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 13
... segments of that side will be to each other as the tangents of the parts into which the vertical angle is divided by the perpendi- cular , or as the cotangents of the angles at the base . 1 If AD be drawn perpendicular to the base BC ...
... segments of that side will be to each other as the tangents of the parts into which the vertical angle is divided by the perpendi- cular , or as the cotangents of the angles at the base . 1 If AD be drawn perpendicular to the base BC ...
Page 16
... segments of the base made by the per- pendicular . Let ABC be the proposed triangle , C the vertex , AB the base , CD the perpendicular di- viding the base into the seg- ments AD , DB . About the centre C , with the radius CB , the less ...
... segments of the base made by the per- pendicular . Let ABC be the proposed triangle , C the vertex , AB the base , CD the perpendicular di- viding the base into the seg- ments AD , DB . About the centre C , with the radius CB , the less ...
Page 17
... 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 given , and the difference of the segments may be found by the proposition . But if the sum and ...
... 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 given , and the difference of the segments may be found by the proposition . But if the sum and ...
Page 19
... segments of the base , by prop . 5 , and then the angles at the base , by prop . 1 . " SECTION II . RULES OF TRIGONOMETRICAL CALCULATION . 67. THE general problem which trigonometry proposes to resolve is this . In any plane triangle ...
... segments of the base , by prop . 5 , and then the angles at the base , by prop . 1 . " SECTION II . RULES OF TRIGONOMETRICAL CALCULATION . 67. THE general problem which trigonometry proposes to resolve is this . In any plane triangle ...
Page 23
... segment will be next to the greater side , and the less segment to the less side . If both the angles at the base be acute , the perpendicular will fall within the triangle ; but if one of them be obtuse , the perpendicular will fall ...
... segment will be next to the greater side , and the less segment to the less side . If both the angles at the base be acute , the perpendicular will fall within the triangle ; but if one of them be obtuse , the perpendicular will fall ...
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.