## Elements of Geometry and Trigonometry |

### From inside the book

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Page 11

... sides unequal . 16. A right - angled triangle is one which has a right angle . The side opposite the right angle is called the hypothenuse . Thus , in the triangle ABC , right - angled at A , the

... sides unequal . 16. A right - angled triangle is one which has a right angle . The side opposite the right angle is called the hypothenuse . Thus , in the triangle ABC , right - angled at A , the

**side BC**is the hypothenuse . B 17. Among ... Page 17

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**side BC**( Ax . 11. ) : therefore , the triangle EDF is equal to the triangle BAC ( Ax . 13. ) . Cor . When two triangles have these three things equal , namely , the side ED = BA , the side DF - AC , and the angle D = A , the ... Page 18

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**side**, their sum will be less than the sum of the two other**sides**of the triangle . Let any point , as O , be taken within the trian- gle BAC , and let the lines OB , OC , be drawn to the extremities of either**side**, as**BC**; then will ... Page 19

... < BC ( Ax . 5. ) ; but we have found GC - EF , therefore , BC > EF . Second Case . If the point G fall on the

... < BC ( Ax . 5. ) ; but we have found GC - EF , therefore , BC > EF . Second Case . If the point G fall on the

**side BC**, it is evident that GC , or its equal EF , will be shorter than BC ( Ax . 8. ) . AA B Third Case . Lastly , if the ... Page 20

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**side**EF must be greater than**BC**; and if the angle D were less than A , it would follow , that the**side**EF must be less than**BC**: but EF is equal to**BC**, by hypothesis ; therefore , the angle D can neither be greater nor less than A ...### Other editions - View all

### Common terms and phrases

adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex