## 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 ed1855 |

### 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 C ABC is equal ABCD altitude angle ABC angle BAC base bisected Book centre circle circle ABC circumference common compounded cone Const contained Corollary cylinder definition demonstration described diameter divided double draw drawn equal angles equiangular equimultiples Exercise extremities fore four fourth given straight line greater half homologous inscribed join less magnitudes manner meet multiple opposite parallel parallelogram parallelopiped pass perpendicular plane polygon prism PROBLEM produced PROP proposition proved pyramid ratio reason rectangle contained rectilineal figure remaining angle right angles segment shown sides similar similarly solid solid angle sphere square Take taken THEOREM third touch triangle ABC vertex Wherefore whole

### Popular passages

Page 23 - 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 42 - 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 130 - 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 5 - LET it be granted that a straight line may be drawn from any one point to any other point.

Page 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.

Page 143 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar.

Page 20 - PROBLEM. At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle.

Page 115 - Similar solid figures are such as have all their solid angles equal, each to each, and are contained by the same number of similar planes.

Page 45 - 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...