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 140
... Similar polygons are divisible into the same number of similar triangles ; these triangles have to one another the same ratio that the polygons have ; and the polygons have to one another the duplicate ratio of that which their ...
... Similar polygons are divisible into the same number of similar triangles ; these triangles have to one another the same ratio that the polygons have ; and the polygons have to one another the duplicate ratio of that which their ...
Σελίδα 141
... similar polygons , & c . Q. E. D. COROLLARY 1. - In like manner it may be proved , that similar four- sided figures , or figures of any number of sides , are , one to another in the duplicate ratio of their homologous sides ; and this ...
... similar polygons , & c . Q. E. D. COROLLARY 1. - In like manner it may be proved , that similar four- sided figures , or figures of any number of sides , are , one to another in the duplicate ratio of their homologous sides ; and this ...
Σελίδα 193
... similar triangular pyramids similar to the whole pyramid , and two equal prisms which are together greater than half of the whole pyramid . Bisect A B , BC , CA , AD , DB , and DC , at the points E , F , G , H , K , and L ; and join E H ...
... similar triangular pyramids similar to the whole pyramid , and two equal prisms which are together greater than half of the whole pyramid . Bisect A B , BC , CA , AD , DB , and DC , at the points E , F , G , H , K , and L ; and join E H ...
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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