## 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 vii

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**circle**, and also teaches to compute the dimensions of the sides and angles of any tri- angle . It supplies fundamental rules for ascertaining the dis- tances and altitudes of objects both terrestrial and celestial . Without the aid of ... Page ix

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**circle**, commonly denominated trigonometrical lines , and the principal geometrical properties of those lines , are fully explained and demonstrated . A perfect knowledge of the changes of the signs of those lines , and of their chief ... Page 1

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**circle**. Let ABC be an angle at the centre of the**circle**ACF , standing on the arc AC ; the angle ABC : four right an- gles :: arc AC : whole circumference ACF . D H K B G F Produce AB till it meet the cir- E cumference in E , and ... Page 2

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**circle**, subtending the same angle ABC . 5. COR . 4. Hence , if a**circle**of any radius whatever be di- vided into 360 equal parts , called degrees , each degree into 60 equal parts , called minutes ; each minute into 60 equal parts ... Page 3

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**circle**is usually as- cribed , thought that the year consisted of 360 days , or that the**circle**which the sun seemed to describe in a year was al- ready distinguished by nature into 360 parts . Another conve- nience in this division is ...### 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.