## Elements of Geometry |

### From inside the book

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**described**from the centre E with the radius EF = B , will cut the side DF in two points F and G situated on the same ...**square**. PROBLEM . 149. To find the centre of a given 38 Elements of Geometry . Page 48

... described square the whole line AC will contain the

... described square the whole line AC will contain the

**square described**upon the part AB , plus the**square described**upon the other part BC , plus twice the rectangle contained by the two parts AB , BC ; which may be thus expressed , -2 2 ... Page 49

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**square described**upon AB , since AF was taken equal to AB ; the second IGDH is the**square described**upon BC ; for , since ACAE , and AB AF , the difference AC - ABAE - AF , which gives BC = EF ; but , on account of the parallels , IG ... Page 50

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**square described**upon the hypothenuse of a right - angled triangle is equal to the sum of the**squares described**upon the two other sides . Demonstration . Let ABC ( fig . 109 ) be a triangle right - angled at A. Having constructed squares ... Page 51

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**described**upon the hy- pothenuse , is equal to the sum of the**squares**ABHL , ACIK , des- BC = -2 -2 cribed the two other sides ; or , BC = AB + AC . upon 187. Corollary 1 . The**square**of one of the sides of a right- angled triangle is ...### Other editions - View all

### Common terms and phrases

ABC fig adjacent angles altitude angle ACB angle BAD base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal and parallel equiangular equilateral equivalent faces figure four right angles frustum Geom gles greater hence homologous sides hypothenuse inclination inscribed circle isosceles join less let fall line AC manner mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism proposition pyramid S-ABC quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium segment semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three plane angles triangle ABC triangular prism triangular pyramids vertex vertices whence