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 BonnycastleF. Nichols, 1811 - 128 |
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Strona 2
... quantity to be measured in the former case is to the magni- tude of the quantity to be measured in the latter case . 6. Since then the whole circumference of a circle consists of 360 degrees , a right angle will be 90 degrees , two ...
... quantity to be measured in the former case is to the magni- tude of the quantity to be measured in the latter case . 6. Since then the whole circumference of a circle consists of 360 degrees , a right angle will be 90 degrees , two ...
Strona 3
... quantity , and the circumferences of circles are as their diame- ters or radii ( 8. 1. Sup . ) . Consequently the angle ABC varies AC as AB Let ac be any other arc , abc any other angle , ab the radius ; then , in the same manner , the ...
... quantity , and the circumferences of circles are as their diame- ters or radii ( 8. 1. Sup . ) . Consequently the angle ABC varies AC as AB Let ac be any other arc , abc any other angle , ab the radius ; then , in the same manner , the ...
Strona 11
... quantity , therefore AL2 varies as AF , that is , the square of the right sine of any arc is as the versed sine of double that arc . Cor . 4. From no . 4 , CLx2 AL - CAXBF , or CLXAL = CAXBF . Hence , if A denote any arc or angle , sine ...
... quantity , therefore AL2 varies as AF , that is , the square of the right sine of any arc is as the versed sine of double that arc . Cor . 4. From no . 4 , CLx2 AL - CAXBF , or CLXAL = CAXBF . Hence , if A denote any arc or angle , sine ...
Strona 13
... quantity of the angle C may be found by seeking the sine in a table of sines and tangents . Again , AC : CB :: R : sine A , and AB : BC :: R : tan . A , and BC : AB :: R : tan . C , and AC : AB :: R : cos . A. Whence the tangents and ...
... quantity of the angle C may be found by seeking the sine in a table of sines and tangents . Again , AC : CB :: R : sine A , and AB : BC :: R : tan . A , and BC : AB :: R : tan . C , and AC : AB :: R : cos . A. Whence the tangents and ...
Strona 15
... quantities be added together , the aggregate will be the greater quantity ; and if the semi - difference be sub- tracted from the semi - sum , the remainder will be the less quantity . This proposition is demonstrated by the writers on ...
... quantities be added together , the aggregate will be the greater quantity ; and if the semi - difference be sub- tracted from the semi - sum , the remainder will be the less quantity . This proposition is demonstrated by the writers on ...
Kluczowe wyrazy i wyrażenia
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
Popularne fragmenty
Strona 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.
Strona 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.
Strona 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.
Strona 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.
Strona 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...
Strona 74 - The sum of any two sides is greater than the third side, and their difference is less than the third side.