Elements of Geometry |
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Results 6-10 of 68
Page 12
... triangles ABE , ABC , and the right angle ABE = ABC , the triangle ABE is equal to the triangle ABC , and AE = AC . 3. In the triangle DFA , the sum of the sides AD , DF , is greater than the sum of the sides AC , CF ( 41 ) ; therefore ...
... triangles ABE , ABC , and the right angle ABE = ABC , the triangle ABE is equal to the triangle ABC , and AE = AC . 3. In the triangle DFA , the sum of the sides AD , DF , is greater than the sum of the sides AC , CF ( 41 ) ; therefore ...
Page 13
... triangle ABC will be equal to the right - angled triangle DEF . The proposition will evidently be true , if the third side BC be equal to the third side EF . If it be possible , let these sides be unequal , and let BC be the greater ...
... triangle ABC will be equal to the right - angled triangle DEF . The proposition will evidently be true , if the third side BC be equal to the third side EF . If it be possible , let these sides be unequal , and let BC be the greater ...
Page 18
... triangle the sum of the three angles is equal to two right angles . Demonstration . Let ABC ( fig . 41 ) be any triangle ; produce the side CA toward D , and draw to the point A the straight line AE parallel to BC . Because AE , CB ...
... triangle the sum of the three angles is equal to two right angles . Demonstration . Let ABC ( fig . 41 ) be any triangle ; produce the side CA toward D , and draw to the point A the straight line AE parallel to BC . Because AE , CB ...
Page 19
... triangle ABC ( fig . 41 ) the exterior Fig . 41 , angle BAD is equal to the two opposite interior angles B and C ... triangles , if it have seven sides , and into six , if it have eight , and in general into as many triangles wanting two ...
... triangle ABC ( fig . 41 ) the exterior Fig . 41 , angle BAD is equal to the two opposite interior angles B and C ... triangles , if it have seven sides , and into six , if it have eight , and in general into as many triangles wanting two ...
Page 33
... triangle ABC , is equal to the sum of the two opposite interior angles , CAB , ABC . But , the triangle BAC being isosceles , the angle CAB = ABC ; hence the angle BCE is double of BAC . The angle BCE , having its vertex at the centre ...
... triangle ABC , is equal to the sum of the two opposite interior angles , CAB , ABC . But , the triangle BAC being isosceles , the angle CAB = ABC ; hence the angle BCE is double of BAC . The angle BCE , having its vertex at the centre ...
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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