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ABCD added angle equal apply assumed Axioms base base BC bisected centre circle circumference coincide common Conc construct contained definition demonstration describe diagonal diameter distance divided draw drawn equal Euclid extremity fall feet figure four Geometry given given line given point given st greater half height impossible inches inference join length less line BC measure meet miles named opposite parallel parallelogram perpendicular plane principle produced PROP proposition proved Quæs reasoning rectangle rectilineal representative right angles scale sides square straight line suppose surface thing third triangle true truth Wherefore whole Нур
Pagina 36 - 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 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.
Pagina 41 - We assume that but one straight line can be drawn through a given point parallel to a given straight line.
Pagina 13 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Pagina 16 - LET it be granted that a straight line may be drawn from any one point to any other point.
Pagina 54 - 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.
Pagina 21 - 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.
Pagina 22 - 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.