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 5
... complement of AB , and the angle HCB is the complement of ACB . 14. DEF . 2. The difference of any arc from a semicircle , or of any angle from 180 degrees , is called the supplement of that arc or angle . Thus , the arc DHB is the ...
... complement of AB , and the angle HCB is the complement of ACB . 14. DEF . 2. The difference of any arc from a semicircle , or of any angle from 180 degrees , is called the supplement of that arc or angle . Thus , the arc DHB is the ...
Page 7
... complement of the arc AB , and the angle HCB is the complement of the angle ACB . Therefore the cosine , cotangent , and cosecant of any arc or angle , are respec- tively equal to the sine , tangent , and secant of the comple- ment of ...
... complement of the arc AB , and the angle HCB is the complement of the angle ACB . Therefore the cosine , cotangent , and cosecant of any arc or angle , are respec- tively equal to the sine , tangent , and secant of the comple- ment of ...
Page 10
... complement ( 23 ) , the cosine of 60 degrees is equal to the sine of 30 degrees , and therefore is equal to half the radius . Thirdly , the versed sine of an arc less than a quadrant be- ing equal to the difference between the radius ...
... complement ( 23 ) , the cosine of 60 degrees is equal to the sine of 30 degrees , and therefore is equal to half the radius . Thirdly , the versed sine of an arc less than a quadrant be- ing equal to the difference between the radius ...
Page 14
... complement ( 23 ) . PROP . IV . 54. The sides of any triangle are to one another as the sines of their opposite angles ; and , conversely , the sines of the angles of any triangle are to one another as the sides which are opposite to ...
... complement ( 23 ) . PROP . IV . 54. The sides of any triangle are to one another as the sines of their opposite angles ; and , conversely , the sines of the angles of any triangle are to one another as the sides which are opposite to ...
Page 20
... complement to a right angle , or 90 degrees . The sine of either of the acute angles is the cosine of the other ( 23 ) , and therefore may be used instead of the other , whenever it renders the operation more simple . In the calculation ...
... complement to a right angle , or 90 degrees . The sine of either of the acute angles is the cosine of the other ( 23 ) , and therefore may be used instead of the other , whenever it renders the operation more simple . In the calculation ...
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.