## Elements of Geometry and Trigonometry |

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Page 41

From the definition of a circle , it follows that all the radii are equal ; that all the

From the definition of a circle , it follows that all the radii are equal ; that all the

**diameters**are equal also , and each double of the radius . 3. A portion of the circumference , such as FHG , is called an arc . Page 42

Every

Every

**diameter**divides the circle and its circumference into two equal parts . Let AEDF be a circle , and AB a**diameter**. Now , if the figure AEB be applied to AFB , their common base AB retaining its position , the curve line AEB must ... Page 43

Every chord is less than the

Every chord is less than the

**diameter**. Let AD be any chord . Draw the radii CA , CD , to its extremities . We shall then have AD < AC + CD ( Book I. Prop . VII . * ) ; A or AD < AB . Cor . Hence the greatest line which can be inscribed ... Page 44

For , since the

For , since the

**diameters**AB , EF , are equal , the semi- circle AMDB may be applied M ཤིས་ ཡོད་ ས exactly to the semicircle ENGF , and the curve line AMDB will coincide entirely with the curve line ENGF . But the part AMD is equal to ... Page 54

Draw the

Draw the

**diameter**AE , and the radii CB , CD . The angle BCE , being exterior to the triangle ABC , is equal to the sum of the two interior angles CAB , ABC ( Book I. Prop . XXV . Cor . 6. ) : but the triangle BAC being isosceles ...### 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