## Euclid's Elements of Geometry, Books 1-6 |

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ABCD AC is equal ADDITIONAL PROPOSITION angle ACB angle BAC angles ABC base bisected Book called centre chord circle ABC coincide common CONSTRUCTION Coroll DEFINITION described diagonal diameter difference distance divided double draw drawn equal equiangular Euclid EXERCISES extremities figure Find fixed formed four given circle given point given straight line greater inscribed intersect length less Let ABC magnitudes meet middle points multiples opposite sides pair parallel parallelogram passes pencil perpendicular polygon position possible produced PROOF Prop proportional PROPOSITION quadrilateral radius range ratio rectangle contained regular required to prove respectively right angles shew sides sides BC similar Similarly similitude square on AC straight line drawn Take taken tangent theorem third touch triangle ABC vertices Wherefore

### Popular passages

Page 59 - Any two sides of a triangle are together greater than the third side.

Page 7 - An angle less than a right angle is called an acute angle; an angle greater than a right angle and less than two right angles is called an obtuse angle.

Page 68 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.

Page 144 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced...

Page 376 - To find a mean proportional between two given straight lines. Let AB, BC be the two given straight lines ; it is required to find a mean proportional between them. Place AB, BC in a straight line, and upon AC describe the semicircle ADC, and from the point B draw (9.

Page 135 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.

Page 76 - ... the same side together equal to two right angles ; the two straight lines shall be parallel to one another.

Page 305 - To inscribe, an equilateral and equiangular pentagon in a given circle. Let ABCDE be the given circle. It is required to inscribe an equilateral...

Page 424 - PROPOSITION 5. The locus of a point, the ratio of whose distances from two given points is constant, is a circle*.

Page 248 - If two straight lines within a circle cut one another, the rectangle contained by the segments of one of them is equal to the rectangle contained by the segments of the other. Let the two straight lines AC, BD, within the circle ABCD, cut one another in the point E : the rectangle contained by AE, EC is equal to the rectangle contained by BE, ED.