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 51
... radius of the circle . In many calculations , it is convenient to consider the radius , whatever be its length , as a unit . ( Alg . 510. ) To this must be referred the numbers expressing the lengths of other lines . Thus 20 will be ...
... radius of the circle . In many calculations , it is convenient to consider the radius , whatever be its length , as a unit . ( Alg . 510. ) To this must be referred the numbers expressing the lengths of other lines . Thus 20 will be ...
Page 53
... radius . But the versed sine of an obtuse angle is equal to the sum of the co- sine and radius . Thus the versed sine of ACG is AB = AC -BC . ( Art . 83. ) But the versed sine of MCG is MB = MC + BC . Relations of Sines , Tangents ...
... radius . But the versed sine of an obtuse angle is equal to the sum of the co- sine and radius . Thus the versed sine of ACG is AB = AC -BC . ( Art . 83. ) But the versed sine of MCG is MB = MC + BC . Relations of Sines , Tangents ...
Page 54
... radius , sin for sine , tan for tangent , sec for secant , cos for cosine , cot for cotangent , cosec for cosecant . By comparing the triangles CBG and CAD , 1. AC BC :: AD : BG , that is , R : cos :: tan sin . 2. CG : CD :: BG : AD 3 ...
... radius , sin for sine , tan for tangent , sec for secant , cos for cosine , cot for cotangent , cosec for cosecant . By comparing the triangles CBG and CAD , 1. AC BC :: AD : BG , that is , R : cos :: tan sin . 2. CG : CD :: BG : AD 3 ...
Page 55
... 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 definition , ( Art . 82. ) is CH , the radius of the circle . 2. Let AS be an ...
... 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 definition , ( Art . 82. ) is CH , the radius of the circle . 2. Let AS be an ...
Page 56
... radius . Cor . The cotangent of 45 ° is also equal to radius . For the complement of 45 ° is itself 45 ° . Thus HD , the cotan- gent of ACD , ( Fig . 5. ) is equal to AC the radius . 96. The sine of 30 ° is equal to half radius . For ...
... radius . Cor . The cotangent of 45 ° is also equal to radius . For the complement of 45 ° is itself 45 ° . Thus HD , the cotan- gent of ACD , ( Fig . 5. ) is equal to AC the radius . 96. The sine of 30 ° is equal to half radius . For ...
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.