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 52
... extended till it meets a line drawn from the center through the other end . Thus AD ( Fig . 3. ) is the tangent of the ... extend from the diameter to the point in which they intersect each other . 87. The lines just defined are sines ...
... extended till it meets a line drawn from the center through the other end . Thus AD ( Fig . 3. ) is the tangent of the ... extend from the diameter to the point in which they intersect each other . 87. The lines just defined are sines ...
Page 58
... extend these tables beyond 90 ° ; because the sines , tangents , and secants , are of the same magnitude , in one of the quadrants of a circle , as in the others . Thus the sine of 30 ° is equal to that of 150 ° . ( Art . 90. ) 99. And ...
... extend these tables beyond 90 ° ; because the sines , tangents , and secants , are of the same magnitude , in one of the quadrants of a circle , as in the others . Thus the sine of 30 ° is equal to that of 150 ° . ( Art . 90. ) 99. And ...
Page 59
... extend from the center , to a point without the circle . 102. The numbers in the table here spoken of , are called natural sines , tangents , & c . They express the lengths of the several lines which have been defined in arts . 82 , 83 ...
... extend from the center , to a point without the circle . 102. The numbers in the table here spoken of , are called natural sines , tangents , & c . They express the lengths of the several lines which have been defined in arts . 82 , 83 ...
Page 81
... Extend CA to G , making AG equal to AB ; then CG is the sum of the two sides AB and AC . On AB set off AD equal to AC ; then BD is the difference of the sides AB and AC . The sum of the two angles ACB and ABC , is equal to the sum of ...
... Extend CA to G , making AG equal to AB ; then CG is the sum of the two sides AB and AC . On AB set off AD equal to AC ; then BD is the difference of the sides AB and AC . The sum of the two angles ACB and ABC , is equal to the sum of ...
Page 82
... extend BA to H. Then by Euc . 35 , 3 , ABXAH AL - AD Therefore , AB : AD :: AL : AH But AD = CD + CA = CB + CA And AL CL - CA - CB - CA And AH = HP - PA = BP - PA ( Euc . 3. 3. ) If then , for the three last terms in the proportion , we ...
... extend BA to H. Then by Euc . 35 , 3 , ABXAH AL - AD Therefore , AB : AD :: AL : AH But AD = CD + CA = CB + CA And AL CL - CA - CB - CA And AH = HP - PA = BP - PA ( Euc . 3. 3. ) If then , for the three last terms in the proportion , we ...
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.