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absurd AC and BD AC and CB AC are equal alternate angles angle ABC angle BAC angle equal arches base bisected centre circumference CKMB constr constructed contained in CD demonstrated double the rectangle double the square draw drawn equal angles equal to AC equal to double equi equi-multiples equi-submultiples equiangular Euclid evident fore four magnitudes proportional fourth given angle given circle given line given right line given triangle half a right Hypoth inscribed JFig less manner multiple oftener opposite parallel parallelogram perpendicular point of contact PROB produced PROP proposition radius rectangle under AC rectilineal figure right line AB Schol segment semicircle side AC similar squares of AC submultiple taken tangent THEOR third tiple triangle ABC vertex
Page 143 - 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.
Page 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.
Page 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.
Page 116 - 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.
Page 144 - 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.
Page 166 - 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...
Page 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.
Page 25 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.