The Elements of Geometry: Or, The First Six Books, with the Eleventh and Twelfth of EuclidCassell, Petter, and Galpin, 1859 - 212 Seiten |
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Seite 209
... sphere a solid polyhedron , the superficies of which shall not meet the less . Let the spheres be cut by a plane passing through the centre ; the common sections of it with the spheres are circles ; for the sphere is described by the ...
... sphere a solid polyhedron , the superficies of which shall not meet the less . Let the spheres be cut by a plane passing through the centre ; the common sections of it with the spheres are circles ; for the sphere is described by the ...
Seite 211
... sphere , to that plane . Therefore the plane K BOS does not meet the less sphere . Also the other planes between the quadrants BX and K X do not meet the less sphere . From the point A draw A I perpendicular to the plane of the ...
... sphere , to that plane . Therefore the plane K BOS does not meet the less sphere . Also the other planes between the quadrants BX and K X do not meet the less sphere . From the point A draw A I perpendicular to the plane of the ...
Seite 212
... sphere . Corollary 2. - Every face of a polyhedron inscribed in a sphere is inscribable in a circle . PROP . XVIII . THEOREM . Spheres have to one another the triplicate ratio of that which their diameters have . Let A B C and D E F be ...
... sphere . Corollary 2. - Every face of a polyhedron inscribed in a sphere is inscribable in a circle . PROP . XVIII . THEOREM . Spheres have to one another the triplicate ratio of that which their diameters have . Let A B C and D E F be ...
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A B and CD A B C D A B is equal adjacent angles altitude angle ABC angle B A C base B C bisected Cassell's centre circle A B C circle ABCD circumference cone cylinder D E F described diagonal diameter draw equal angles equal Ax equal Const equiangular equimultiples Euclid exterior angle given rectilineal given straight line gnomon greater homologous Illustrated inscribed join less Let A B C multiple opposite angles parallelopiped pentagon perpendicular polygon prism proposition pyramid Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid angle sphere squares of AC straight line drawn straight lines A B THEOREM three plane angles touches the circle triangle A B C triplicate ratio twice the rectangle vertex Wherefore