Elements of Geometry: With, Practical ApplicationsD. Appleton and Company, 1850 - 320 σελίδες |
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Σελίδα 234
With, Practical Applications George Roberts Perkins. greater cylinder , or of a smaller one . Suppose it first to be the measure of a smaller one ; of a cylinder , for example , which has CD for the radius of its base , H being the ...
With, Practical Applications George Roberts Perkins. greater cylinder , or of a smaller one . Suppose it first to be the measure of a smaller one ; of a cylinder , for example , which has CD for the radius of its base , H being the ...
Σελίδα 235
... cylinder . Hence , finally , the solidity of a cylinder is equal to the product of its base by its altitude . Cor . 1. Cylinders of the same altitude are to each other as their bases ; and cylinders of the same base are to each other as ...
... cylinder . Hence , finally , the solidity of a cylinder is equal to the product of its base by its altitude . Cor . 1. Cylinders of the same altitude are to each other as their bases ; and cylinders of the same base are to each other as ...
Σελίδα 236
... cylinder is greater than the convex surface of any inscribed prism , and less than the convex surface of any circumscribed prism . For the concave surface of the cylin- der and that of the prism may be con- sidered as having the same ...
... cylinder is greater than the convex surface of any inscribed prism , and less than the convex surface of any circumscribed prism . For the concave surface of the cylin- der and that of the prism may be con- sidered as having the same ...
Σελίδα 237
... cylinder might be shown to be less than that of any circumscribed prism BCDKLKH . THEOREM . PROPOSITION IV . The convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude . Let CA be the radius of ...
... cylinder might be shown to be less than that of any circumscribed prism BCDKLKH . THEOREM . PROPOSITION IV . The convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude . Let CA be the radius of ...
Σελίδα 238
... cylinder whose base has CD for its radius , which cyl- inder is inscribed in the prism ; hence the convex surface of ... cylinder's base , multiplied by its altitude , cannot be the measure of a smaller cylinder . Neither can this ...
... cylinder whose base has CD for its radius , which cyl- inder is inscribed in the prism ; hence the convex surface of ... cylinder's base , multiplied by its altitude , cannot be the measure of a smaller cylinder . Neither can this ...
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Elements of Geometry With Practical Applications George R Perkins Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2023 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 28 - If two sides and the included angle of the one are respectively equal to two sides and the included angle of the other...
Σελίδα 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.
Σελίδα 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...
Σελίδα 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'.
Σελίδα 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.
Σελίδα 232 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Σελίδα 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.