## Elements of Geometry and Trigonometry |

### From inside the book

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Page 12

In both cases , the equal sides , or the equal angles , are named

In both cases , the equal sides , or the equal angles , are named

**homologous**sides or angles . Definitions of terms employed in Geometry . An axiom is a self - evident proposition . A theorem is a truth , which becomes evident by means ... Page 68

Any two sides , or any two angles , which have like po- sitions in two similar figures , are called

Any two sides , or any two angles , which have like po- sitions in two similar figures , are called

**homologous**sides or angles . 3. In two different circles , similar arcs , sectors , or segments , are those which correspond to equal ... Page 84

Two equiangular triangles have their

Two equiangular triangles have their

**homologous**sides propor- tional , 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**... Page 85

When the

When the

**homologous**sides are de- termined , it is easy to form the proportions : AB : DC : AC : DE :: BC : CE . PROPOSITION XIX . THEOREM . Two triangles , which have their**homologous**sides proportional , are equiangular and similar . Page 87

Two triangles , which have their

Two triangles , which have their

**homologous**sides parallel , or perpendicular to each other , are similar . Let BAC , EDF , be two triangles . First . If the side AB is parallel to DE , and BC to EF , the angle ABC will be equal to DEF ...### 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 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