Treatise on Geometry and Trigonometry: For Colleges, Schools and Private Students. Written for the Mathematical Course of Joseph Ray, M.D.Sargent, Wilson & Hinkle, 1868 - 420 σελίδες |
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Σελίδα 280
... SINE of the given angle is the ratio of the perpen- dicular to the hypotenuse of the right angled triangle thus formed . The TANGENT of the angle is the ratio of the perpen- Idicular to the base . The SECANT of the angle is the ratio of ...
... SINE of the given angle is the ratio of the perpen- dicular to the hypotenuse of the right angled triangle thus formed . The TANGENT of the angle is the ratio of the perpen- Idicular to the base . The SECANT of the angle is the ratio of ...
Σελίδα 281
... sine of the angle A is written sin . A. These six are all the ratios that can be formed by the simple combination of the sides of the triangle . They are called , therefore , the simple functions of an angle . Other functions have been ...
... sine of the angle A is written sin . A. These six are all the ratios that can be formed by the simple combination of the sides of the triangle . They are called , therefore , the simple functions of an angle . Other functions have been ...
Σελίδα 282
... sine , tangent , and secant of the angle C. The names tangent and secant are taken from the geometrical tangent and secant . Arc , chord , and sine are derived from the fancied resemblance of the figure to the bow of the archer . The ...
... sine , tangent , and secant of the angle C. The names tangent and secant are taken from the geometrical tangent and secant . Arc , chord , and sine are derived from the fancied resemblance of the figure to the bow of the archer . The ...
Σελίδα 283
... sine is ; one whose tangent is ; one whose secant is 7 . SIGNS OF ANGLES AND OF THEIR FUNCTIONS . 822. An angle may be conceived to be generated by the revolution of a line about a point . Thus , the line AB beginning at AX , may take ...
... sine is ; one whose tangent is ; one whose secant is 7 . SIGNS OF ANGLES AND OF THEIR FUNCTIONS . 822. An angle may be conceived to be generated by the revolution of a line about a point . Thus , the line AB beginning at AX , may take ...
Σελίδα 284
... sine and cosecant of obtuse angles are positive . For , when the revolving line is in the second quarter of its revolution , that is , between AY and AX ' , the side AC ' of the triangle AB'C ' is the only negative term . Hence , the ...
... sine and cosecant of obtuse angles are positive . For , when the revolving line is in the second quarter of its revolution , that is , between AY and AX ' , the side AC ' of the triangle AB'C ' is the only negative term . Hence , the ...
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adjacent angles altitude angles equal apothem axis base bisect chord circle circumference circumscribed coincide cone Corollary Corollary.-The cosine Cotang curved surface cylinder demonstrated diagonals diameter dicular diedral angle distance divided draw equally distant equivalent EXERCISES faces figure formula four right angles frustum functions Geometry given angle given line given point given straight line given triangle greater Hence homologous homologous lines hypotenuse included angle inscribed intersection isosceles join less let fall mantissa measured number of sides opposite sides parallel lines parallelogram parallelopiped perimeter perpen perpendicular plane polyedral polyedron prism Problem.-Given pyramid quadrilateral radius ratio regular polygon respectively equal right angled triangle secant similar similarly arranged slant hight sphere spherical excess spherical polygon spherical triangle square student subtracting symmetrical Tang tangent tetraedrons theorem Theorem.-The triangles are equal triedral trirectangular vertex vertices volume
Δημοφιλή αποσπάσματα
Σελίδα 183 - If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal.
Σελίδα 238 - The volume of any parallelopiped is equal to the product of its base by its altitude.
Σελίδα 72 - Problem. — To draw a line through a given point parallel to a given line.
Σελίδα 141 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Σελίδα 91 - Conversely, if two angles of a triangle are equal, the sides opposite them are also equal, and the triangle is isosceles.
Σελίδα 173 - The areas of two circles are to each other as the squares of their radii ; or, as the squares of their diameters. 502. Corollary. — When the radius is unity, the area is expressed by -. 503. Theorem — The area of a sector is measured by half the product of its arc by its radius.
Σελίδα 240 - Corollary — The volume of any pyramid is equal to one-third of the product of its base by its altitude. For any pyramid...
Σελίδα 260 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Σελίδα 137 - The squa/re described on the difference of two straight lines is equivalent to the sum of the squares described on the two lines, diminished by twice the rectangle contained by the lines.
Σελίδα 274 - The areas of the surfaces of two spheres are to each other as the squares of their radii, or as the squares of their diameters.