## 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 37

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**three sides**and the three angles three parts being given , and one of these being a side , it is required to find the other three parts . This problem contains four cases , and the solutions of them depend upon the preceding ... Page 24

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**third side**BC . Solution . AC : AB :: s . B : s . C ( 54 ) . Hence ∠A = 180 ° -B - C . Then , s . B : s . A :: AC : CСВ . Case 3. Given two sides AB , AC , and the angle A contained between them , to find the other angles B and C , and the ... Page 27

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**three**angles of an oblique triangle be denoted by A , B , C , and their opposite**sides**by a , b , c , then propositions IV , V , VI , VII , may be expressed by general equations , by means of which all the cases of plane triangles may ... Page 28

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**three**dif- ferent methods of solution . 1. By geometrical construction . 2. By arithmetical calculation . 3. Instrumentally . In the first method , the triangle is constructed by laying down the**sides**...**third**terms together , and ... Page 40

... side 40 , another 70 , and the inclu- ded angle 76 ° 14 ' , to find the rest . Answer . The other two angles are 71 ° 3 and 32 ° 43 ′ , and the

... side 40 , another 70 , and the inclu- ded angle 76 ° 14 ' , to find the rest . Answer . The other two angles are 71 ° 3 and 32 ° 43 ′ , and the

**third side**is 71.88 . Case 4. Given the**three sides**, AB 350 , AC 240 , BC 200 , to find the ...### 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.