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

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

### 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.