The elements of plane trigonometry |
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Página 145
... characteristic of the logarithm of the number ; the decimal part is called the mantissa * of the significant digits of which the number is composed . Thus , in 11,600 = 2 · 7781513 , 2 is the characteristic of the logarithm of the ...
... characteristic of the logarithm of the number ; the decimal part is called the mantissa * of the significant digits of which the number is composed . Thus , in 11,600 = 2 · 7781513 , 2 is the characteristic of the logarithm of the ...
Página 146
John Charles Snowball. Hence , the characteristic of the logarithm of a decimal frac- tion having n 1 cyphers after ... characteristics of the logarithms of 2:54 , 254 , 000254 are 0 , 1 , 4 . The mantissa given in the tables for 1,3652 ...
John Charles Snowball. Hence , the characteristic of the logarithm of a decimal frac- tion having n 1 cyphers after ... characteristics of the logarithms of 2:54 , 254 , 000254 are 0 , 1 , 4 . The mantissa given in the tables for 1,3652 ...
Página 157
... , since n and n + 10 have the same number of integral places , their logarithms have the same characteristic ; m- m1 = = 120 ( " = a n + - 110 n n + n a 10 10 a Art . 5. = 110 ( 1 + 10n ( 1 a which , by expanding 110 ( 1 157.
... , since n and n + 10 have the same number of integral places , their logarithms have the same characteristic ; m- m1 = = 120 ( " = a n + - 110 n n + n a 10 10 a Art . 5. = 110 ( 1 + 10n ( 1 a which , by expanding 110 ( 1 157.
Página 160
... characteristic , the number required is 3696-38 . Ex . 2. Required the logarithm of 367 · 654 . By p . 165. , 110 367.65 = = 2.5654346 And " Diff . " being 118 , Part for 4 = 47 .. 1 , 367-654 = 2.5654393 10 24. To find the mantissa of ...
... characteristic , the number required is 3696-38 . Ex . 2. Required the logarithm of 367 · 654 . By p . 165. , 110 367.65 = = 2.5654346 And " Diff . " being 118 , Part for 4 = 47 .. 1 , 367-654 = 2.5654393 10 24. To find the mantissa of ...
Página 176
... characteristics , the logarithms to base of 10 of all goniometrical quantities have been increased by 10 , and the resulting numbers being re- gistered are called " Tables of logarithmic sines , cosines , & c . " Hence if any one of ...
... characteristics , the logarithms to base of 10 of all goniometrical quantities have been increased by 10 , and the resulting numbers being re- gistered are called " Tables of logarithmic sines , cosines , & c . " Hence if any one of ...
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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.