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ABCD added altitude angle equal apply argument assumed Axiom base base BC bisected centre circle circumference coincide common Conc construct contained definition demonstration describe diagonal diameter difference distance divided draw drawn earth's equal Euclid extremity fall feet figure four Geometry given given point greater half height impossible inches inference intersect join length less line BC measure meet miles named opposite parallel parallelogram perpendicular plane practical principle produced PROP proposition proved reasoning rectangle rectil rectilineal representative right angles scale sides square straight line suppose surface thing third triangle true truth units Wherefore whole
Page 38 - 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.
Page 17 - Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the same are equal to one another.
Page 43 - We assume that but one straight line can be drawn through a given point parallel to a given straight line.
Page 13 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Page 16 - LET it be granted that a straight line may be drawn from any one point to any other point.
Page 56 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Page 23 - If two angles of a triangle be equal to one another, the sides also which subtend, or are opposite to, the equal angles, shall be equal to one another.
Page 24 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base, equal to one another, and likewise those which are terminated in the other extremity.