Book Iv of Euclid’s Elements and Ancient Greek Mosaics

I.4: “If two triangles have the two sides equal to two sides respectively, and have the angles contained by the equal straight lines equal, they will also have the base equal to the base, the triangle will be equal to the remaining angles respectively, namely those which the equal sides subtend.” I.9: “To bisect a given rectilinear angle.” I.10: “To bisect a given finite straight line.” I.11: “To draw a straight line at right angles to a given straight line from a given point on it.” I.12: “To a given infinite straight line, from a given point which is not on it, to draw a perpendicular straight line.” I.13: “If a straight line set up on a straight line make angles, it will make either two right angles or angles equal to two right angles.” I.23: “On a given straight line and at a point on it to construct a rectilinear angle equal to a given rectilinear angle.” I.26: “If two triangles have the two angles equal to two angles respectively, and one side equal to one side, namely, either the side adjoining the equal angles, or that subtending one of the equal angles, they will also have the remaining sides equal to the remaining sides and the remaining angle to the remaining angle.” I.32: “In any triangle, if one of the sides be produced, the exterior angle is equal to the two interior and opposite angles, and the three interior angles of the triangle are equal to two right angles.” I.36: “Parallelograms which are on equal bases and in the same parallels are equal to one another.” I.38: “Triangles which are on equal bases and in the same parallels are equal to one another.” I.41: “If a parallelogram have the same base with a triangle and be in the same parallels, the parallelogram is double of the triangle.” I.46: “On a given straight line to describe a square.” I.47: “In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides containing the right angle.”