## 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 |

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Page 25

Therefore the two

Therefore the two

**angles BGH , GHD , are less than two right angles . But those straight lines , which with another straight line falling upon**them , make the two interior angles on the same side less than two right angles , will meet ...### What people are saying - Write a review

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

### 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 6 - 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 6 - 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...