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 11
... nearly proportioned to the differences of the num bers . Thus The log . of 1000 is 3.00000 , 3.00043 , Here the differences in the numbers are , 1 , 2 , 3 , 4 , & c . of 1001 of 1002 3.00087 , of 1003 3.00130 , of 1004 and the ...
... nearly proportioned to the differences of the num bers . Thus The log . of 1000 is 3.00000 , 3.00043 , Here the differences in the numbers are , 1 , 2 , 3 , 4 , & c . of 1001 of 1002 3.00087 , of 1003 3.00130 , of 1004 and the ...
Page 13
... nearly . And the log . 5.55931 + 9 = 5.55940 , the log . required . Ex . 2. The log . of 78264 is 4.89356 3 . The log . of 143542 is 5.15698 4. The log . of 1129535 is 6.05290 . By a little practice , such a facility , in abridging ...
... nearly . And the log . 5.55931 + 9 = 5.55940 , the log . required . Ex . 2. The log . of 78264 is 4.89356 3 . The log . of 143542 is 5.15698 4. The log . of 1129535 is 6.05290 . By a little practice , such a facility , in abridging ...
Page 15
... nearly , found in the tables , it will be necessary to reverse the rule in art . 28 . Take from the tables two logarithms , one the next greater , the other the next less than the given logarithm . Find the difference of the two ...
... nearly , found in the tables , it will be necessary to reverse the rule in art . 28 . Take from the tables two logarithms , one the next greater , the other the next less than the given logarithm . Find the difference of the two ...
Page 40
... nearly . Subtracting this correction from the first assumed number 4.011 , we have the value of x = 4 , which satisfies the condi- tions of the proposed equation ; for 41 = 256 . 2. Reduce the equation 4x = 100x3 . 3. Reduce the ...
... nearly . Subtracting this correction from the first assumed number 4.011 , we have the value of x = 4 , which satisfies the condi- tions of the proposed equation ; for 41 = 256 . 2. Reduce the equation 4x = 100x3 . 3. Reduce the ...
Page 61
... nearly pro- portional to the variations in the angle . Hence , To find the sine , tangent , & c . to seconds : Take out the number corresponding to the given degree and minute ; and also that corresponding to the next greater minute ...
... nearly pro- portional to the variations in the angle . Hence , To find the sine , tangent , & c . to seconds : Take out the number corresponding to the given degree and minute ; and also that corresponding to the next greater minute ...
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.