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 15
... angles may be found ; or , if two angles and a side opposite to one of them be given , the other angle and sides may be found . Thus , if the sides AC , AB , and the angle C , be given , to find the rest , then AB : s . C :: AC : s . B ...
... angles may be found ; or , if two angles and a side opposite to one of them be given , the other angle and sides may be found . Thus , if the sides AC , AB , and the angle C , be given , to find the rest , then AB : s . C :: AC : s . B ...
Page 18
... angles at the base . The triangles AFE , AHB , having the angles AFE and AHB equal ( 29. 1 ) , and the angle at A ... find its supplement to 180 ° ( 18. 1 ) , equal to the angle HCB , half of which is the semi - sum of the angles ...
... angles at the base . The triangles AFE , AHB , having the angles AFE and AHB equal ( 29. 1 ) , and the angle at A ... find its supplement to 180 ° ( 18. 1 ) , equal to the angle HCB , half of which is the semi - sum of the angles ...
Page 19
... angles may be found immediately from art . 65. When the sides are expressed by great numbers it will be more conve- nient to find the difference of the segments of the base , by prop . 5 , and then the angles at the base , by prop . 1 ...
... angles may be found immediately from art . 65. When the sides are expressed by great numbers it will be more conve- nient to find the difference of the segments of the base , by prop . 5 , and then the angles at the base , by prop . 1 ...
Page 20
... angles in degrees , minutes , & c .; and the sides in feet , or any other known measure . The reader must remember ... find the other three parts of the triangle . If one angle of a triangle be right , the other two angles are ...
... angles in degrees , minutes , & c .; and the sides in feet , or any other known measure . The reader must remember ... find the other three parts of the triangle . If one angle of a triangle be right , the other two angles are ...
Page 21
... find a side ; but a given side must always be made radius to find an angle . Hence , to find an angle , begin the ... angles are given , to find the rest . 2. When a side and one of the acute angles are given . 3. When the ...
... find a side ; but a given side must always be made radius to find an angle . Hence , to find an angle , begin the ... angles are given , to find the rest . 2. When a side and one of the acute angles are given . 3. When the ...
Common terms and phrases
90 degrees adjacent angle AHDL algebra analogy angle ABC angle ACB Answer arc AC arc or angle base centre chord circle comp complement cosecant cosine cotangent Euclid's Elements find the angles find the rest formulæ 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 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.