## Elements of Euclid [selections from book 1-6] adapted to modern methods in geometry, by J. Bryce and D. Munn |

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Elements of Euclid [selections from book 1-6] adapted to modern methods in ... Euclid,James Bryce,David Munn (F.R.S.E.) No preview available - 1874 |

Elements of Euclid [selections from book 1-6] adapted to modern methods in ... Euclid,James Bryce,David Munn (F.R.S.E.) No preview available - 1874 |

### Common terms and phrases

ABCD altitude base bisected BOOK called centre chord circle circumference cloth coincide common compounded Const construction conv Conversely definition describe diagonal diameter difference divided double draw equal extremities Fcap figure follows formed four fourth GEOGRAPHY geometrical given circle given line given point greater half hence inscribed intersecting Join less Let ABC magnitudes manner mean measure meet method middle point multiple opposite sides parallel parallelogram pass perpendicular polygon problem produced PROP proportional Proposition radius ratio rectangle contained regular remaining required to prove respectively right angles schol segments shew shewn sides similar Similarly square straight line taken tangent THEOREM third touch triangle triangle ABC units vertical whole

### Popular passages

Page 68 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.

Page 77 - 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 50 - If a parallelogram and a triangle be upon the same base, and between the same parallels; the parallelogram is double of the triangle.

Page 87 - If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the points of section.

Page 30 - Any two sides of a triangle are together greater than the third side.

Page 206 - Tin; rectangle, contained by the diagonals of a quadrilateral inscribed in a circle, is equal to the sum of the rectangles contained by its opposite sides. Let ABCD be any quadrilateral inscribed in a circle...

Page 89 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part.

Page 98 - Guido, with a burnt stick in his hand, demonstrating on the smooth paving-stones of the path, that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.