A Treatise of Plane Trigonometry: To which is Prefixed a Summary View of the Nature and Use of Logarithms : Being the Second Part of a Course of Mathematics, Adapted to the Method of Instruction in the American Colleges |
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Page 3
... term index , as it is used here , may possibly lead to some confusion in the mind of the learner . For the logarithm itself is the index or exponent of a power . The characteristic , therefore , is the index of an index . 8. The index ...
... term index , as it is used here , may possibly lead to some confusion in the mind of the learner . For the logarithm itself is the index or exponent of a power . The characteristic , therefore , is the index of an index . 8. The index ...
Page 7
... term is the product of the preceding term into the ratio . But the logarithm of this product is the sum of the logarithms of the preceding term and the ratio ; that is , the logarithms increase by a common addition , and are , therefore ...
... term is the product of the preceding term into the ratio . But the logarithm of this product is the sum of the logarithms of the preceding term and the ratio ; that is , the logarithms increase by a common addition , and are , therefore ...
Page 12
... of a unit to the last significant figure . Thus , For 36843 , take 36840 , and 36850 , For 792674 , For 6537825 , 792600 , 792700 , 6537000 , 6538000 , & c . The first term of the proportion will then be 10 12 THE LOGARITHMIC TABLES .
... of a unit to the last significant figure . Thus , For 36843 , take 36840 , and 36850 , For 792674 , For 6537825 , 792600 , 792700 , 6537000 , 6538000 , & c . The first term of the proportion will then be 10 12 THE LOGARITHMIC TABLES .
Page 13
... term of the proportion will then be 10 , or 100 , or 1000 , & c . Ex . 1. Required the logarithm of 362572 . The logarithm of 362600 is 5.55943 of 362500 5.55931 The differences are 100 , and 12 . Then 100 12 :: 72 : 8.64 , or 9 nearly ...
... term of the proportion will then be 10 , or 100 , or 1000 , & c . Ex . 1. Required the logarithm of 362572 . The logarithm of 362600 is 5.55943 of 362500 5.55931 The differences are 100 , and 12 . Then 100 12 :: 72 : 8.64 , or 9 nearly ...
Page 17
... term required in single and com- pound proportion . The principle on which all these calcu- lations are conducted , is this ; If the logarithms of two numbers be added , the sum will be the logarithm of the PRODUCT of the numbers ; and ...
... term required in single and com- pound proportion . The principle on which all these calcu- lations are conducted , is this ; If the logarithms of two numbers be added , the sum will be the logarithm of the PRODUCT of the numbers ; and ...
Other editions - View all
A Treatise of Plane Trigonometry: To Which Is Prefixed, a Summary View of ... Jeremiah Day No preview available - 2017 |
A Treatise of Plane Trigonometry: To Which Is Prefixed, a Summary View of ... Jeremiah Day No preview available - 2018 |
A Treatise of Plane Trigonometry: To Which Is Prefixed a Summary View of the ... Jeremiah Day No preview available - 2018 |
Common terms and phrases
ABC Fig ABCD altitude axis base breadth bung diameter calculation cask circle circular sector circular segment circumference column cosecant cosine cotangent course cube cubic decimal departure Diff difference of latitude difference of longitude distance divided earth equal to half equator figure find the area find the SOLIDITY frustum given sides gles greater hypothenuse inches inscribed lateral surface length less logarithm longitude measured Mercator's meridian meridional difference middle diameter miles multiply the sum number of degrees number of sides oblique parallelogram parallelopiped perpendicular perpendicular height plane sailing prism PROBLEM proportion pyramid quadrant quantity quotient radius ratio regular polygon right angled triangle right cylinder rods rule secant sector segment ship sine sines and cosines slant-height sphere spherical subtract tables tangent term theorem trapezium triangle ABC Trig trigonometry wine gallons zone
Popular passages
Page 81 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 43 - A cone is a solid figure described by the revolution of a right angled triangle about one of the sides containing the right angle, which side remains fixed.
Page 50 - The surface of a sphere is equal to the product of its diameter by the circumference of a great circle.
Page 55 - ... the square of the hypothenuse is equal to the sum of the squares of the other two sides.
Page 69 - It will be sufficient to lay the edge of a rule on C, so as to be parallel to a line supposed to pass through B and D, and to mark the point of intersection G. 126. If after a field has been surveyed, and the area computed, the chain is found to be too long or too short ; the true contents may be found, upon the principle that similar figures are to each other as the squares of their homologous sides.
Page 118 - The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference.
Page 89 - Divide the height of the segment by the diameter of the circle ; look for the quotient in the column of heights in the table ; take out the corresponding number in the column of areas ; and multiply it by the square of the diameter.