## 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 1-5 of 19

Page 15

... 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 the angle C , be given , to

... 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 the angle C , be given , to

**find the rest**, then AB : s ... Page 21

...

...

**find**a side ; but a given side must always be made radius to**find**an angle ...**rest**. 2. When a side and one of the acute angles are given . 3. When the ...**found**. GIVEN SOUGHT SOLUTION I. AC & C , the hyp . & AB R : s . C :: AC : AB BCR ... Page 23

... find the other three parts . This problem contains four cases , and the solutions of them depend upon the preceding propositions . Case 1. When two angles and a side are given , to

... find the other three parts . This problem contains four cases , and the solutions of them depend upon the preceding propositions . Case 1. When two angles and a side are given , to

**find the rest**. 2. When two sides and an angle opposite ... Page 25

...

...

**find the rest**. Upon one of the given sides , as BC , let fall a perpen- dicular AD from the opposite angle A. Then , in the right - angled triangle ABD the hyp . AB and all the an- gles are given ; therefore R : cos . B :: AB : BD ( 49 ) ... Page 32

...

...

**find the rest**. Answer . BC = 99-719 yards , AB = 68.535 , angle C = 34 ° 30 ' . Case 2. Given the side AB 125 , and the angle A 51 ° 19 ′ , to**find the rest**. By Construction . Draw an indefinite line AB , and from A to B set off 125 ...### 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.