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

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Page 6

... is not true universally , except in the

... is not true universally , except in the

**case**in which each of the solid angles of the Figures is contained by no ... in other**Cases**, two solid Figures may be contained by 6milar Planes of the fame Number and Magnitude , and yet be ... Page 19

... and like . wise their fides CB , DB that are ter minated in B. Join CD ; then , in the

... and like . wise their fides CB , DB that are ter minated in B. Join CD ; then , in the

**case**in which the vertex of each of the triangles is without the other triangle , because AC is equal to AD , the angle a 5. Page 20

The

The

**case**in which the ver . tex of one triangle is upon a side of the other , needs 110 de . monstration . Therefore upon the same base , and on the same ide of it , there cannot be two triangles that have their fides which are ... Page 33

AB to DE ; likewise in this

AB to DE ; likewise in this

**case**, the other fides shall be equal , AC to DF , and BC B HC E to EF ; and also the third angle BAC to the third EDF . For , if BC be not equal to EF , let BC be the greater of them , and make BH equal to ... Page 86

В. ment BADC is greater than a semiD circle ; and the angles in it BAC , BEC are equal , by the first

В. ment BADC is greater than a semiD circle ; and the angles in it BAC , BEC are equal , by the first

**case**: For FT the same reason , because CBED is greater than a semicircle , the angles CAD ; CED are equal : Therefore the whole angle ...### 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.