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

W. & C. Tait, and Longman, Hurst, Rees, Orme, & Brown, London, 1820 - Geometry, Modern - 465 pages
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### Contents

 Section 1 5 Section 2 29 Section 3 60 Section 4 71 Section 5 101 Section 6 115 Section 7 128 Section 8 181
 Section 15 260 Section 16 262 Section 17 283 Section 18 302 Section 19 319 Section 20 328 Section 21 339 Section 22 372

 Section 9 201 Section 10 202 Section 11 204 Section 12 207 Section 13 210 Section 14 225
 Section 23 378 Section 24 390 Section 25 431 Section 26 444 Section 27 Section 28

### Popular passages

Page 110 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Page 334 - 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 30 - 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 334 - 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 88 - ... a circle. 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. The opposite angles of any quadrilateral inscribed in a circle are supplementary; and the converse.
Page 295 - 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 10 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Page 293 - Thus, for" example, he to whom the geometrical proposition, that the angles of a triangle are together equal to two right angles...
Page 129 - The first and last terms of a proportion are called the extremes, and the two middle terms are called the means.
Page 93 - UPON a given straight line to describe a segment of a circle containing an angle equal to a given rectilineal angle.