## Elements of Geometry: Containing the First Six Books of Euclid with a Supplement on the Quadrature of the Circle, and the Geometry of Solids : to which are Added, Elements of Plane and Spherical Trigonometry |

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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder definition demonstrated diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet multiple opposite angle parallel parallelogram perpendicular polygon prism PROB PROP proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore

### Popular passages

Page 51 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.

Page 9 - ... angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it. 11. An obtuse angle is that which is greater than a right angle. 12. An acute angle is that which is less than a right angle. 13. A term or boundary is the extremity of any thing.

Page 9 - 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 80 - 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 55 - Again, because the angle at B is half a right angle, and FDB a right angle, for it is equal...

Page 101 - 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 283 - If a straight line meet 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 35 - Parallelograms upon the same base and between the same parallels, are equal to one another.

Page 140 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Page 71 - THE diameter is the greatest straight line in a circle; and, of all others, that which is nearer to the centre is always greater than one more remote ; and the greater is nearer to the centre than the less.* Let ABCD be a circle, of which...