The Principles of Plane Trigonometry, Mensuration, Navigation and Surveying |
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Page 51
... SINE of an arc is a straight line drawn from one end of the arc , perpendicular to a diameter which passes through the other end . Thus BG ( Fig . 3. ) is the sine SINES , TANGENTS , & C . 51.
... SINE of an arc is a straight line drawn from one end of the arc , perpendicular to a diameter which passes through the other end . Thus BG ( Fig . 3. ) is the sine SINES , TANGENTS , & C . 51.
Page 52
... sine is half the 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 ...
... sine is half the 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 ...
Page 53
... sine of the COMPLEMENT of that angle . Thus , if the diameter HO ( Fig . 3. ) be perpendicular to MA , the angle HCG is the complement of ACG ; ( Art . 77. ) and LG , or its equal CB , is the sine of HCG . ( Art . 82. ) It is ...
... sine of the COMPLEMENT of that angle . Thus , if the diameter HO ( Fig . 3. ) be perpendicular to MA , the angle HCG is the complement of ACG ; ( Art . 77. ) and LG , or its equal CB , is the sine of HCG . ( Art . 82. ) It is ...
Page 54
... 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 . 34. 1. ) so that one may taken for the other , in any calculation . be ...
... 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 . 34. 1. ) so that one may taken for the other , in any calculation . be ...
Page 55
... sine of 90 ° - Sec = √1 + tan 2 Cosec = 1 + cot3 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 ...
... sine of 90 ° - Sec = √1 + tan 2 Cosec = 1 + cot3 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 ...
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The Principles of Plane Trigonometry, Mensuration, Navigation and Surveying ... Jeremiah Day No preview available - 2016 |
Common terms and phrases
ABCD altitude axis base breadth calculation circle circular segment circumference column cone cosecant cosine cotangent course cube cylinder decimal departure diameter Diff difference of latitude difference of longitude divided earth equator feet figure find the SOLIDITY frustum given sides gles greater horizon hypothenuse inches inscribed ISOPERIMETRY JEREMIAH DAY lateral surface length line of chords loga logarithm measured Mercator's Merid meridional difference miles multiplied negative number of degrees number of sides object oblique opposite parallel of latitude parallelogram parallelopiped perimeter perpendicular perpendicular height plane sailing prism PROBLEM proportion pyramid quadrant quantity quotient radius regular polygon right angled triangle right cylinder rods secant segment sine sines and cosines slant-height sphere spherical subtracting tables tangent term theorem trapezium triangle ABC Trig trigonometry whole 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 61 - When a quantity is greater than any other of the same class, it is called a maximum. A multitude of straight lines, of different lengths, may be drawn within a circle. But among them all, the diameter is a maximum. Of all sines of angles, which can be drawn in a circle, the sine of 90° is a maximum. When a quantity is less than any other of the same class, it is called a minimum. Thus, of all straight lines drawn from a given point to a given straight line, that which is perpendicular to the given...
Page 71 - 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 29 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...