Elements of plane geometry, book i, containing nearly the same propositions as the first book of Euclid's Elements1865 |
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AB is equal ABC and DEF ABC is equal acute adjacent angles ancient geometers angle ACD angle AGH angle BAC angles ABC angles equal angular magnitude base BC bisect centre circumference coincide diagonal drawn EBCF equal alternate angles equal Def equal to BC Euclid EUCLID'S ELEMENTS exterior angle figure has sides four right angles geometers given point given straight line greater than AC included angle interior opposite angle intersect isosceles triangle join less Let ABC Let the straight method method of exhaustions parallel lines parallel to CD parallelogram ABCD perpendicular PLANE GEOMETRY point F PROB proof properties of parallel PROPOSITION Pythagoras radius rectangle rectilineal figure reductio ad absurdum Scholium side AB side AC straight line BC THEOR theorem three angles three sides triangle ABC triangle DEF triangles are equal truths unequal vertex vertical angle wherefore
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الصفحة 43 - 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.
الصفحة 46 - Any two angles of a triangle are together less than two right angles.
الصفحة 37 - 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.
الصفحة 57 - 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.
الصفحة 38 - ... 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.
الصفحة 68 - 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.
الصفحة 34 - LET it be granted that a straight line may be drawn from any one point to any other point.
الصفحة 64 - Parallelograms upon the same base, and between the same parallels, are equal to one another.
الصفحة 46 - If one side of a triangle be produced, the exterior angle is greater than either of the interior, and opposite angles.
الصفحة 34 - Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal.