## Elements of Geometry |

### From inside the book

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**isosceles**( fig . 8 ) , when two only of its sides Fig . 9. are equal , and scalene ( fig . 9 ) , when no two of its sides are equal . 16. A right - angled triangle is that which has one right angle . The side opposite to the right ... Page 9

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**isosceles**triangle the angles opposite to the equal sides are equal . Demonstration . Let the side AB = AC ( fig . 28 ) , then will the Fig . 28 . angle C be equal to B. Draw the straight line AD from the vertex A to the point D the ... Page 10

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**isosceles**triangle , to the middle of the base , is perpendicular to the base , and divides the ver- tical angle into two equal parts . In a triangle that is not**isosceles**, any one of its sides may be taken indifferently for a base ... Page 33

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**isosceles**, and the angle BAC = ABC ; the triangle CAD is also**isosceles**, and the angle CAD = ADC ; hence BAC + CAD , or BAD = ABD + ADB . But , if the two angles B and D of the triangle ABD are together equal to the third BAD , the ... Page 51

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**isosceles**, we 2 -2 = 2 -2 have AC AB + BC = 2AB ; therefore the square described upon the diagonal AC is double of the square described upon the side AB . This property may be rendered sensible by drawing , through the points A and C ...### 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