## Elements of Geometry: Containing the First Six Books of Euclid: With a Supplement ... to which are Added, Elements of Plane and Sphericale Trigonometry ... From the Last London Ed., Enl |

### From inside the book

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**diameter**of a circle is a straight line drawn through the centre , and terminated both ways by the circumference . 14. A semicircle is the figure contained by a**diameter**and the part of the circumference cut off by the**diameter**4 15 ... Page 33

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**diameter**is a straight line joining two of its opposite angles . Let ACDB be a parallelogram , of which BC is a**diameter**; the oppo- site sides and angles of the figure are equal to one another ; and the diam- eter BC bisects it ... Page 35

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**diameter**AB bisects ( 34. 1. ) it ; and the triangle DBC is the half of the parallelogram DBCF , because the**diameter**DC bisects it ; and the halves of equal things are equal ( 7 . Ax . ) ; therefore the triangle ABC is equal to the ... Page 36

... is double ( 34. 1. ) of the triangle ABC , because the

... is double ( 34. 1. ) of the triangle ABC , because the

**diameter**AC divides it A B D E C into two equal parts ; wherefore ABCD is also double of the triangle EBC PROP . XLII . PROB . To describe a parallelogram 86 ELEMENTS. Page 37

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**diameter**of any parallelogram , are equal to one another . Let ABCD be a parallelogram of which the**diameter**is AC ; let EH , FG be the parallelograms about AC , that is , through which AC passes , and let BK , KD be the other ...### Other editions - View all

### Common terms and phrases

ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore