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
... chord of double the arc . The sine BG is half PG , which is the chord of the arc PAG , double the arc AG . 83. The VERSED SINE of an arc is that part of the diameter which is between the sine and the arc . Thus BA is the versed sine of ...
... chord of double the arc . The sine BG is half PG , which is the chord of the arc PAG , double the arc AG . 83. The VERSED SINE of an arc is that part of the diameter which is between the sine and the arc . Thus BA is the versed sine of ...
Page 55
... chord of 60 ° are , in any circle , each equal to And the tangent of 45 ° the radius , and therefore equal to each other . Demonstration . 1. In the quadrant ACH , ( Fig . 5. ) the arc AH is 90 ° . The sine of this , according to the ...
... chord of 60 ° are , in any circle , each equal to And the tangent of 45 ° the radius , and therefore equal to each other . Demonstration . 1. In the quadrant ACH , ( Fig . 5. ) the arc AH is 90 ° . The sine of this , according to the ...
Page 56
... chord of 60 ° , is equal to CS the radius . 3. Let AR be an arc of 45 ° . AD will be its tangent , and the angle ACD ... chord of 60 ° . ( Art . 82. cor . ) But by the preceding article , the chord of 60 ° is equal to radius . Its half ...
... chord of 60 ° , is equal to CS the radius . 3. Let AR be an arc of 45 ° . AD will be its tangent , and the angle ACD ... chord of 60 ° . ( Art . 82. cor . ) But by the preceding article , the chord of 60 ° is equal to radius . Its half ...
Page 57
... chord , as the chord to the versed sine . In Fig . 6th , let the arc AD - a , and ADB = 2a . Draw BF perpendicular to AH . This will divide the right angled tri- angle ABH into two similar triangles . ( Euc . 8. 6. ) The an- gles ACD ...
... chord , as the chord to the versed sine . In Fig . 6th , let the arc AD - a , and ADB = 2a . Draw BF perpendicular to AH . This will divide the right angled tri- angle ABH into two similar triangles . ( Euc . 8. 6. ) The an- gles ACD ...
Page 91
... chords . In forming a given triangle , or any other right lined figure , the parts which must be made to agree with the conditions proposed , are the lines , and the angles . For the former , a scale of equal parts is used ; for the ...
... chords . In forming a given triangle , or any other right lined figure , the parts which must be made to agree with the conditions proposed , are the lines , and the angles . For the former , a scale of equal parts is used ; for the ...
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.