Elements of GeometryHilliard, Gray,, 1841 - 235 Seiten |
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Seite vii
... cylinder . The measure of the surfaces and solidities of these bodies is deter- mined by a method analogous to that of Archimedes , and found- ed , as to surfaces , upon the same principles , which we have endeavoured to demonstrate ...
... cylinder . The measure of the surfaces and solidities of these bodies is deter- mined by a method analogous to that of Archimedes , and found- ed , as to surfaces , upon the same principles , which we have endeavoured to demonstrate ...
Seite 177
... cylinder the solid generated by the revolution of a rectangle ABCD ( fig . 250 ) , which may be conceived to Fig ... cylinder , and the side CD describes the convex surface of the cylinder . The fixed line AB is called the axis of the ...
... cylinder the solid generated by the revolution of a rectangle ABCD ( fig . 250 ) , which may be conceived to Fig ... cylinder , and the side CD describes the convex surface of the cylinder . The fixed line AB is called the axis of the ...
Seite 178
... cylinder , a polygon ABCDE be inscribed , and upon the base ABCDE a right prism be erected equal in altitude to the cylinder , the prism is said to be inscribed in the cylinder , or the cylinder to be circumscribed about the prism . It ...
... cylinder , a polygon ABCDE be inscribed , and upon the base ABCDE a right prism be erected equal in altitude to the cylinder , the prism is said to be inscribed in the cylinder , or the cylinder to be circumscribed about the prism . It ...
Seite 180
... cylinder is equal to the product of its base by its altitude . Demonstration . Let CA ( fig . 258 ) be the radius of the base of the given cylinder , H its altitude ; and let surf . CA represent the surface of a circle whose radius is ...
... cylinder is equal to the product of its base by its altitude . Demonstration . Let CA ( fig . 258 ) be the radius of the base of the given cylinder , H its altitude ; and let surf . CA represent the surface of a circle whose radius is ...
Seite 181
... cylinder by its altitude cannot be the measure of a less cylinder . We say , in the second place , that this same product cannot be the measure of a greater cylinder ; for , not to multiply figures , let CD be the radius of the base of ...
... cylinder by its altitude cannot be the measure of a less cylinder . We say , in the second place , that this same product cannot be the measure of a greater cylinder ; for , not to multiply figures , let CD be the radius of the base of ...
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ABC fig adjacent angles altitude angle ACB angle BAC base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal angles equiangular equilateral equivalent faces figure formed four right angles frustum GEOM given point gles greater hence homologous sides hypothenuse inclination intersection isosceles triangle join less Let ABC let fall Let us suppose line AC mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced proposition radii radius ratio rectangle regular polygon right angles Scholium sector segment semicircle semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM third three angles triangle ABC triangular prism triangular pyramids vertex vertices whence
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Seite 67 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Seite 9 - 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.
Seite 65 - 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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Seite 160 - ABC (fig. 224) be any spherical triangle ; produce the sides AB, AC, till they meet again in D. The arcs ABD, ACD, will be...
Seite 168 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.
Seite 157 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Seite 8 - Any side of a triangle is less than the sum of the other two sides...
Seite 82 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Seite 29 - Two equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre.
Seite 182 - CD, &c., taken together, make up the perimeter of the prism's base : hence the sum of these rectangles, or the convex surface of the prism, is equal to the perimeter of its base multiplied by its altitude.