## Elements of Geometry and Trigonometry |

### From inside the book

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Page 4

The proposition in Book V. , which proves that a polygon and circle may be made to coincide so nearly , as to differ from each other by

The proposition in Book V. , which proves that a polygon and circle may be made to coincide so nearly , as to differ from each other by

**less**than any assignable quantity , has been taken from the Edinburgh Encyclopedia . Page 10

When two straight lines , AB , AC , meet each other , their inclination or opening is called an angle , which is greater or

When two straight lines , AB , AC , meet each other , their inclination or opening is called an angle , which is greater or

**less**as the lines are more or**less**inclined or opened . The point of intersection A is the vertex of the A4 ... Page 18

If from any point within a triangle , two straight lines be drawn to the extremities of either side , their sum will be

If from any point within a triangle , two straight lines be drawn to the extremities of either 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 triangle BAC ... Page 19

For , if not , the angle BAC must be equal to EDF , or

For , if not , the angle BAC must be equal to EDF , or

**less**than it . In the first case , the side BC would be equal to EF , ( Prop . V. Cor . ) ; in the second , CB would be**less**than EF ; but either of these results contradicts the ... Page 20

... if the angle D were

... 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 ; therefore it must be equal to it .### 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