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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... most trigonometrical calculations are founded , the proportion between the parts of the given tri- angle , and a similar one formed from the sines , tangents , & c . in the tables . CONTENTS . LOGARITHMS . Page . Section I. Nature of.
... most trigonometrical calculations are founded , the proportion between the parts of the given tri- angle , and a similar one formed from the sines , tangents , & c . in the tables . CONTENTS . LOGARITHMS . Page . Section I. Nature of.
Page 11
... similar manner . For , by art . 14 , the decimal part of the logarithm of any number is the same , as that of the number multiplied into 10 , 100 , & c . All the difference will be in the index ; and this may be supplied by the same ...
... similar manner . For , by art . 14 , the decimal part of the logarithm of any number is the same , as that of the number multiplied into 10 , 100 , & c . All the difference will be in the index ; and this may be supplied by the same ...
Page 53
... similar triangles . ( Euc . 4. 6. ) In the quadrant ACH , ( Fig . 3. ) these lines form three similar triangles , viz . ACD , BCG or LCG , and HCF . For , in each of these , there is one right angle , because the sines and tangents are ...
... similar triangles . ( Euc . 4. 6. ) In the quadrant ACH , ( Fig . 3. ) these lines form three similar triangles , viz . ACD , BCG or LCG , and HCF . For , in each of these , there is one right angle , because the sines and tangents are ...
Page 54
... similar . It should also be observed , that the line BC , between the sine and the center of the circle , is parallel and equal to the cosine ; and that LC , between the cosine and center , is par- allel and equal to the sine ; ( Euc ...
... similar . It should also be observed , that the line BC , between the sine and the center of the circle , is parallel and equal to the cosine ; and that LC , between the cosine and center , is par- allel and equal to the sine ; ( Euc ...
Page 56
... , and AF the versed sine . The angle ABH is a right angle , ( Euc . 31. 3. ) and the triangles ABH and ABF are similar . ( Euc . 8. 6. ) Therefore , AH : AB :: AB : AF . That is , the diameter is to the chord , 56 TRIGONOMETRY .
... , and AF the versed sine . The angle ABH is a right angle , ( Euc . 31. 3. ) and the triangles ABH and ABF are similar . ( Euc . 8. 6. ) Therefore , AH : AB :: AB : AF . That is , the diameter is to the chord , 56 TRIGONOMETRY .
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.