## 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 |

### From inside the book

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**equilateral**triangle is that which has three equal fides . XX . An isosceles triangle is that which has only two fides equal . XXI . scalene triangle , is that which has three unequal fides , ΧΧΙΙ . A right angled triangle , is that ... Page 7

... . " Two straight lines cannot be drawn through the same point , " parallel to the same straight line , without coinciding with " one another . Book I. PROPO- Book I. PROPOSITION I. PROBLEM . O describe an

... . " Two straight lines cannot be drawn through the same point , " parallel to the same straight line , without coinciding with " one another . Book I. PROPO- Book I. PROPOSITION I. PROBLEM . O describe an

**equilateral**OF GEOMETRY . 7. Page 8

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**equilateral**triangle upon a given finite straight line . T Let AB be the given straight line ; it is required to describe an**equilateral**triangle upon it . From the centre A , at the distance AB , de- a 3. Postu- scribe a the circle BCD ... Page 9

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**equilateral**triangle DAB , and produce the straight lines DA , DB , to E and F ; from the centre B , at the distance BC , describe d the circle CGH , and from the centre D , at the distance DG , describe the circle GKL . AL shall be ... Page 12

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**equilateral**triangle is also equi- angular . : PROP . VI . THEOR . Ito angles of a triangle be equal to one another . the fides which fubtend , or are opposite to , those angles , shall also be equal to one another . Let ABC be a ...### Other editions - View all

### Common terms and phrases

ABCD alfo alſo alſo equal angle ABC angle ACB angle BAC arch baſe baſe BC BC is equal becauſe becauſe the angle biſected Book VII caſe cauſe centre circle ABC circumference co-fine demonſtrated deſcribed diameter draw drawn equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fame reaſon fides fimilar fince firſt folid fore given ſtraight line greater inſcribed interfect join leſs Let ABC line BC magnitudes oppoſite parallel parallelepiped parallelogram paſs paſſes perpendicular plane polygon priſm proportionals propoſition Q. E. D. PROP radius rectangle contained rectilineal figure remaining angle right angles ſame ſame manner ſame ratio ſecond ſection ſegment ſhall be equal ſhewn ſide ſolid ſpace ſpherical triangle ſquare of AC ſtand ſuch ſum ſuppoſed tangent THEOR theſe thoſe touches the circle triangle ABC wherefore

### Popular passages

Page 19 - 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 155 - 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 17 - 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 23 - 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 156 - 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 44 - 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...