## Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and Illustrations |

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applied base bisect Book centre chord circle circumference common consequently construction contained continued corresponding denote derived describe determined diameter difference direction distance divided double draw drawn equal equivalent evidently excess expressed exterior angle extreme fall feet figure follows four fourth Geometry given greater half Hence inscribed isosceles triangle join less likewise manner mean measure meet multiple objects observed opposite parallel perpendicular polygon portion position PROB produce PROP proportional Proposition quantities radius ratio reason rectangle regular remaining rhomboid right angles segments sides similar sine square square of AC station straight line successive suppose tangent THEOR third tion triangle ABC twice vertical angle whence Wherefore whole

### Popular passages

Page 32 - ... if a straight line, &c. QED PROPOSITION 29. — Theorem. 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 the same side ; and likewise the two interior angles upon the same side together equal to two right angles.

Page 335 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when any...

Page 296 - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...

Page 12 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.

Page 139 - Componendo, by composition ; when there are four proportionals, and it is inferred that the first together with the second, is to the second, as the third together with the fourth, is to the fourth.

Page 86 - The angle at the centre of a circle is double of the angle at the circumference upon the same base, that is, upon the same part of the circumference.

Page 294 - Thus, for" example, he to whom the geometrical proposition, that the angles of a triangle are together equal to two right angles...

Page 95 - UPON a given straight line to describe a segment of a circle containing an angle equal to a given rectilineal angle.

Page 40 - 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 60 - The rectangle contained by the sum and difference of two straight lines is equivalent to the difference of the squares of these lines.