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ABCD altitude angle ABC angle ACB angle BAC base bisected called chord circle circumference coincide common cone consequently construct contained convex surface curve described diameter difference distance divided draw drawn ellipse equal equal to AC equivalent extremities faces fall figure foci formed four frustum given greater half hence hyperbola included inscribed intersection join less major axis manner mean measured meet multiplied opposite ordinate parallel parallelogram parallelopiped pass perpendicular plane plane MN polygon prism PROBLEM Prop proportional PROPOSITION proved pyramid radii radius ratio reason rectangle regular remaining represent right angles Scholium segment sides similar sphere spherical square straight line tangent THEOREM third triangle ABC vertex vertices VIII whole
Side 17 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal.
Side 63 - IF a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the' rectangle contained by the parts.
Side 18 - BC common to the two triangles, which is adjacent to their equal angles ; therefore their other sides shall be equal, each to each, and the third angle of the one to the third angle of the other, (26.
Side 101 - When you have proved that the three angles of every triangle are equal to two right angles...
Side 10 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Side 37 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Side 32 - 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.
Side 15 - Wherefore, when a straight line, &c. QED PROP. XIV. THEOR. If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.