## 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 10

Page 62

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**versed sine**AF increases from O during the first and second quadrants AH , HD , till it becomes the diameter AD , which is its utmost limit . It then decreases during the third and fourth quadrants DL , LA , till it becomes O. Being ... Page 64

... sine , cosine , tangent , secant , cotangent , and cose- cant , all positive . If a line , supposed to be positive ...

... sine , cosine , tangent , secant , cotangent , and cose- cant , all positive . If a line , supposed to be positive ...

**versed sine**is always set off from A in the same direc- tion , and therefore continues positive through the whole ... Page 72

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**sine**of 1 ' being thus found , the**sine**of 2 ' , 3 ′ , or of any number of minutes , may be found by the following ...**versed**sines are found by subtracting the cosines from radius ( 32 ) . 134. The tangent of any arc is found by ... Page 74

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**versed**sines , as well as the sines and tangents . But they are of so little use , and , when occasion for them ...**sine**and cosine , the tangent and cotangent of any arc greater than a quadrant , are the same as the**sine**and co-**sine**... Page 97

... sine of ( the sum of the same two sides the third side ) x the sine of ( the sum of the same two sides - the third ...

... sine of ( the sum of the same two sides the third side ) x the sine of ( the sum of the same two sides - the third ...

**versed sine**C , therefore 2 cos.2 C = r2 + r cos . C. N the sine of 88. Now each of these three formulæ SPHERICAL ...### 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.