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 viii
... contain the elements of plane trigonometry , the practical and numerical solutions of all the cases of rectilinear triangles , and the mensuration of the heights and distances of objects . These two sections are com- plete of themselves ...
... contain the elements of plane trigonometry , the practical and numerical solutions of all the cases of rectilinear triangles , and the mensuration of the heights and distances of objects . These two sections are com- plete of themselves ...
Strona x
... contained in the introduction to spherical trigonometry are intended to be an- nexed , with their demonstrations , to the second edition of Playfair's Geometry , under the title of Elements of Spherical Geometry . They properly belong ...
... contained in the introduction to spherical trigonometry are intended to be an- nexed , with their demonstrations , to the second edition of Playfair's Geometry , under the title of Elements of Spherical Geometry . They properly belong ...
Strona 2
... contained in any arc AC of one cir- cle , subtending a given angle ABC , the same number of parts will be contained in the arc GH of the other circle , subtending the same angle ABC . 5. COR . 4. Hence , if a circle of any radius ...
... contained in any arc AC of one cir- cle , subtending a given angle ABC , the same number of parts will be contained in the arc GH of the other circle , subtending the same angle ABC . 5. COR . 4. Hence , if a circle of any radius ...
Strona 18
... 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 angie con- tained by the two sides . Let ABC be any triangle ; 2 AB . BC ...
... 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 angie con- tained by the two sides . Let ABC be any triangle ; 2 AB . BC ...
Strona 24
... contained between them , to find the other angles B and C , and the third side BC . 1⁄2 Solution . AB + AC : AB — AC :: tan . ( B + C ) : tan . ( B - C ) ( 61 ) . Since ( B + C ) and ( B - C ) are given , the angles B and C may be found ...
... contained between them , to find the other angles B and C , and the third side BC . 1⁄2 Solution . AB + AC : AB — AC :: tan . ( B + C ) : tan . ( B - C ) ( 61 ) . Since ( B + C ) and ( B - C ) are given , the angles B and C may be found ...
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.