Elements of Geometry: With Practical Applications ...H.H. Howley and Company, 1847 - 308 páginas |
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Página 90
... ratio can be accurately expressed but many magnitudes are incommensurable ; that is , their ratio can be expressed only by approximation ; which approximation may , however , be carried to any extent we desire . Such is the ratio of the ...
... ratio can be accurately expressed but many magnitudes are incommensurable ; that is , their ratio can be expressed only by approximation ; which approximation may , however , be carried to any extent we desire . Such is the ratio of the ...
Página 91
... ratio . Let AB and CD be the given lines . From the greater AB cut off parts equal to the lesser line CD , as many times as possible ; for example , twice , with the remainder FB . From the line CD cut off parts equal to FB , as many ...
... ratio . Let AB and CD be the given lines . From the greater AB cut off parts equal to the lesser line CD , as many times as possible ; for example , twice , with the remainder FB . From the line CD cut off parts equal to FB , as many ...
Página 92
... ratio , the arithmetical value of which can only be found approximately . 3. Similar figures are those which have the angles of the one equal to the angles of the other , each to each , and the sides about the equal angles proportional ...
... ratio , the arithmetical value of which can only be found approximately . 3. Similar figures are those which have the angles of the one equal to the angles of the other , each to each , and the sides about the equal angles proportional ...
Página 93
... ratios , we AD DB :: AF : FC . have : In a similar manner , the theorem is proved when the sides of the triangle are cut in prolongation beyond either the vertex or the base , Cor . Hence , also , the whole lines AB BOOK IV . 93.
... ratios , we AD DB :: AF : FC . have : In a similar manner , the theorem is proved when the sides of the triangle are cut in prolongation beyond either the vertex or the base , Cor . Hence , also , the whole lines AB BOOK IV . 93.
Página 112
... ratios , we have AC GK : CD : KL . Hence the two triangles ACD and GKL have an angle of the one equal to an angle of the other , and the sides about those angles proportional , and consequently the triangles are similar . In the same ...
... ratios , we have AC GK : CD : KL . Hence the two triangles ACD and GKL have an angle of the one equal to an angle of the other , and the sides about those angles proportional , and consequently the triangles are similar . In the same ...
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Términos y frases comunes
a+b+c AC² altitude angle ACD angle BAC bisect centre chord circ circular sector circumference cone consequently convex surface cylinder diagonal diameter distance draw equal and parallel equiangular equilateral triangle equivalent exterior angle figure formed four right angles given line greater half the arc hypothenuse inscribed circle intersection isosceles join less Let ABC lines drawn magnitude measured by half meet multiplied number of sides opposite angles parallel planes parallelogram parallelopipedon pendicular perimeter perpendicular plane MN point G prism PROBLEM produced Prop PROPOSITION pyramid radii radius rectangle regular polygon respectively equal right angles right-angled triangle Sabc Schol Scholium semicircle semicircumference side AC similar similar triangles solid angle solid described sphere spherical triangle square straight line suppose tangent THEOREM three sides triangle ABC triangular prism vertex VIII
Pasajes populares
Página 37 - The sum of all the angles of a polygon is equal to twice as many right angles as the polygon has sides, less two.
Página 180 - THEOREM. If one of two parallel lines is perpendicular to a plane, the other will also be perpendicular to this plane. Let AP & ED be parallel lines, of which AP is perpendicular to the plane MN ; then will ED be also perpendicular to this plane.
Página 139 - PROBLEM. To inscribe a circle in a given triangle. Let ABC be the given triangle : it is required to inscribe a circle in the triangle ABC.
Página 224 - The radius of a sphere is a straight line, drawn from the centre to any point of the...
Página 43 - In a right-angled triangle, the side opposite the right angle is" called the Hypothenuse ; and the other two sides are cal4ed the Legs, and sometimes the Base and Perpendicular.
Página 184 - THEOREM. If two angles, not situated in the same plane, have their sides parallel and lying in the same direction, they will be equal, and the planes in which they are situated will be parallel.
Página 10 - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another.
Página 226 - We conclude then, that the solidity of a cylinder is equal to the product of its base by its altitude.
Página 22 - If two sides and the included angle of the one are respectively equal to two sides and the included angle of the other...
Página 12 - If equals be added to unequals, the wholes are unequal. V. If equals be taken from unequals, the remainders are unequal. VI. Things which are double of the same, are equal to one another.