The Elements of Geometry: Or, The First Six Books, with the Eleventh and Twelfth of EuclidCassell, Petter, and Galpin, 1859 - 212 σελίδες |
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Σελίδα 33
... manner it can be proved that no other straight line but A D is parallel to B C. Therefore A D is parallel to B C. Wherefore , equal triangles upon , & c . Q. E. D. Exercise 1. - If two sides of a triangle be bisected , the straight line ...
... manner it can be proved that no other straight line but A D is parallel to B C. Therefore A D is parallel to B C. Wherefore , equal triangles upon , & c . Q. E. D. Exercise 1. - If two sides of a triangle be bisected , the straight line ...
Σελίδα 172
... manner , it may be shown , that the other solid angles of the figures are equal to one another . Let the solid ... manner , the figure A H coincides with the figure K R , and the straight line D H with NR , and the point H with the point ...
... manner , it may be shown , that the other solid angles of the figures are equal to one another . Let the solid ... manner , the figure A H coincides with the figure K R , and the straight line D H with NR , and the point H with the point ...
Σελίδα 211
... manner it may be proved , that the plane TPR Y does not meet the same sphere , as also the triangle Y RX ( XII . Lem . 2 , Cor . ) . In the same manner it may be demonstrated , that all the planes , or faces of the polyhedron , do not ...
... manner it may be proved , that the plane TPR Y does not meet the same sphere , as also the triangle Y RX ( XII . Lem . 2 , Cor . ) . In the same manner it may be demonstrated , that all the planes , or faces of the polyhedron , do not ...
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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