## The First Six Books: Together with the Eleventh and Twelfth |

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alſo angle ABC angle BAC baſe BC BC is equal BC is given becauſe the angle becauſe the ratio Book XI caſe cauſe centre circle ABCD circumference conſequently cylinder demonſtrated deſcribed equal angles equiangular equimultiples exceſs fides figure firſt fore given angle given in magnitude given in poſition given in ſpecies given magnitude given ratio given ſtraight line gnomon greater laſt leſs likewiſe muſt oppoſite parallel parallelepipeds parallelogram paſſes perpendicular priſm prop propoſition pyramid Q. E. D. P R O reëtangle contained reëtilineal right angles ſaid ſame manner ſame multiple ſame ratio ſame reaſon ſecond ſegment ſhall ſhown ſides ſimilar ſolid angle ſome 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 482 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, &c.

Page 168 - 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 79 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...

Page 103 - DEF are likewise equal (13. i.) to two right angles ; therefore the angles AKB, AMB are equal to the angles DEG, DEF, of which AKB is equal to DEG ; wherefore the remaining angle AMB is equal to the remaining angle DEF.

Page 165 - AC the same multiple of AD, that AB is of the part which is to be cut off from it : join BC, and draw DE parallel to it : then AE is the part required to be cut off.

Page 10 - 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 61 - 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 110 - To describe an equilateral and equiangular pentagon about a given circle. • Let ABCDE be the given circle; it is required to describe an equilateral and equiangular pentagon about the circle ABCDE. Let the angles of a pentagon, inscribed in the circle...

Page 198 - 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 38 - F, which is the common vertex of the triangles ; that is, together with four right angles. 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.