## The Elements of geometry; or, The first six books, with the eleventh and twelfth, of Euclid, with corrections, annotations, and exercises, by R. Wallace. Cassell's ed |

### Other editions - View all

The Elements of Geometry: Or, the First Six Books, with the Eleventh and ... Euclides No preview available - 2016 |

### Common terms and phrases

A B and CD ABC is equal adjacent angles altitude angle ABC angle ACB angle BAC angle EDF bisected centre circle ABCD circumference common section cone Corollary cylinder described diameter draw equal angles equal Ax equal Const equal Hyp equiangular equimultiples Euclid exterior angle fore given rectilineal given straight line gnomon homologous inscribed join less Let the straight lines A B meet multiple opposite angle parallel parallelogram parallelopiped pentagon perpendicular polygon prism produced proposition Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid A B solid angle sphere squares of AC straight line AB straight line drawn straight lines A B THEOREM three plane angles three straight lines touches the circle triangle ABC triplicate ratio twice the rectangle vertex Wherefore

### Popular passages

Page 21 - 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 41 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.

Page 2 - 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 93 - 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 25 - 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 126 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Page 93 - A LESS magnitude is said to be a part of a greater magnitude, when the less measures the greater, that is, ' when the less is contained a certain number of times exactly in the greater.

Page 40 - 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 2 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.

Page 19 - THEOREM. IF two triangles have two sides of the one equal to two sides of the...