## 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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Page 130

**Ratio**is a mutual relation of two magnitudes , of the same kind , to one another , in respect of quantity . IV . Magnitudes are said to be of the same kind ... Page 131

... equal to it , or less ; then the first of the magnitudes is said to have to the second the same

... equal to it , or less ; then the first of the magnitudes is said to have to the second the same

**ratio**that the third has to the fourth . VI . Page 132

Book V. N. X. When there is any number of magnitudes of the same kind , the first is said to have to the last of them the

Book V. N. X. When there is any number of magnitudes of the same kind , the first is said to have to the last of them the

**ratio**compounded of the**ratio**... Page 133

If four magnitudes are continual proportionals , the

If four magnitudes are continual proportionals , the

**ratio**of the first to the fourth is said to be triplicate of the**ratio**of the first to the second ... Page 137

Ik F the first of four magnitudes has the same

Ik F the first of four magnitudes has the same

**rațio**to the second which the ... the multiple of the first shall have the same**ratio**to the multiple of the ...### What people are saying - Write a review

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### Common terms and phrases

ABCD alſo altitude angle ABC angle BAC arch baſe becauſe biſected Book caſe centre circle circle ABC circumference coincide common cylinder definition demonſtrated deſcribed diameter difference divided draw drawn equal equal angles equiangular Euclid extremity fall fame fides firſt folid fore four fourth given given ſtraight line greater half inſcribed join leſs Let ABC magnitudes meet multiple muſt oppoſite parallel parallelogram perpendicular plane polygon priſm produced PROP proportionals propoſition proved Q. E. D. PROP radius ratio rectangle contained remaining right angles ſame ſecond ſegment ſhall ſides ſimilar ſin ſolid ſpherical ſquare ſtraight line ſuch ſum taken tangent THEOR theſe third thoſe touches triangle ABC wherefore whole

### Popular passages

Page 27 - 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 172 - 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 42 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.

Page 84 - 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 106 - 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 22 - 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 64 - 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 166 - 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 54 - 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 2 - 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.