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 iv
... functions are defined as ratios . This method has the advantages of being more simple and more brief , yet more comprehensive than the ancient geometrical method . For many things in these chapters , credit is due to the works of Mr. I ...
... functions are defined as ratios . This method has the advantages of being more simple and more brief , yet more comprehensive than the ancient geometrical method . For many things in these chapters , credit is due to the works of Mr. I ...
Σελίδα viii
... FUNCTIONS OF ANGLES , 279 CONSTRUCTION AND USE OF TABLES , 296 RIGHT ANGLED TRIANGLES , 302 SOLUTION OF PLANE TRIANGLES , 304 CHAPTER XIII . SPHERICAL TRIGONOMETRY . SPHERICAL ARCS AND ANGLES , 314 RIGHT ANGLED SPHERICAL TRIANGLES , 324 ...
... FUNCTIONS OF ANGLES , 279 CONSTRUCTION AND USE OF TABLES , 296 RIGHT ANGLED TRIANGLES , 302 SOLUTION OF PLANE TRIANGLES , 304 CHAPTER XIII . SPHERICAL TRIGONOMETRY . SPHERICAL ARCS AND ANGLES , 314 RIGHT ANGLED SPHERICAL TRIANGLES , 324 ...
Σελίδα 277
... functions , and the methods of calculating these functions . MEASURE OF ANGLES . 812. In Elementary Geometry , the unit for the meas- ure of angles is usually the right angle . The frequent fractions which the use of this unit gives ...
... functions , and the methods of calculating these functions . MEASURE OF ANGLES . 812. In Elementary Geometry , the unit for the meas- ure of angles is usually the right angle . The frequent fractions which the use of this unit gives ...
Σελίδα 279
... FUNCTIONS OF ANGLES . 816. When two quantities are so related that any variation in one causes a variation in the other , each is a function of the other . Thus , x is a function of x ; the area of a circle is a function of its radius ...
... FUNCTIONS OF ANGLES . 816. When two quantities are so related that any variation in one causes a variation in the other , each is a function of the other . Thus , x is a function of x ; the area of a circle is a function of its radius ...
Σελίδα 280
... functions of the given angle . For , if any number of tri- angles were thus formed with a given angle , all of these tri- angles would be similar ( 306 ) , A. and their sides would have the same ratios ( 309 ) . When the given angle is ...
... functions of the given angle . For , if any number of tri- angles were thus formed with a given angle , all of these tri- angles would be similar ( 306 ) , A. and their sides would have the same ratios ( 309 ) . When the given angle is ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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.