Elements of Geometry: With, Practical ApplicationsD. Appleton and Company, 1850 - 320 páginas |
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Página 144
... angle of a regular polygon , which is 1800 360 ° n shows that no polygon can have angles consisting of a whole ... solid blocks , as in flooring , paving , or by their superposition as in masonry . The poly- gons used in such cases must ...
... angle of a regular polygon , which is 1800 360 ° n shows that no polygon can have angles consisting of a whole ... solid blocks , as in flooring , paving , or by their superposition as in masonry . The poly- gons used in such cases must ...
Página 181
... angle they form between them , is the angle contained by two lines drawn from any point in their intersection , and ... solid angle is the angular space included be- tween three or more planes which meet at the same point . 16 ...
... angle they form between them , is the angle contained by two lines drawn from any point in their intersection , and ... solid angle is the angular space included be- tween three or more planes which meet at the same point . 16 ...
Página 197
... solid angle is formed by three plane angles , the sum of any two of these angles will be greater than the third . The proposition requires de- monstration only when the plane angle , which is compared to the sum of the other two , is ...
... solid angle is formed by three plane angles , the sum of any two of these angles will be greater than the third . The proposition requires de- monstration only when the plane angle , which is compared to the sum of the other two , is ...
Página 198
... angle BSD = BSC ; draw the straight line ADB at pleasure ; and , having taken SC SD , join AC , BC . The two sides ... solid angle , is always less than four right - angles . Conceive the solid angle S to be cut by any plane ABCDE : from ...
... angle BSD = BSC ; draw the straight line ADB at pleasure ; and , having taken SC SD , join AC , BC . The two sides ... solid angle , is always less than four right - angles . Conceive the solid angle S to be cut by any plane ABCDE : from ...
Página 199
... solid angle S , is less than four right- angles . Schol . This demonstration is founded on the supposi- tion that the solid angle is convex , or that the plane of no one surface produced can ever meet the solid angle . If it were ...
... solid angle S , is less than four right- angles . Schol . This demonstration is founded on the supposi- tion that the solid angle is convex , or that the plane of no one surface produced can ever meet the solid angle . If it were ...
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Términos y frases comunes
a+b+c altitude angle ABC angle BAC angle BCD bisect centre chord circ circular sector circumference circumscribed polygon coincide cone consequently convex surface cylinder denote diagonal diameter dicular distance draw equal and parallel equiangular equilateral triangle equivalent exterior angle figure formed given line greater half the arc hypothenuse inscribed circle intersection isosceles join less Let ABC line AC line CD lines drawn measured by half meet multiplied number of sides parallel planes parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN point G prism PROBLEM produced Prop PROPOSITION pyramid radii radius rectangle regular polygon respectively equal right-angled triangle Sabc Schol Scholium scribed semicircle semicircumference side AC similar similar triangles solid angle sphere spherical triangle square straight line suppose tangent THEOREM three sides triangle ABC triangular prism vertex VIII
Pasajes populares
Página 231 - THE sphere is a solid terminated by a curve surface, all the points of which are equally distant from a point within, called the centre.
Página 147 - 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 17 - 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 28 - If two sides and the included angle of the one are respectively equal to two sides and the included angle of the other...
Página 233 - The volume of a cylinder is equal to the product of its base by its altitude. Let the volume of the cylinder be denoted by V, its base by B, and its altitude by H.
Página 276 - THEOREM. Two triangles on the same sphere, or on equal spheres, are equal in all their parts, when they have each an equal angle included between equal sides. Suppose the side...
Página 120 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Página 18 - 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.
Página 232 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Página 96 - Similar figures, are those that have all the angles of the one equal to all the angles of the other, each to each, and the sides about the equal angles proportional.