## 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 6-10 of 61

Page 15

... sides and an an- gle opposite to one of them be given , the remaining

... sides and an an- gle opposite to one of them be given , the remaining

**side and angles**may be found ; or , if two angles and a side opposite to one of them be given , the other angle and sides may be found . Thus , if the sides AC , AB , and ... Page 17

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**sides**of the proposed triangle , and whose bases AD , DB are the segments of its base . Now if all the three**sides**...**angles**at the base CAD , CBD may be found by art . 49 , and consequently the**angle**ACB , which is the supplement ... Page 18

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**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 given , the other ... Page 19

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**sides**of any plane triangle are given , the**angles**may be found immediately from art . 65. When the**sides**are expressed by great numbers it will be more conve- nient to find the difference of the segments of the base , by prop . 5 , and ... Page 20

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**angles**only be given , the magnitudes of the**sides**cannot be determined , but only the ratios of their magnitudes . Innumerable triangles , equiangu- lar to one another , may exist ; but the**sides**of none of them may be equal to the**sides**...### Common terms and phrases

90 degrees adjacent angle AHDL algebra analogy angle ABC angle ACB Answer arc AC arc or angle base centre chord circle comp complement cosecant cosine cotangent Euclid's Elements find the angles find the rest formulæ 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 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.