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 55.
Σελίδα 35
... fall on FD , for when two straight lines coin- cide in part , they must coincide throughout their mutual extent ( 51 ) . Therefore , the sum of all C F E the angles upon AB exactly coincides with the sum of all the angles upon CD , and ...
... fall on FD , for when two straight lines coin- cide in part , they must coincide throughout their mutual extent ( 51 ) . Therefore , the sum of all C F E the angles upon AB exactly coincides with the sum of all the angles upon CD , and ...
Σελίδα 38
... fall from the same point upon a given straight line , the perpendicular is shorter than any oblique line . If AD is perpendicular and AC oblique to BE , then AD is shorter than AC . Let the figure revolve upon BE as upon an axis ( 61 ) ...
... fall from the same point upon a given straight line , the perpendicular is shorter than any oblique line . If AD is perpendicular and AC oblique to BE , then AD is shorter than AC . Let the figure revolve upon BE as upon an axis ( 61 ) ...
Σελίδα 39
... fall from the same point upon a given straight line , and if two oblique lines meet the given line at equal dis- tances from the foot of the perpendicular , the two are equal . Let AD be the perpendicular and AC and AE the oblique lines ...
... fall from the same point upon a given straight line , and if two oblique lines meet the given line at equal dis- tances from the foot of the perpendicular , the two are equal . Let AD be the perpendicular and AC and AE the oblique lines ...
Σελίδα 40
... fall from the same point on a given straight line , of two oblique lines , that which meets the given line at a ... fall from D upon the line AC . This perpendicular must fall on the same side of BF 40 ELEMENTS OF GEOMETRY .
... fall from the same point on a given straight line , of two oblique lines , that which meets the given line at a ... fall from D upon the line AC . This perpendicular must fall on the same side of BF 40 ELEMENTS OF GEOMETRY .
Σελίδα 41
... fall on the same side of BF as the point D , for if it crossed the line BF , there would be from the point of intersection two perpendiculars on AC , which is impossible ( 103 ) . Now , since AB is equal to BC , AE must be greater than ...
... fall on the same side of BF as the point D , for if it crossed the line BF , there would be from the point of intersection two perpendiculars on AC , which is impossible ( 103 ) . Now , since AB is equal to BC , AE must be greater than ...
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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.