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

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Page 13

If equals be added to unequals , the wholes are unequal . but its 24 y . If equals be taken from unequals , the remainders are unequal . VI . Things which are

If equals be added to unequals , the wholes are unequal . but its 24 y . If equals be taken from unequals , the remainders are unequal . VI . Things which are

**double**of the same , are equal to one another . VII . Page 40

I. of the parallelograms is

I. of the parallelograms is

**double**of the triangle BDC ; and they are therefore equal to one another . But , if the sides AD , EF , opposite eB to the base BC of the parallelograms ABCD , EBCF , be not terminated in the same point ... Page 43

THE O R. IF a parallelogram and triangle be upon the same bale , and between the fame parallels ; the parallelogram shall be

THE O R. IF a parallelogram and triangle be upon the same bale , and between the fame parallels ; the parallelogram shall be

**double**of the triangle . Lies Book 1 . Let the parallelogram ABCD and the triangle OF EUCLID . Page 44

I. ABCD is

I. ABCD is

**double**b of the triangle ABC , because the diameter AC divides it into two equal parts ; where- B fore ABCD is alto**double**of the tri . angle EBC . Therefore , if a parallelogram , & c . Q. E. D. PRO P. XLII . PROB a 1o . 1 . Page 49

FBC : Now the parallelogram BL is

FBC : Now the parallelogram BL is

**double**6 of the triangle 8 41 . ... BD , AL ; and the square GB is**double**of the triangle FBC , because these allo are upon the fame base FB , and between the fame parallels FB , GC . But the**doubles**of ...### What people are saying - Write a review

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### Common terms and phrases

added alſo altitude angle ABC angle BAC baſe becauſe Book caſe centre circle circle ABCD circumference common cone cylinder definition demonſtrated deſcribed diameter divided double draw drawn equal equal angles equiangular equimultiples exceſs fame fides figure firſt folid fore four fourth given angle given in poſition given in ſpecies given magnitude given ratio given ſtraight line greater Greek half join leſs likewiſe magnitude manner meet muſt oppoſite parallel parallelogram perpendicular plane priſm produced prop proportionals propoſition pyramid reaſon rectangle rectangle contained rectilineal remaining right angles ſame ſecond ſegment ſhall ſides ſimilar ſolid ſphere ſquare ſquare of AC Take taken theſe third triangle ABC wherefore whole

### Popular passages

Page 483 - 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 170 - 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 81 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...

Page 105 - 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 167 - 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 62 - 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 112 - 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 200 - 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.