## 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 37

... scale of chords make the angle A = 49 ° 25 ′ , and the an- gle B = 66 ° 47 ′ . Draw AC and BC meeting each other in C. Then AC and BC

... scale of chords make the angle A = 49 ° 25 ′ , and the an- gle B = 66 ° 47 ′ . Draw AC and BC meeting each other in C. Then AC and BC

**measured**by the scale PLANE TRIGONOMETRY . 37 Solution of the Cases of Oblique-angled Triangles. Page 38

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**measured**by the scale of equal parts is 299.6 , and the angles A and B**measured**by the scale of chords are 39 ° 53 ' and 32 ° 27 ' . As the angle C is obtuse , the radius BA cannot in- tersect CA in more points than one ; therefore ... Page 42

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**measured**a distance of 200 feet from the bottom of a steeple , in a direct horizontal line , I then took the angle of elevation of its top , Abc = 47 ° 30 ′ . Required the height of the steeple . R : bc 200 tan . b 47 ° 30 ′ : Ac . A ... Page 44

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**measured**from its bottom a distance of 40 feet , and there found the angle of elevation formed by the plain and an imaginary line drawn to the top of the object to be 41 ° . I then mea- sured 60 feet farther , in the same direction ... Page 45

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**measuring**a horizontal base B AB of 100 feet in a direct A E D line from the hill , he found the elevation CBE 33 ° 45 ′ of the top of the castle . Required the height of the castle . CAE - B ACB = 17 ° 15 ' . = Sine ACB 17 ° 15 ′ : s ...### 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.