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AB is equal AC and CD adjacent angles alternate angles angle ABC angle ACB angle BAC angle BCD angle DEF angle EDF angle EGB angle equal angles BGH angles CBA base BC BC is equal bisect centre circle ABC circumference Construction.—Join diagonal diameter double draw equal circles equal to CD equal to tho equal to twice EUCLID'S ELEMENTS exterior angle given circle given point given rectilineal angle given straight line gnomon interior and opposite isosceles triangle less Let ABC Let the straight lino opposite angles parallel to CD parallelogram perpendicular produced Proof.—Because Q.E.D. Proposition rectangle AE rectangle contained remaining angle right angles Ax semicircle side BC square described square on AC straight line AB straight line AC touches the circle triangle ABC triangle DEF twice the rectangle
الصفحة 37 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are equal to two right angles.
الصفحة 13 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal. Let ABC be an isosceles triangle, of which the side AB is equal to AC, and let the straight lines AB, AC be produced to D and E.
الصفحة 7 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
الصفحة 17 - If two triangles have two sides of the one equal to two sides of the...
الصفحة 53 - If the square described upon one of the sides of a triangle, be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle.
الصفحة 9 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
الصفحة 71 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
الصفحة 9 - Things which are double of the same, are equal to one another. 7. Things which are halves of the same, are equal to one another.
الصفحة 34 - Wherefore, if a straight line, &c. QED PROPOSITION XXVIII. THEOREM. If a straight line falling upon two other straight lines, make the exterior angle equal to the interior and opposite upon the same side of the line ; or make the interior angles upon the same side together equal to two right angles ; the two straight lines shall be parallel to one another.
الصفحة 69 - If a straight line be bisected, and produced to any point; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line, which is made up of the half and the part produced.