Elements of Geometry, Conic Sections, and Plane TrigonometryHarper & Bros., 1877 - 443 σελίδες |
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Σελίδα 8
... pyramid and cone , and cultivated the theory of the conic sections . After the time of Plato , the most remarkable epoch in the history of Geometry was the establishment of the school of Alexandria , about 300 years before Christ . It ...
... pyramid and cone , and cultivated the theory of the conic sections . After the time of Plato , the most remarkable epoch in the history of Geometry was the establishment of the school of Alexandria , about 300 years before Christ . It ...
Σελίδα 153
... pyramid . The triangular faces taken together constitute its lateral or convex surface . 13. The altitude of a pyramid is the perpendicu- lar let fall from the vertex upon the plane of the base produced , if necessary . 14. A triangular ...
... pyramid . The triangular faces taken together constitute its lateral or convex surface . 13. The altitude of a pyramid is the perpendicu- lar let fall from the vertex upon the plane of the base produced , if necessary . 14. A triangular ...
Σελίδα 163
... ) , AB2 × AF : ab2 × aƒ :: AF3 : aƒ3 :: AB3 : al3 . Hence ( B. II . , Pr . 4 ) we have solid FD : solid fd :: AB3 : ab3 :: AF3 : aƒ3 . Therefore similar prisms , etc. F PROPOSITION XIII . THEOREM . If a pyramid be BOOK VIII . 163.
... ) , AB2 × AF : ab2 × aƒ :: AF3 : aƒ3 :: AB3 : al3 . Hence ( B. II . , Pr . 4 ) we have solid FD : solid fd :: AB3 : ab3 :: AF3 : aƒ3 . Therefore similar prisms , etc. F PROPOSITION XIII . THEOREM . If a pyramid be BOOK VIII . 163.
Σελίδα 164
... pyramid , etc. Cor . 1. If two pyramids having the same altitude , and their bases situated in the same plane , are cut by a plane parallel to their bases , the sections will be to each other as the bases . Let A - BCDEF , A - MNO be ...
... pyramid , etc. Cor . 1. If two pyramids having the same altitude , and their bases situated in the same plane , are cut by a plane parallel to their bases , the sections will be to each other as the bases . Let A - BCDEF , A - MNO be ...
Σελίδα 165
... pyramid is equal to the product of the perimeter of its base by half its slant height . Let A - BDE be a regular pyramid whose base is the polygon BCDEF , and its slant height AH ; then will its lateral surface be equal to the pe ...
... pyramid is equal to the product of the perimeter of its base by half its slant height . Let A - BDE be a regular pyramid whose base is the polygon BCDEF , and its slant height AH ; then will its lateral surface be equal to the pe ...
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Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angle ABC angle ACB angle BAC base bisect centre centre of symmetry chord circle circumference cone conjugate conjugate hyperbola Cosine Cotang curve described diagonals diameter directrix distance divided draw ellipse equal to AC equilateral equivalent figure foci frustum given angle given line given point given straight line greater half Hence hyperbola hypothenuse inscribed intersection join latus rectum less Let ABC line drawn logarithm major axis meet multiplied number of sides ordinate parabola parallel to BC parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced projection Prop PROPOSITION pyramid quadrant quadrilateral radical axis radii radius ratio rectangle regular polygon right-angled triangle Scholium secant segment side AC similar sine solid angle sphere spherical square subtangent symmetrical Tang tangent THEOREM transverse axis triangle ABC vertex vertices
Δημοφιλή αποσπάσματα
Σελίδα 68 - Any two rectangles are to each other as the products of their bases by their altitudes.
Σελίδα 35 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Σελίδα 187 - 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 64 - BEC, taken together, are measured by half the circumference ; hence their sum is equal to two right angles.
Σελίδα 71 - IF a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the' rectangle contained by the parts.
Σελίδα 23 - BC common to the two triangles, which is adjacent to their equal angles ; therefore their other sides shall be equal, each to each, and the third angle of the one to the third angle of the other, (26.
Σελίδα 20 - Wherefore, when a straight line, &c. QED PROP. XIV. THEOR. If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Σελίδα 124 - The area of a circle is equal to the product of its circumference by half the radius.* Let ACDE be a circle whose centre is O and radius OA : then will area OA— ^OAxcirc.
Σελίδα 177 - THEOREM. The sum of the sides of a spherical polygon, is less than the circumference of a great circle. Let...
Σελίδα 27 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.