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 CollegesPublished and sold by Hezekiah Howe, 1831 - 155 pages |
From inside the book
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Page 82
... SEGMENTS MADE BY THE PERPENDICULAR . In the triangle ABC , ( Fig . 26. ) if a perpendicular be drawn from C upon AB ; AB ... segment is next the greater side . If BC is greater than AC , ( Fig . 26. ) PB is * See note F. greater than AP ...
... SEGMENTS MADE BY THE PERPENDICULAR . In the triangle ABC , ( Fig . 26. ) if a perpendicular be drawn from C upon AB ; AB ... segment is next the greater side . If BC is greater than AC , ( Fig . 26. ) PB is * See note F. greater than AP ...
Page 83
... segment NP - AP . ( Euc . 3. 3. ) But BP is greater than NP . 147. The two segments are to each other , as the tangents of the opposite angles , or the cotangents of the adjacent an- gles . For , in the right angled triangles ACP and ...
... segment NP - AP . ( Euc . 3. 3. ) But BP is greater than NP . 147. The two segments are to each other , as the tangents of the opposite angles , or the cotangents of the adjacent an- gles . For , in the right angled triangles ACP and ...
Page 88
... segments may be found by theorem III . ( Art . 145. ) There will then be given , in each of the right angled trian- gles , the hypothenuse and one of the legs , from which the angles may be determined , by rectangular trigonometry ...
... segments may be found by theorem III . ( Art . 145. ) There will then be given , in each of the right angled trian- gles , the hypothenuse and one of the legs , from which the angles may be determined , by rectangular trigonometry ...
Page 89
... segments is AP , because it is next the side AC , which is greater than BC . ( Art . 146. ) To and from half the sum of the segments 19.5 Adding and subtracting half their difference , ( Art . 153. ) 6.36 We have the greater segment AP ...
... segments is AP , because it is next the side AC , which is greater than BC . ( Art . 146. ) To and from half the sum of the segments 19.5 Adding and subtracting half their difference , ( Art . 153. ) 6.36 We have the greater segment AP ...
Page 140
... , the side on which the perpendicular falls , is to the sum of the other two ; as the difference of the latter , to the sum of the segments made by the perpendicular . The demonstration is the same , as in the other 140 NOTES .
... , the side on which the perpendicular falls , is to the sum of the other two ; as the difference of the latter , to the sum of the segments made by the perpendicular . The demonstration is the same , as in the other 140 NOTES .
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.