## Elements of Geometry and Trigonometry |

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Page 53

By a process of reasoning entirely

By a process of reasoning entirely

**similar**, it may be shown that the fourth term of the proportion cannot be less than AD ; hence it is AD itself ; therefore we have Angle ACB angle ACD arc AB arc AD . Cor . Page 68

**Similar**figures are those which have the angles of the one equal to the angles of the other , each to each , and the sides about the equal angles proportional . 2. Any two sides , or any two angles , which have like positions in two ... Page 73

that the area of any other rectangle is computed in a

that the area of any other rectangle is computed in a

**similar**manner , by measuring its sides with the same linear unit ; a second product is thus obtained , and the ratio of the two products is the same as that of the rectangles ... Page 84

Two equiangular triangles have their homologous sides proportional , and are

Two equiangular triangles have their homologous sides proportional , and are

**similar**. = Let ABC , CDE be two triangles which have their angles equal each to each , namely , BAC - CDE , ABC - DCE and ACB DEC ; then the homologous sides ... Page 85

Observe , that in

Observe , that in

**similar**triangles , the homologous sides are opposite to the equal angles ; thus the angle ACB being equal to DEC , the side AB is homologous to DC ; in like manner , AC and DE are homologous , because opposite to the ...### What people are saying - Write a review

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Elements of Geometry and Trigonometry from the Works of A. M. Legendre A. M. Legendre No preview available - 2017 |

### Common terms and phrases

ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently construction contained corresponding Cosine Cotang cylinder described diameter difference distance divided draw drawn equal equation equivalent evident expressed extremities fall figure follows formed formulas four frustum give given gles greater half hence homologous included inscribed intersection less likewise logarithm manner means measured meet middle multiplied opposite parallel parallelogram parallelopipedon pass perpendicular plane polygon prism PROBLEM produced Prop proportional PROPOSITION pyramid quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment shown sides similar sine solid solid angle sphere spherical triangle square straight line Suppose surface taken tang tangent THEOREM third triangle triangle ABC vertex whole