## Elements of Geometry |

### From inside the book

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Page 40

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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 40 Elements of Geometry . Page 50

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**square described**upon 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 ... Page 51

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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 AC AE , and ABAF , the difference AC - AB — AE — AF , which gives BC = EF ; but , on account of the parallels , IG ... Page 52

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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 53

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**square**AI ; but the two rectangles BDEF , CDEG , taken together , make the**square**BCGF ; therefore the**square**BCGF ,**described**upon the hypothenuse , is equal to the sum of the**squares**ABHL , ACIK ,**described**upon the two other sides ...### Other editions - View all

### Common terms and phrases

ABC fig adjacent angles altitude angle ACB angle BAC 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 angles equiangular equilateral equivalent faces figure formed four right angles frustum GEOM given point gles greater hence homologous sides hypothenuse inclination intersection isosceles triangle JOHN CRERAR LIBRARY join less Let ABC let fall line AC mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced proposition radii radius ratio rectangle regular polygon right angles Scholium sector segment semicircle semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three angles triangle ABC triangular prism triangular pyramids vertex vertices whence