## Elements of Geometry;: Containing the First Six Books of Euclid, with Two Books on the Geometry of Solids. To which are Added, Elements of Plane and Spherical Trigonometry |

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Page 177

Containing the First Six Books of Euclid, with Two Books on the Geometry of Solids. To which are Added, Elements of Plane and Spherical ... SIMPLE IMILAR

Containing the First Six Books of Euclid, with Two Books on the Geometry of Solids. To which are Added, Elements of Plane and Spherical ... SIMPLE IMILAR

**triangles are to one another**in the diplicate**ratio of their homologous**fides . Page 178

THE O R. Imilar polygons may be divided into the same number of similar

THE O R. Imilar polygons may be divided into the same number of similar

**triangles**, having the same ratio to**one another**that the polygons have ; and the polygons have to**one another**the**duplicate ratio**of that which**their homologous**... Page 179

Containing the First Six Books of Euclid, with Two Books on the Geometry of Solids. ... Also these

Containing the First Six Books of Euclid, with Two Books on the Geometry of Solids. ... Also these

**triangles**have , each to each , the same**ratio**which the polygons have to**one another**, the antecedents being ABE , EBC , ECD , and the ... Page 180

Containing the First Six Books of Euclid, with Two Books

Containing the First Six Books of Euclid, with Two Books

**on**the Geometry of Solids. ... or of any number of fides , are**one**to**another in the duplicate ratio of their homologous**fides , and it has already been proved in**triangles**.### What people are saying - Write a review

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### Common terms and phrases

ABCD alſo altitude angle ABC angle BAC arch baſe BC is equal becauſe biſected Book Book VII caſe centre circle circle ABC circumference common cylinder definition demonſtrated deſcribed diameter difference divided double 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 manner meet multiple muſt oppoſite parallel parallelogram perpendicular plane polygon priſm produced PROP proportionals propoſition proved radius ratio rectangle contained remaining right angles ſame ſame reaſon ſecond ſegment ſhall ſides ſimilar ſolid ſquare ſtraight line ſum taken tangent THEOR theſe third thoſe touches triangle 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 165 - 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 18 - If, at a point in a straight line, two other straight lines upon the opposite sides of it, make the adjacent angles, together equal to two right angles, these two straight lines shall be in one and the same straight line.

Page 9 - Wherefore, from the given point A, a straight line AL has been drawn equal to the given straight line BC.

Page 3 - 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 33 - Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Page 12 - ABC: and it has also been proved that the angle FBC is equal to the angle GCB, which are the angles upon the other side of the base. Therefore the angles at the base, &c.

Page 6 - Let it be granted that a straight line may be drawn from any one point to any other point.

Page 166 - But by the hypothesis, it is less than a right angle ; which is absurd. Therefore the angles ABC, DEF are not unequal, that is, they are equal : And the angle at A is equal to the angle at D ; wherefore...

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...