## 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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**Solution**of Plane Triangles**Solution**of the Cases of Right - angled Triangles**Solution**of the Cases of Oblique - angled Triangles Mensuration of Heights and Distances 5 7 12 19 27 30 37 41 ° Problems for the Exercise of Learners TM 53 ... Page vii

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**solution**of the common cases of triangles , and the larger and more comprehensive works , designed for the use of mathematicians , or of students who have time , ability , and inclination to enter deeply into such curious and difficult ... Page viii

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**solutions**of all the cases of rectilinear triangles , and the mensuration of the heights and distances of objects . These two sections are com- plete of themselves . * This useful and meritorious writer appears to have followed Legen ... Page ix

... Trigonometry , with a few additions . " Though the

... Trigonometry , with a few additions . " Though the

**solution**of triangles forms a distinct and ma- terial part of trigonometry , yet a treatise , which should be now b confined to that object , would be justly deemed defective PREFACE . ix. Page x

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**solution**of the cases of triangles , and to the mensuration of heights and dis- tances , & c . But this confined plan does not accord with the import and object of trigonometry , which is the art of finding the dimensions of the sides ...### 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.