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An Introduction to Geometry, Consisting of Euclid's Elements, Book I ...
No preview available - 2018
ABCD adjacent angles angle ABC angle ACD angle BAC angle equal apply axiom base base BC bisects called centre circle common conclusion construction contained deduce definition describe diagonal Diagram diameter divided double draw drawn enunciation equal angles equilateral triangle Euclid EXAMINATION EXERCISE exterior fall figure follow four Geometry Give given point given straight line greater half Hence hypothesis inference interior angles intersect isosceles triangle join less letters magnitude means meet opposite sides pair of equal parallel parallelogram perpendicular plane Postulate problems produced proof Prop proposition prove quadrilateral questions reasoning referred remaining right angles right-angled triangle sides equal square Suppose taken theorems thesis things third triangle ABC unequal vertex Wherefore whole Write
Page 132 - 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 139 - 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 133 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Page 134 - Prove that parallelograms on the same base and between the same parallels are equal in area.
Page 134 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through the point A, parallel to the straight hue BC.
Page 50 - if two straight lines" &c. QED COR. 1. From this it is manifest, that if two straight lines cut one another, the angles which they make at the point where they cut, are together equal to four right angles.
Page 20 - PROB. from a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line : it is required to draw from the point A a straight line equal to BC.
Page 96 - Parallelograms upon the same base and between the same parallels, are equal to one another.