## Elements of plane (solid) geometry (Higher geometry) and trigonometry (and mensuration), being the first (-fourth) part of a series on elementary and higher geometry, trigonometry, and mensuration |

### From inside the book

Results 1-5 of 48

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**cosine**of that angle . Thus , sin . ( 90 ° -9 ) = cos . 4 , hence cos . ( 90 ° -4 ) = sin . 4 . 9. The tangent of the complement of any given angle , is called the cotangent of that angle . Thus , tan . ( 90 ° -9 ) = cot . 6 , hence cot ... Page 36

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**cosines**of angles in the different quadrants . PS In the first quadrant , sin . 8 : CA CS . cos . = CA B Here ...**cosine**negative . PS , In the third quadrant , sin . = CA CS , COS . = CA 3 3 Here P , S , = Cc , is reckoned from C ... Page 37

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**cosine**positive . Hence we conclude , that the sine is positive in the first and second quadrants , and negative in the third and fourth ; and the**cosine**is positive in the first and fourth , and negative in the second and third , or ... Page 38

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**cosine**for angles of different magnitudes . In the first quadrant : Let CP , CP ,, CP ,, ... be different positions ...**cosine**diminishes ; for CS CS . CA CA CS , CS . and C2 > CA СА When the angle is very small , CS is very 38 ... Page 39

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**cosine**increases ; for CS , CS , and CS5 CS CA < CA CA CA and when the revolving radius coincides with CD and the an- gle becomes 180 ° , CP coincides with CD and is equal to it . CS Hence since , generally , cos . = CS = CD ; and since ...### Other editions - View all

Elements of Plane (Solid) Geometry (Higher Geometry) and Trigonometry (and ... Nathan Scholfield No preview available - 2015 |

### Common terms and phrases

ABCD abscissa altitude axis bisect chord circle circular segment circum circumference circumscribing cone conjugate construction convex surface cosec cosine cube curve cylinder described diameter distance divided draw ellipse equal to half equation equivalent feet figure formed frustum Geom geometry given hence hyperbola hypothenuse inches inscribed inscribed sphere latus rectum length logarithm magnitude measured multiplied by one-third number of sides opposite ordinates parabola parallel parallelogram perimeter perpendicular plane polyedroid polyedron polygon portion prism PROBLEM Prop proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon revoloid rhomboid right angled triangle right line root Scholium sector segment similar similar triangles sine slant height solid angle sphere spherical square straight line tangent THEOREM triangle ABC triangular triangular prism ungula vertex vertical virtual centre

### Popular passages

Page 36 - Prove that parallelograms on the same base and between the same parallels are equal in area.

Page 35 - The sum of any two sides of a triangle, is greater than the third side.

Page 60 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.

Page 56 - In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs.

Page 38 - The volumes of similar solids are to each other as the cubes of their like dimensions.

Page 75 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.

Page 86 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let...

Page 211 - To find the solidity of a hyperbolic conoid, or otherwise called a hyperboloid. RULE. To the square of the radius of the base, add the square of the diameter...

Page 48 - Hence, the interior angles plus four right angles, is equal to twice as many right angles as the polygon has sides, and consequently, equal to the sum of the interior angles plus the exterior angles.