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AB is equal AC is equal acute alternate angles ancient angle ACD angle BAC angles ABC appears application assume axiom base BC bisect called centre circle circumference coincide common conclusion construction definition demonstration describe determined diagonal draw drawn elements employed established Euclid evident extended exterior angle extremities fall figure four right angles geometers geometry given straight line greater half Hence included angle interior opposite angle intersect introduced join knowledge less Let ABC magnitudes manner means meet method mind mode necessary obtuse parallel lines parallelogram perpendicular plane position principle produced proof properties PROPOSITION proved radiant reason rectangle rectilineal figure remaining respects side AC supposed surfaces THEOR theorem thing third triangle ABC triangles are equal truths unequal vertex wherefore whole
Side 41 - 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 35 - The angles which one straight line makes with another upon one tide of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it the angles CBA, ABD ; these are either two right angles, or are together equal to two right angles. For, if the angle CBA be equal to ABD, each of them is a right angle (Def.
Side 55 - Through a given point to draw a straight line parallel to a given straight line, Let A be the given point, and BC the given straight line : it is required to draw through the point A a straight line parallel to BC.
Side 36 - ... in one and the same straight line. At the point B in the straight line AB, let the two straight lines BC, BD upon the opposite sides of AB, make the adjacent angles ABC, ABD, equal together to two right angles. BD is in the same straight line with CB.
Side 66 - 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 32 - LET it be granted that a straight line may be drawn from any one point to any other point.
Side 62 - Parallelograms upon the same base, and between the same parallels, are equal to one another.
Side 44 - If one side of a triangle be produced, the exterior angle is greater than either of the interior, and opposite angles.