## Euclid's Elements of Geometry, Books 1-6; Book 11 |

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ABCD angle ABC angle BAC base bisected Book called centre chord circle ABC coincide common CONSTRUCTION corresponding DEFINITION described diagonals diameter difference distance divided double draw drawn edges equal equiangular EXERCISES faces figure Find follows formed four given circle given point given straight line greater inscribed intersect inverse length less Let ABC locus magnitudes meet middle points opposite sides pairs parallel parallelogram passes perpendicular plane polygon position possible produced PROOF Prop proportional PROPOSITION quadrilateral radius ratio rectangle rectangle contained regular required to prove respectively right angles rotation shew side BC sides similar Similarly similitude sphere square straight line drawn straight line joining taken tangent tetrahedron theorem third touch triangle ABC trihedral angle twice vertices Wherefore

### Popular passages

Page 70 - 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 219 - The angle which an arc of a circle subtends at the centre is double that which it subtends at any point on the remaining part of the circumference.

Page 281 - 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, together •with the square...

Page 148 - If a straight line be divided into any two parts, the squares on the whole line, and on one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square on the other part.

Page 137 - 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 374 - 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 78 - ... 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 422 - PROPOSITION 5. The locus of a point, the ratio of whose distances from two given points is constant, is a circle*.

Page 302 - To inscribe a circle in a given square. Let ABCD be the given square ; it is required to inscribe a circle in ABCD.