## 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 48

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**an arc**under 90**degrees**, or of an**angle**less than a right an- gle , are respectively equal to the sine , tangent ...**degrees**, or a quadrant PLANE**TRIGONOMETRY**. 7 Properties and Relations of Trigonometrical Lines. Page 8

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**angle**, is equal to**radius**. This is manifest from an inspection of the figure . 28. The tangent of 45**degrees**is**radius**. For then the**angle**...**an arc**equal to the excess of the proposed**arc**above a semicircle . Thus , the sine 8 PLANE ... Page 10

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**angle**BCA = ECA ; therefore BF , the sine of the**arc**BA , is half the chord ...**an arc**being equal to the cosine of its complement ( 23 ) , the cosine of 60 ...**angle**to the base , into two triangles AFB , DFB , similar to the tri- D ... Page 11

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**angle**LAC common , are similar to each other , and to the two triangles AFB ...**arc**. 2. Again , the triangles AFB , DFB give the following analogy . AF ...**Trigonometry**to the Mensuration of the Sides PLANE**TRIGONOMETRY**. 11 . Page 12

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**radius**AD , describe the**arc**DE ; from D draw DF at right**angles**to AB , and from E draw EG touching the**arc**in E , and meeting AC in G. Then DF is the sine , and AF the cosine of the**arc**DE , or**angle**A ; also EG is the tan- gent , and ...### 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.