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 58.
Σελίδα 23
... pass through any two points . 48. Problem . There may be a straight line from any point , in any direction , and of any extent . These two propositions are corollaries of the post- ulates . 49. From a point , straight lines may extend ...
... pass through any two points . 48. Problem . There may be a straight line from any point , in any direction , and of any extent . These two propositions are corollaries of the post- ulates . 49. From a point , straight lines may extend ...
Σελίδα 25
... pass through the points A and E B , a second through B and C , and a third through A and C. Each of these lines ( 58 ) lies wholly in each of the planes m and p . Now it is to be proved that any point D , in the plane m , must also be ...
... pass through the points A and E B , a second through B and C , and a third through A and C. Each of these lines ( 58 ) lies wholly in each of the planes m and p . Now it is to be proved that any point D , in the plane m , must also be ...
Σελίδα 32
... pass through the common point and another point in each line , making three in all . These three points determine the position of the plane ( 60 ) . DEFINITIONS . C 84. Let the line AB be fixed 32 ELEMENTS OF GEOMETRY . ANGLES,
... pass through the common point and another point in each line , making three in all . These three points determine the position of the plane ( 60 ) . DEFINITIONS . C 84. Let the line AB be fixed 32 ELEMENTS OF GEOMETRY . ANGLES,
Σελίδα 34
... pass through or cut each other , four angles are formed , each direction of one line making a difference with each direction of the other . The opposite angles formed by two lines cutting each other are called VERTICAL angles . A line ...
... pass through or cut each other , four angles are formed , each direction of one line making a difference with each direction of the other . The opposite angles formed by two lines cutting each other are called VERTICAL angles . A line ...
Σελίδα 46
... pass through the point H , parallel to DC . makes a corresponding angle equal to CGF , and therefore equal to AHF . This sup- E F H B D posed parallel line lies in the same plane as CD and H ( 121 ) ; that is , by hypothesis , in the ...
... pass through the point H , parallel to DC . makes a corresponding angle equal to CGF , and therefore equal to AHF . This sup- E F H B D posed parallel line lies in the same plane as CD and H ( 121 ) ; that is , by hypothesis , in the ...
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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.