## Elements of Geometry |

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ABCD altitude approach axis base bisect bisector called centre chord circle circumscribed coincide common Comparing Conclusion cone construction contained Corollary corresponding curve definition describe diagonals diameter difference dihedral angle direction distance divided draw drawn edges ellipse equal angles equally distant expressed exterior angle faces fall figure four geometry given greater half Hence hyperbola Hypothesis identically equal indefinitely inscribed intersection Join lateral length less limit magnitude mean measured meet pair parallel parallelogram pass perpendicular plane poles polygon position prism PROBLEM produced Proof proportion pyramid radii radius ratio rectangle regular respectively right angles segments shown sides similar solid sphere spherical square straight angle straight line suppose surface tangent THEOREM third touch triangle turned vertex vertices volume whence whole

### Popular passages

Page 146 - In an obtuse-angled triangle the square on the side opposite the obtuse angle is greater than the sum of the squares on the other two sides by twice the rectangle contained by either side and the projection on it of the other side.

Page 184 - 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 44 - Every point in the bisector of an angle is equally distant from the sides of the angle...

Page 149 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

Page 45 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.

Page 103 - A rectilineal figure is said to be described about a circle, when each side of the circumscribed figure touches the circumference of the circle. V. In like manner, a circle is said to be inscribed...

Page 235 - ten decimals are sufficient to give the circumference of the earth to the fraction of an inch, and thirty decimals would give the circumference of the whole visible universe to a quantity imperceptible with the most powerful microscope.

Page 90 - The sum of the three straight lines drawn from any point within a triangle to the three vertices, is less than the sum and greater than the half sum of the three sides of the triangle (I . 33, 66).

Page 168 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.

Page 196 - If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means.