## 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 angle ABC angle ACB angle BAC arch AC base BC bisected Book centre circle ABC circumference co-sine cylinder demonstrated described desinition diameter draw drawn E. D. PROP equal angles equiangular equilateral polygon equimultiples Euclid exterior angle faid fame altitude fame base fame manner fame plane fame ratio fame reason fame straight line fore given straight line greater hypotenuse inscribed join less Let ABC line BC magnitudes meet opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism proportionals proposition radius rectangle contained rectilineal sigure remaining angle segment semicircle shewn side BC sine sirst solid angle spherical angle spherical triangle square straight line AC supersicies T H E O THEOR third touches the circle triangle ABC triangle DEF wherefore

### Popular passages

Page 29 - 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 174 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Page 44 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.

Page 86 - 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...

Page 108 - IF from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it ; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle be equal to the square of the line which meets it, the line which meets shall touch the circle.

Page 24 - THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it. Let ABC be a triangle, of which the angle ABC is greater than the angle BCA : the side AC is likewise greater than the side AB. For, if it be not greater, AC must...

Page 66 - If then the sides of it, BE, ED are equal to one another, it is a square, and what was required is now done: But if they are not equal, produce one of them BE to F, and make EF equal to ED, and bisect BF in G : and from the centre G, at the distance GB, or GF, describe the semicircle...

Page 168 - IN a right angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another. Let ABC be a right angled triangle, having the right angle BAC ; and from the point A let AD be drawn perpendicular to the base BC : the triangles ABD, ADC are similar to the whole triangle ABC, and to one another.

Page 56 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced...

Page 4 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.