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ABCD altitude antecedent appears base bisected centre chord circle circumference circumscribed coincide common consequently construction contained continually converse definition demonstration described diagonals diameter difference distance divided double draw equal equivalent Euclid expressed extremities figure follows former four Geometry given greater half hence hypothesis included inscribed intersect isosceles join less line drawn longer magnitudes manner mean measure meet method middle multiple necessary opposite parallel perimeter perpendicular polygon portion PROBLEM produced Prop proportion proposed PROPOSITION proved quadrilateral radii radius reasoning rectangle regular remain respectively equal rhomboid right angles Scholium shown sides similar space square straight line subtended suppose surface taken tangent THEOREM third triangle ABC twice vertex VIII whence whole
Side 177 - ... if a straight line, &c. QED PROPOSITION 29. — Theorem. If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.
Side 185 - If a straight line meets two straight lines, so as to make "the two interior angles on the same side of it taken " together less than two right angles...
Side 196 - BAG is a right angle (Def. 30.), the two straight lines AC, AG upon the opposite sides of AB, make with it at the point A the adjacent angles equal to two right angles; therefore CA is in the same straight line (i.
Side 38 - Any side of a triangle is less than the sum of the other two sides...