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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Αποτελέσματα 1 - 5 από τα 87.
Σελίδα 33
... VERTEX . The definition shows that the angle depends upon the directions only , and not upon the length of the sides . 85. Three letters may be used to mark an angle , the one at the vertex being in the middle , as the angle BAC . When ...
... VERTEX . The definition shows that the angle depends upon the directions only , and not upon the length of the sides . 85. Three letters may be used to mark an angle , the one at the vertex being in the middle , as the angle BAC . When ...
Σελίδα 37
... vertices at one point is equal to two right angles , the extreme sides form one straight line . If the sum of AGB , BGC , etc. , be equal to two right an- gles , then will AGF be one straight line . A B. Ꭰ F For the sum of all these ...
... vertices at one point is equal to two right angles , the extreme sides form one straight line . If the sum of AGB , BGC , etc. , be equal to two right an- gles , then will AGF be one straight line . A B. Ꭰ F For the sum of all these ...
Σελίδα 49
... vertices , the two angles are equal . If the directions BA and DC are the same , and the directions DE and BF are the same , then the angles ABF and CDE are equal . For each of these angles is equal to the angle CGF ( 124 ) . 139. Let ...
... vertices , the two angles are equal . If the directions BA and DC are the same , and the directions DE and BF are the same , then the angles ABF and CDE are equal . For each of these angles is equal to the angle CGF ( 124 ) . 139. Let ...
Σελίδα 64
... vertex at the center of a circle are called , for this reason , angles at the center . The arc between the sides of an angle is called the in- tercepted arc of the angle . 197. Theorem . - The radii being equal , any two angles at the ...
... vertex at the center of a circle are called , for this reason , angles at the center . The arc between the sides of an angle is called the in- tercepted arc of the angle . 197. Theorem . - The radii being equal , any two angles at the ...
Σελίδα 67
... vertices in the curve , may be diminished at will , and the broken line made to approximate the curve indefinitely . Hence , a curve is the limit of those broken lines which have all their vertices in the curve . 200. The arc BC , which ...
... vertices in the curve , may be diminished at will , and the broken line made to approximate the curve indefinitely . Hence , a curve is the limit of those broken lines which have all their vertices in the curve . 200. The arc BC , which ...
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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.