## Elements of geometry, containing books i. to vi.and portions of books xi. and xii. of Euclid, with exercises and notes, by J.H. Smith |

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### Other editions - View all

Elements of Geometry: Containing Books 1. to VI. and Portions of Books XI ... James Hamblin Smith No preview available - 2016 |

Elements of Geometry: Containing Books 1-6 and Portions of Books 11 and 12 ... Euclid,J. Hamblin Smith No preview available - 2008 |

### Common terms and phrases

ABCD applied base bisected Book called centre chord circle circumference coincide common construction describe diagonals diameter difference distance divided double draw drawn equal Euclid exterior angle extremities fall figure four given point given straight line greater half Hence inscribed intersect isosceles triangle join length less Let ABC line joining lines be drawn magnitudes measure meet method middle points multiple NOTE opposite sides parallel parallelogram pass perpendicular PROBLEM produced proof Prop PROPOSITION prove Q. E. D. Ex quadrilateral ratio rect rectangle contained respectively right angles segment shew shewn sides square suppose Take taken tangent THEOREM third touch triangle triangle ABC twice vertex vertical whole

### Popular passages

Page 51 - 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 38 - 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. either the sides adjacent to the equal...

Page 178 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.

Page 46 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon...

Page 50 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.

Page 104 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through the point A, parallel to the straight hue BC.

Page 187 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.

Page 89 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle, Let ABC be any triangle, and the angle at B one of its acute angles, and upon BC, one of the sides containing it, let fall the perpendicular AD from the opposite angle.

Page 5 - 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 5 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.