The elements of plane trigonometry |
Dentro del libro
Resultados 1-5 de 31
Página viii
... Observations on the selection of a proper formula ..................... 181 12 , 13. Rule for supplying the TENS when the Tabular functions of Gonio- metric Logarithms are used ...... 181 14-22 . To determine very small angles from ...
... Observations on the selection of a proper formula ..................... 181 12 , 13. Rule for supplying the TENS when the Tabular functions of Gonio- metric Logarithms are used ...... 181 14-22 . To determine very small angles from ...
Página 72
... observed . Here we have two angles given and a side of the ABAD . By determining the side BA we can , from the right - angled triangle BAC , find the height of BC . sin BDA D sin ( BAC – BDA ) - BA sin BDA Thus , = = AD sin DBA sin BDA ...
... observed . Here we have two angles given and a side of the ABAD . By determining the side BA we can , from the right - angled triangle BAC , find the height of BC . sin BDA D sin ( BAC – BDA ) - BA sin BDA Thus , = = AD sin DBA sin BDA ...
Página 73
... observations . At A let the angles BAC and BAD be observed , and at D the angle BDA . Then in the ABDA we have the D- angles BDA , BAD and the side AD given . If then BA be determined from these data , we can find BC from the right ...
... observations . At A let the angles BAC and BAD be observed , and at D the angle BDA . Then in the ABDA we have the D- angles BDA , BAD and the side AD given . If then BA be determined from these data , we can find BC from the right ...
Página 74
... observation of the angle in Example 1 . Let BC = h , AC = a , 4 BAC = A. Let Sh be the error in height produced by an error SA of the observed angle . B Then h = a . tan A , h + dh = a . tan ( A + dA ) ; .. Sh = a . { tan ( 4 + SA ) ...
... observation of the angle in Example 1 . Let BC = h , AC = a , 4 BAC = A. Let Sh be the error in height produced by an error SA of the observed angle . B Then h = a . tan A , h + dh = a . tan ( A + dA ) ; .. Sh = a . { tan ( 4 + SA ) ...
Página 75
... observed angle , will be the least . For Sha sin & A ( cos A ) 2 h sin & A tan A ( cos A ) 2 h . sin & A 2h . sin & A = sin A. cos A 2 sin A. cos A 2h . sin SA = sin 2 A Now h being constant , and 84 being given , this expres- sion ...
... observed angle , will be the least . For Sha sin & A ( cos A ) 2 h sin & A tan A ( cos A ) 2 h . sin & A 2h . sin & A = sin A. cos A 2 sin A. cos A 2h . sin SA = sin 2 A Now h being constant , and 84 being given , this expres- sion ...
Otras ediciones - Ver todas
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.