...
... directions , and is best learned from some person who is acquainted with their use . Practical Examples . 1. Having measured a distance of 200 feet from the bottom of a steeple , in a direct horizontal line , I then took the angle of ...
Σελίδα 44
... direction , and found the angle of elevation , formed as before , 23 ° 45 ' . Re- quired the height of the obelisk . Angle BAC ACD - ABC = = 41 ° -23 ° 45 ' = 17 ° 15 ' . Sine BAC 17 ° 15 ' s . ABC A 23 ° 45 ′ :: BC 60 : AC . B Log ...
... direction , and found the angle of elevation , formed as before , 23 ° 45 ' . Re- quired the height of the obelisk . Angle BAC ACD - ABC = = 41 ° -23 ° 45 ' = 17 ° 15 ' . Sine BAC 17 ° 15 ' s . ABC A 23 ° 45 ′ :: BC 60 : AC . B Log ...
Σελίδα 52
... direction of the point of the compass , which is denoted by the letters NNE , it makes an angle with the meridian of 22 ° 30 ' , from the north toward the east ; and if an object bear SW , it makes an angle with the meridian of 45 ...
... direction of the point of the compass , which is denoted by the letters NNE , it makes an angle with the meridian of 22 ° 30 ' , from the north toward the east ; and if an object bear SW , it makes an angle with the meridian of 45 ...
Σελίδα 53
... direction NW 22 degrees , it bore NE 50 ° 37. Required its distance at the last place of observation . Answer . 13.14 miles . 3. From a ship at sea a point of land C bore NE by N. The ship sailed NW 23 miles , and the same point then ...
... direction NW 22 degrees , it bore NE 50 ° 37. Required its distance at the last place of observation . Answer . 13.14 miles . 3. From a ship at sea a point of land C bore NE by N. The ship sailed NW 23 miles , and the same point then ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 74 - The sum of any two sides is greater than the third side, and their difference is less than the third side.