## 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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**triangle**. Because the point A is the cen- tre of the circle BCD , AC is equal מן C A B E ( 11.**Definition**) to AB ; and because the point B is the centre of the cir- cle ACE , BC is equal to AB : But it has been proved that CA is equal ... Page 13

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**triangles**shall be equal ; and their other angles shall be equal , each to - each , viz . those to which the equal sides are oppos ̊te . * D Let ABC ,**DEF**be two**triangles**which have the two sides AB , AC equal to the two sides DE DF ... Page 14

... triangle ABC shall coincide with the whole

... triangle ABC shall coincide with the whole

**triangle DEF**, so that the spaces which they contain or their areas are ... DEF , and the angle ACB to the angle DFE . Therefore , if two triangles have two sides of the one equal to two ... Page 16

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**triangle**ACB ; produce AC , AD to E , F ; therefore , because AC is equal to AD in the**triangle**ACD , the angles ECD ...**DEF**be two**triangles**having the two sides AB , AC , equal to the two sides DE , DF , each to each , viz . AB ... Page 17

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**triangle DEF**; then join AF ; the straight line AF bisects the angle BAC . Because AD is equal to AE , and AF is com- mon to the two triangles DAF , EAF ; the two sides DA , AF , are equal to the two sides EA , AF , each to each ; but ...### 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 solid parallelopiped spherical angle spherical triangle square straight line BC THEOR touches the circle triangle ABC triangle DEF wherefore