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 |
From inside the book
Results 1-5 of 12
Page 8
... half a right angle , the other acute angle ATC must also be half a right ... difference of the cosine and radius , namely , the sum in the two middle ... their sines bf and BF be equal . Because Ab + AB = 180 ° = Ab + bD , the arc AB = 6D ...
... half a right angle , the other acute angle ATC must also be half a right ... difference of the cosine and radius , namely , the sum in the two middle ... their sines bf and BF be equal . Because Ab + AB = 180 ° = Ab + bD , the arc AB = 6D ...
Page 16
... there- A E D B C fore DE or DB is half the differ- ence of the magnitudes AB , BC . But AB = BD + DA , that is , to half the difference added to half the sum ; and BC = DC - DB , that is , to the excess of half the sum above half the ...
... there- A E D B C fore DE or DB is half the differ- ence of the magnitudes AB , BC . But AB = BD + DA , that is , to half the difference added to half the sum ; and BC = DC - DB , that is , to the excess of half the sum above half the ...
Page 17
... difference of the segments may be found by the proposition . But if the sum ... their difference , as the tangent of half the sum of the opposite angles is ... the centre , with the same radius FB , PLANE TRIGONOMETRY . 17.
... difference of the segments may be found by the proposition . But if the sum ... their difference , as the tangent of half the sum of the opposite angles is ... the centre , with the same radius FB , PLANE TRIGONOMETRY . 17.
Page 18
... the sum of the sides : difference of the sides :: tan . of half the sum of the angles at the base : tan . of half their difference . 62. Scholium . If two sides AC , BC of any triangle ABC , and the angle ACB included between them , be ...
... the sum of the sides : difference of the sides :: tan . of half the sum of the angles at the base : tan . of half their difference . 62. Scholium . If two sides AC , BC of any triangle ABC , and the angle ACB included between them , be ...
Page 69
... half their difference . If A = 90 ° , and B = 2x , then R + s . 2x : R s . 2 x :: tan . ( 45 ° + x ) : tan . ( 45 ... the preceding theorems the radius R is PLANE TRIGONOMETRY . 69.
... half their difference . If A = 90 ° , and B = 2x , then R + s . 2x : R s . 2 x :: tan . ( 45 ° + x ) : tan . ( 45 ... the preceding theorems the radius R is PLANE TRIGONOMETRY . 69.
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.