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 12
... becomes the tangent , and the hypothenuse AC the secant of the angle at the base CAB . This is manifest from the definitions . PROP . I. 49. In any right - angled plane triangle , the hypothe- nuse is to either of the sides , as the ...
... becomes the tangent , and the hypothenuse AC the secant of the angle at the base CAB . This is manifest from the definitions . PROP . I. 49. In any right - angled plane triangle , the hypothe- nuse is to either of the sides , as the ...
Page 24
... their complement A ( 23 ) . Also , 180 ° - AB + C. Hence the first analogy becomes , AB + AC : AB - AC :: cot . A or tan . ( 180 ° -A ) : tan . ( BC ) . Otherwise . Given AB , BC , and the included 24 PLANE TRIGONOMETRY .
... their complement A ( 23 ) . Also , 180 ° - AB + C. Hence the first analogy becomes , AB + AC : AB - AC :: cot . A or tan . ( 180 ° -A ) : tan . ( BC ) . Otherwise . Given AB , BC , and the included 24 PLANE TRIGONOMETRY .
Page 36
... becomes more easy . Thus , the opera- tion by the last analogy , where radius is the first term , will be more easy than that by the former analogy , where the sine of A is the first term . Ex . 2. Given the base AB = 20 , and the ...
... becomes more easy . Thus , the opera- tion by the last analogy , where radius is the first term , will be more easy than that by the former analogy , where the sine of A is the first term . Ex . 2. Given the base AB = 20 , and the ...
Page 59
... becomes equal to radius at the point H. Then it decreases during the second quadrant HD , till it again becomes O at the end of it . After this the sine passes to the other side of the diameter AD ; and there- fore , being reckoned ...
... becomes equal to radius at the point H. Then it decreases during the second quadrant HD , till it again becomes O at the end of it . After this the sine passes to the other side of the diameter AD ; and there- fore , being reckoned ...
Page 60
... becomes negative as often as it meets the radius CB produced on the side of the point A or diame- ter AD opposite to that in which it is first drawn ; and as this happens both when the arc AB becomes greater than AH , and also when , by ...
... becomes negative as often as it meets the radius CB produced on the side of the point A or diame- ter AD opposite to that in which it is first drawn ; and as this happens both when the arc AB becomes greater than AH , and also when , by ...
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.