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An Introduction to Geometry, Consisting of Euclid's Elements, Book I ...
Sin vista previa disponible - 2018
ABCD ABGD adjacent angles alternate angle angle ABC angle AGB angle equal angles CBA apply axiom base BG BG is equal centre circle circumference Constr construction definition describe diagonal Diagram diameter draw a straight enunciation equal and parallel equal angles equal sides equal triangles Equiangular Polygons equilateral triangle Euclid Euclid's Elements exterior four right angles Geometry given angle given point given straight line greater hypotenuse hypothesis inference interior angles isosceles triangle join less magnitude meet middle point opposite angles opposite interior angle opposite sides pair of equal parallelogram perpendicular Postulate produced proof Prop Proposition prove Q. E. D. Exercise quadrilateral rectilineal figure respectively equal rhombus right angles right-angled triangle sides equal square theorems thesis third angle trapezium triangle ABC triangles are equal unequal vertex Wherefore
Página 136 - 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.
Página 143 - 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.
Página 137 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Página 138 - Prove that parallelograms on the same base and between the same parallels are equal in area.
Página 138 - 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.
Página 54 - 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.
Página 24 - 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.
Página 100 - Parallelograms upon the same base and between the same parallels, are equal to one another.