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absurd acute added alternate angle ABC applied arches base bisected centre circle circumference common Constr constructed contained contained in CD continued definition demonstrated described difference divided draw drawn equal equal angles equi-multiples equi-submultiples equiangular equilateral Euclid evident external angle extremities fall figure fore four magnitudes fourth given line given right line greater half Hence Hypoth inscribed internal join less line AC manner meet multiple oftener parallel parallelogram pass perpendicular placed possible PROB produced Prop proportional proposition proved radius ratio rectangle rectilineal figure remaining right angles right line Schol segment side AC similar squares of AC submultiple taken tangent THEOR third triangle ABC vertex whole
Side 145 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Side 28 - 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.
Side 22 - 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.
Side 118 - A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment as the greater segment is to the less.
Side 146 - A plane angle is the inclination of two lines to one another in a plane, which meet together, but are not in the same direction.
Side 168 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Side 3 - 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. 4. Things which coincide with one another are equal to one another.
Side 25 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.