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
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Page 12
... hypothenuse AC be made radius , the perpendicular BC be- comes the sine , and the base AB the cosine of the angle at the base CAB . But if the base AB be made radius , the per- pendicular BC becomes the tangent , and the hypothenuse AC ...
... hypothenuse AC be made radius , the perpendicular BC be- comes the sine , and the base AB the cosine of the angle at the base CAB . But if the base AB be made radius , the per- pendicular BC becomes the tangent , and the hypothenuse AC ...
Page 17
... hypothenuses AC , BC are the sides of the proposed triangle , and whose bases AD , DB are the segments of its base . Now if all the three sides of the triangle ABC be given , then the base AB , or the sum of the segments AD , DB , is ...
... hypothenuses AC , BC are the sides of the proposed triangle , and whose bases AD , DB are the segments of its base . Now if all the three sides of the triangle ABC be given , then the base AB , or the sum of the segments AD , DB , is ...
Page 21
... hypothenuse and one of the acute angles are given , to find the rest . 2. When a side and one of the acute angles are given . 3. When the hypothenuse and one of the sides are given . 4. When the two sides are given . In the following ...
... hypothenuse and one of the acute angles are given , to find the rest . 2. When a side and one of the acute angles are given . 3. When the hypothenuse and one of the sides are given . 4. When the two sides are given . In the following ...
Page 22
... hypothenuse AC , a solution may also be obtained by help of the secant . For AB : AC :: R : sec . A , therefore R : sec . A :: AB : AC . In the third case , when the hypothenuse AC and the side BC are given , to find AB , a solution may ...
... hypothenuse AC , a solution may also be obtained by help of the secant . For AB : AC :: R : sec . A , therefore R : sec . A :: AB : AC . In the third case , when the hypothenuse AC and the side BC are given , to find AB , a solution may ...
Page 30
... hypothenuse AC 324 , and the angle at the base BAC 48 ° 17 ' , to find the other parts of the triangle . By Construction . * Draw an indefinite line AC . From the point A , with the chord of 60 ° as radius , describe an arc , upon which ...
... hypothenuse AC 324 , and the angle at the base BAC 48 ° 17 ' , to find the other parts of the triangle . By Construction . * Draw an indefinite line AC . From the point A , with the chord of 60 ° as radius , describe an arc , upon which ...
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.