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AC is equal altitude angle ABC base ABC bisected circle ABCD circumference cone Construction contained Corollary cylinder Demonstration diameter divided draw EFGH equal angles equal in area equi equiangular equilateral equimultiples Euclid external angle fore fourth given circle given line given rectilineal given straight line greater ratio Hypoth Hypotheses inscribed join less line AC lines be drawn meet multiple opposite angle parallel parallelogram perpendicular polygon prism produced proposition pyramid ABCG pyramid DEFH rectangle rectilineal figure remaining angles right angles Scholia Scholium segment side AC solid angle solid CD solid parallelopipeds sphere square on AC straight line syllogism Theorem Theorem.—If third three plane angles tiple triangle ABC triplicate ratio vertex wherefore
Pagina 115 - A cone is a solid figure described by the revolution of a right-angled triangle about one of the sides containing the right angle, which side remains fixed.
Pagina 20 - Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike equal to, or alike fall short of, the latter equimultiples respectively taken in corresponding...
Pagina 84 - From the point A draw a straight line AC, making any angle with AB ; and in AC take any point D, and take AC the same multiple of AD, that AB is of the part which is to be cut off from it : join BC, and draw DE parallel to it : then AE is the part required to be cut off. Because ED is parallel to one of the sides of the triangle ABC, viz. to BC ; as CD is to DA, so is (2.
Pagina 119 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Pagina 124 - ... plane, from a given point above it. Let A be the given point above the plane BH; it is required to draw from the point A a straight line perpendicular to the plane BH.
Pagina 123 - For the same reason, CD is likewise at right angles to the plane HGK. Therefore AB, CD are each of them at right angles to the plane HGK.
Pagina 51 - IF magnitudes, taken jointly, be proportionals, they shall also be proportionals when taken separately ; that is, if two magnitudes together have to one of them the same ratio which two others have to one of these, the remaining one of the first two shall have to the other the same ratio which the remaining one of the last two has to the other of these. Let AB, BE, CD...
Pagina 34 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.