The elements of plane trigonometry |
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Página 145
... digits of which the number is composed . Thus , in 11,600 = 2 · 7781513 , 2 is the characteristic of the logarithm of the number 600 , 7781513 is the mantissa of the significant digit 6 . 9. In the common system , to determine the ...
... digits of which the number is composed . Thus , in 11,600 = 2 · 7781513 , 2 is the characteristic of the logarithm of the number 600 , 7781513 is the mantissa of the significant digit 6 . 9. In the common system , to determine the ...
Página 146
... digits minus one , -where if the number be a decimal fraction , the cyphers which follow the decimal point are alone counted , and are reckoned nega- tively . Conversely therefore , if logarithms be given having cha- racteristics 1 , 2 ...
... digits minus one , -where if the number be a decimal fraction , the cyphers which follow the decimal point are alone counted , and are reckoned nega- tively . Conversely therefore , if logarithms be given having cha- racteristics 1 , 2 ...
Página 148
... digits corresponding to the mantissa 5658478 are 3680 ; .. 113680 or 1,0368 = 2 · 5658478 ; and 368 is the product sought . ( 2 ) . To multiply 0172 by 00241 . 110 01722-2355284 11000214 = 3.3304138 , 5.5659422 , 1 , 000036808 . 1 10 ...
... digits corresponding to the mantissa 5658478 are 3680 ; .. 113680 or 1,0368 = 2 · 5658478 ; and 368 is the product sought . ( 2 ) . To multiply 0172 by 00241 . 110 01722-2355284 11000214 = 3.3304138 , 5.5659422 , 1 , 000036808 . 1 10 ...
Página 149
... digits 72 ; ... 2 · 8573325 = 110 072 ; and 072 is the quotient sought . ( 4 ) . To find the values of ( 154 ) 3 , and ( 650 ) . Art . 6 . 1101541-1875207 3 . P. 164 . 3.5625621 = 1103652.3 , nearly , p . 165 . ... 3652.3 is the ...
... digits 72 ; ... 2 · 8573325 = 110 072 ; and 072 is the quotient sought . ( 4 ) . To find the values of ( 154 ) 3 , and ( 650 ) . Art . 6 . 1101541-1875207 3 . P. 164 . 3.5625621 = 1103652.3 , nearly , p . 165 . ... 3652.3 is the ...
Página 157
... digits each , and α let m be the mantissa of the number n + which contains 10 six digits , the last of which ( a ) is after the decimal point . a Now , since n and n + 10 have the same number of integral places , their logarithms have ...
... digits each , and α let m be the mantissa of the number n + which contains 10 six digits , the last of which ( a ) is after the decimal point . a Now , since n and n + 10 have the same number of integral places , their logarithms have ...
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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.