## The Elements of Euclid |

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### Common terms and phrases

AC is equal alſo angle ABC angle BAC baſe BC BC is given becauſe the angle Book caſe cauſe circle ABCD circumference cone conſequently conſtrućtion cylinder demonſtrated deſcribed drawn equal angles equiangular equimultiples exceſs figure firſt fore given angle given in magnitude given in poſition given in ſpecies given magnitude given ratio given ſtraight line gnomon greater join laſt leſs likewiſe muſt oppoſite P R O parallel parallelepipeds parallelogram paſs thro perpendicular plane angles priſms Prop proportionals Propoſition pyramid reëtangle right angles ſaid ſame manner ſame multiple ſame ratio ſame reaſon ſecond ſegment ſhall ſhewn ſides ſides BA ſimilar ſince ſolid angle ſome ſšuare ſpace ſphere ſquare of AC ſtraight line AB ſtraight line BC ſum T H E O theſe thoſe triangle ABC uſe wherefore

### Popular passages

Page 156 - 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 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 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Page 92 - 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 80 - EA : and because AD is equal to DC, and DE common to the triangles ADE, CDE, the two sides AD, DE are equal to the two CD, DE, each to each ; and the angle ADE is equal to the angle CDE, for each of them is a right angle ; therefore the base AE is equal (4.

Page 52 - If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half and the part produced.

Page 36 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

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.

Page 54 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.

Page 74 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...