## Elements of Geometry |

### From inside the book

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Page 27

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**right**-**angled triangles**CAF , DCG , have the hypothe- nuses CA , CD , equal ; moreover the side AF , the half of AB , is equal to the side DG , the half of DE ; the triangles then are equal ( 59 ) , and consequently the third side CF ... Page 39

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**right angle**( 128 ) ; therefore AB , being a perpendicular at the extremity ... angled**triangles**CBA , CDA , have the hypothenuse CA common , and the side CB = CD ; therefore AD = AB , and at the same time the angle CAD CAB . = PROBLEM . 153. Page 50

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**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 upon the three sides , let fall , from the ... Page 51

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**right**-**angled triangle**is equal to the square of the hypothenuse minus -2 the square of the other side ; or AB = BC — AC . - 188. Corollary 1. Let ABCD ( fig . 118 ) be a square , AC its Fig . 119 . diagonal ; the triangle ABC being right - ... Page 52

... triangle ABC ( fig . 110 ) , if the angle C be acute , the square of the side opposite to it will be less than the ...

... triangle ABC ( fig . 110 ) , if the angle C be acute , the square of the side opposite to it will be less than the ...

**right**-**angled triangles**ABD , ADC , give AD + BD = AB , -2 CD + AD = AC ; therefore AB = BC + AC — 2BC × CD . - 2. If the ...### 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