The elements of plane trigonometry |
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Página vii
... base , to form tables to any other base ......... 142 4-6 . The methods of performing Multiplication , Division , Involution , and Evolution by Logarithms ..... 143 8-10 . Description of the common , or Briggs ' , system of logarithms ...
... base , to form tables to any other base ......... 142 4-6 . The methods of performing Multiplication , Division , Involution , and Evolution by Logarithms ..... 143 8-10 . Description of the common , or Briggs ' , system of logarithms ...
Página 72
... base , and observing the angle BAC with a proper instrument . For BC AC . tan BAC ; = .. 110 BC1104C + L tan BAC - 10 . A 2. If it be not possible to come to the foot of the object , let a base AD be measured , such that the points D ...
... base , and observing the angle BAC with a proper instrument . For BC AC . tan BAC ; = .. 110 BC1104C + L tan BAC - 10 . A 2. If it be not possible to come to the foot of the object , let a base AD be measured , such that the points D ...
Página 73
... base AD be measured in any direction from A , and the angles BAC , BAD , BDA be observed , we shall be provided with sufficient data for finding the height of B above the horizontal plane passing through A. 4. Required to find the ...
... base AD be measured in any direction from A , and the angles BAC , BAD , BDA be observed , we shall be provided with sufficient data for finding the height of B above the horizontal plane passing through A. 4. Required to find the ...
Página 75
... base and between the same parallels , = 1⁄2 AB . CD = ↓ AB . AC . sin CAB = 1 / cb . 2 bc • √ { S. ( S − a ) . ( S − b ) . ( S − c ) } . Art . 76. Cor . 1 . - = \ / { S ' . ( S. − a ) · ( S − b ) . ( S − c ) } . = = 2 sin B. sin ...
... base and between the same parallels , = 1⁄2 AB . CD = ↓ AB . AC . sin CAB = 1 / cb . 2 bc • √ { S. ( S − a ) . ( S − b ) . ( S − c ) } . Art . 76. Cor . 1 . - = \ / { S ' . ( S. − a ) · ( S − b ) . ( S − c ) } . = = 2 sin B. sin ...
Página 141
... base is that power to which the base must be raised to give the number . If a logarithmic formula be generally true , whatever value the base may be of , the logarithms of the quantities involved will be written thus , log m , logn ...
... base is that power to which the base must be raised to give the number . If a logarithmic formula be generally true , whatever value the base may be of , the logarithms of the quantities involved will be written thus , log m , logn ...
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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
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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.