## Elements of Geometry and Trigonometry |

### From inside the book

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Page 41

Every straight line , CA , CE , CD , drawn from the centre to the circum- ference , is called a

Every straight line , CA , CE , CD , drawn from the centre to the circum- ference , is called a

**radius**or semidiam- F E eter ; every line which , like AB , passes through the centre , and is terminated on both sides by the circumference ... Page 44

... are equal , it is plain that the

... are equal , it is plain that the

**radius**CD will fall on the**radius**OG , and the point D on the point G ; therefore the arc AMD is equal to the arc ENG . PROPOSITION V. THEOREM . In the same circle , or in equal circles , a greater ... Page 45

The

The

**radius**which is perpendicular to a chord , bisects the chord , and bisects also the subtended arc of the chord . Let AB be a chord , and CG the ra dius perpendicular to it : then will AD = DB , and the arc AG - GB . Page 46

... are equal ; there- fore the circumference described from the centre O , with the

... are equal ; there- fore the circumference described from the centre O , with the

**radius**OB , will pass through the three given points A , B , C. We have now shown that one circumference can always be made to pass through three given ... Page 47

A straight line perpendicular to a

A straight line perpendicular to a

**radius**, at its extremity , is a tangent to the circumference . Let BD be perpendicular to the B**radius**CA , at its extremity A ; then will it be tangent to the circumfe- rence .### 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