The elements of plane trigonometry |
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Página 1
... produced to a point C such that BC shall be equal to C ' B C that given line , and if from AB we have to take a given line , we must cut off from BA a part BC ' equal to the given line , and AC ' will be the required remainder . Let AB ...
... produced to a point C such that BC shall be equal to C ' B C that given line , and if from AB we have to take a given line , we must cut off from BA a part BC ' equal to the given line , and AC ' will be the required remainder . Let AB ...
Página 2
... produced , if ne- cessary , indefinitely . Then the position of any point P , in the plane of these lines is known , X if we know the magnitudes of the perpendiculars let fall from P1 upon the lines XAX ' and YAY ' , viz . PN , and PM ...
... produced , if ne- cessary , indefinitely . Then the position of any point P , in the plane of these lines is known , X if we know the magnitudes of the perpendiculars let fall from P1 upon the lines XAX ' and YAY ' , viz . PN , and PM ...
Página 8
... produced if necessary , and through A draw DAD ' perpen- dicular to AB . Now , for the reasons given in Arts . 2 and 3 , in these figures the signs of NC are + , + , those of AN are 15. DEFINITIONS . - respectively , and + , " 9 + ...
... produced if necessary , and through A draw DAD ' perpen- dicular to AB . Now , for the reasons given in Arts . 2 and 3 , in these figures the signs of NC are + , + , those of AN are 15. DEFINITIONS . - respectively , and + , " 9 + ...
Página 27
... produced ; let CEF be perpendicular to AB , DF parallel to AB , DB perpendicular to AB . Then FB is a parallelogram , and EF = DB . Now , sin ( A - B ) : BD EF = = AD AD = CF - CE B ' = AD CF CD CE AC CD AD AC AD = cos FCD.sin DAC - sin ...
... produced ; let CEF be perpendicular to AB , DF parallel to AB , DB perpendicular to AB . Then FB is a parallelogram , and EF = DB . Now , sin ( A - B ) : BD EF = = AD AD = CF - CE B ' = AD CF CD CE AC CD AD AC AD = cos FCD.sin DAC - sin ...
Página 56
... produced either way . 44 Then sin CAB = sin CAD = = DC CA ( With reference to the third figure , see Art . 26. ) Also , sin CBA = sin CBD = DC CB sin A sin B sin CAB CB = CA sin CBA = a b or , sin A a = sin B b In like manner , if a ...
... produced either way . 44 Then sin CAB = sin CAD = = DC CA ( With reference to the third figure , see Art . 26. ) Also , sin CBA = sin CBD = DC CB sin A sin B sin CAB CB = CA sin CBA = a b or , sin A a = sin B b In like manner , if a ...
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Términos y frases comunes
A₁ AC AC angle containing Asin base C₁ centre circle coefficient cosec cosines decimal determined Diff difference digit equal errors Eucl expression formulæ given goniometric functions greater Hence increment integer last Article less m₁ magnitude mantissa measured Napier's rules nearly negative number of seconds P₁ perpendicular plane triangle planes AOB polar triangle pole polygon positive proved quantity radius Regular Polyhedron right angles right-angled triangle S₁ secants shew shewn Similarly sin A sin sines sines and cosines small angle solid angle sphere spherical excess spherical triangle SPHERICAL TRIGONOMETRY subtended subtraction tabular logarithmic tangents THEOREM triangle ABC triangle whose sides TRIGONOMETRY versin Wherefore π π
Pasajes populares
Página 141 - Logarithm of a number to a given base is the index of the power to which the base must be raised to give the number.
Página 10 - Any two sides of a spherical triangle are together greater than the third, and the sum of the three sides is less than the circumference of a great circle.
Página 56 - Mathematics which treats of the solution of plane triangles. In every plane triangle there are six parts : three sides and three angles. When three of these parts are given, one being a side, the remaining parts may be found by computation. The operation of finding the unknown parts is called the solution of the triangle.
Página 57 - ... the three interior angles of a triangle are together equal to two right angles.
Página 12 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Página 143 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor.
Página 27 - For example, let it be required to prove the formula sin ( A - B) = sin A. cos В - cos A. sin В from the annexed figure, where ВАC' = A, and C'AD — В ; each angle being greater than a right angle.
Página 5 - ... stretched taut from one point to the other. The string will not lie on the parallel, but will evidently be in a plane which passes through the centre of the sphere. If the two points be on a meridian, the stretched string will lie on the meridian. By angular distance between two points on a sphere is meant the angle subtended at the centre of the sphere by the arc joining the given points. Thus in Fig. 4 the angle NOA is the angular distance of A from N.
Página 6 - If a solid angle be contained by three plane angles, any two of them are together greater than the third. Let the solid angle at A be contained by the three plane angles BAC, CAD, DAB : any two of them shall be together greater than the third.
Página 200 - Three circles whose radii are a, b, c touch each other externally ; prove that the tangents at the points of contact meet in a point whose distance from any one of them is (aba Nj a+b + cj 12.