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 13
... known in feet , inches , or any other measure , the an gles may be found by the following proportions . AC : AB :: R :: sine C. Whence the sine of the angle C is known , and consequently the quantity of the angle C may be found by ...
... known in feet , inches , or any other measure , the an gles may be found by the following proportions . AC : AB :: R :: sine C. Whence the sine of the angle C is known , and consequently the quantity of the angle C may be found by ...
Strona 17
... known , the segments may be found by article 57. Thus , in the two right - angled triangles ACD , BCD , the hypothenuses . AC , BC are given , and the bases AD , BD are found by the proposition ; whence the angles at the base CAD , CBD ...
... known , the segments may be found by article 57. Thus , in the two right - angled triangles ACD , BCD , the hypothenuses . AC , BC are given , and the bases AD , BD are found by the proposition ; whence the angles at the base CAD , CBD ...
Strona 18
... known , the angles themselves , CBA and CAB , may be found by art . 57. Two sides and all the angles of the proposed triangle being now known , the third side AB may be found by art . 54 , as follows . Sine ZA : BC :: S. LACB : AB ...
... known , the angles themselves , CBA and CAB , may be found by art . 57. Two sides and all the angles of the proposed triangle being now known , the third side AB may be found by art . 54 , as follows . Sine ZA : BC :: S. LACB : AB ...
Strona 20
... known measure . The reader must remember , that the sines , cosines , & c . which are used in the calculations in this section , are the nume- rical measures of the geometrical lines bearing the same names , the measure of the radius of ...
... known measure . The reader must remember , that the sines , cosines , & c . which are used in the calculations in this section , are the nume- rical measures of the geometrical lines bearing the same names , the measure of the radius of ...
Strona 25
... C . When the sides are not expressed by great numbers , the angles may be easily found by art . 65 . Cos . B = AB + ( BC + AC ) × ( BC — AC ) 2 AB . BC D It may always be known whether the angle sought is PLANE TRIGONOMETRY . 25.
... C . When the sides are not expressed by great numbers , the angles may be easily found by art . 65 . Cos . B = AB + ( BC + AC ) × ( BC — AC ) 2 AB . BC D It may always be known whether the angle sought is PLANE TRIGONOMETRY . 25.
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.