## 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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**AC**( fig . 1 ) , will be to the sine , cosine , & c . of the same angle ACB , in any other circle whose radius is**AC**...**side**is radius . 25. Hence , if the radius of any circle be divided into 10,000,000 equal parts , and the length of ... Page 8

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**AC**= AT ( 6.1 ) . 29. The secant of 0 ( or at the beginning of the circle ) is radius . 30. The cosine of no degrees ...**side**of the centre C , whence the cosines have their origin . 36. Again , At the tangent , and Ct the secant of Ab ... Page 12

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**sides**, as the radius to the sine of the angle opposite to that**side**, or to the cosine of the angle adjacent to that**side**. C G D Let ABC be a right - angled triangle , of which the hypothenuse is**AC**. From the centre A , with any ... Page 13

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**AC**and CB , or**AC**and AB , or AB and CB , be known in feet , inches , or any other measure , the an gles may be ...**side**, the segments of that**side**will be to each other as the tangents of the parts into which the vertical angle is ... Page 14

... sides which are opposite to the angles . In the triangle ABC , the side AB :

... sides which are opposite to the angles . In the triangle ABC , the side AB :

**side AC**:: sine ZACB , opposite to the former side AB : sine ZABC , opposite to the latter**side AC**; and conversely . B E F A C D On the side BA ( produced if ...### 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.