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

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**cylinder**is a folid figure defcribed by the revolution of a right angled parallelogram about one of its fides which re- mains fixed . XXII . The axis of a**cylinder**is the fixed straight line about which the parallelogram revolves . Page 269

OVERY cone is the third part of a

OVERY cone is the third part of a

**cylinder**which has the fame bafe , and is of an equal altitude with Let a cone have the fame bafe with a**cylinder**, viz . the circle ABCD , and the fame altitude . The cone is the third part of the ... Page 270

Upon the fquare ABCD erect a prifm of the fame altitude with the

Upon the fquare ABCD erect a prifm of the fame altitude with the

**cylinder**; this prifm is greater than half of the**cylinder**; becaufe if a fquare be defcribed about the circle , and a prifm erected upon the fquare , of the fame altitude ... Page 271

Therefore the rest of the cylin- Book XII . der , that is , the prifm of which the bafe is the polygon AEBFCGDH , and of which the altitude is the fame with that of the

Therefore the rest of the cylin- Book XII . der , that is , the prifm of which the bafe is the polygon AEBFCGDH , and of which the altitude is the fame with that of the

**cylinder**, is greater than the triple of the cone : But this prifm ... Page 272

Therefore this prifm is great- er than the

Therefore this prifm is great- er than the

**cylinder**of which the bafe is the circle ABCD . But it is alfo lefs , for it is contained within the**cylinder**; which is impoffible . linder is not less than the triple of the cone ...### What people are saying - Write a review

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### Common terms and phrases

added alfo alſo altitude angle ABC angle BAC bafe baſe becauſe bifected Book Book XI centre circle circle ABCD circumference common cone cylinder defcribed definition demonftrated diameter divided double draw drawn equal equal angles equiangular equimultiples excefs fame fame multiple fecond fegment fhall fides fimilar firft folid folid angle fore four fourth fquare fquare of AC ftraight line given angle given in fpecies given in pofition given magnitude given ratio greater Greek half join lefs magnitude meet oppofite parallel parallelogram perpendicular plane prifms produced PROP propofition proportionals pyramid rectangle rectangle contained remaining right angles Take taken thefe THEOR theſe third triangle ABC wherefore whole

### Popular passages

Page 474 - 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.