## Elements of Geometry and Trigonometry |

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Page 4

The proposition in

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 5

Ratios and Proportions ,

Ratios and Proportions ,

**BOOK**III . The Circle and the Measurement of Angles , Problems relating to the First and Third**Books**,**BOOK**IV . Planes and Solid Angles , Polyedrons , The Proportions of Figures and the Measurement of Areas ... Page 7

SHOWING THE PROPOSITIONS OF LEGENDRE WHICH CORRESPOND TO THE PRINCIPAL PROPOSITIONS OF THE FIRST SIX

SHOWING THE PROPOSITIONS OF LEGENDRE WHICH CORRESPOND TO THE PRINCIPAL PROPOSITIONS OF THE FIRST SIX

**BOOKS**OF EUCLID . Euclid . Legendre .**Book**I.**Book**I. 4 Prop . 5 Prop . Cor . of 5 11 5 Cor . of 11 6 12 8 10 13 1 14 3 15 4 4 16 Cor ... Page 11

20. Two polygons are mutually equilateral , when they have their sides equal each to each , and placed in the same order ; that is to say , when following their perimeters in

20. Two polygons are mutually equilateral , when they have their sides equal each to each , and placed in the same order ; that is to say , when following their perimeters in

**BOOK**I. 11. Page 19

... have the three sides of the one equal to the three sides of the other , each to each , the three angles will also be equal , each to each , and the triangles themselves will be equal . Let the side ED = BA , the side EF

... have the three sides of the one equal to the three sides of the other , each to each , the three angles will also be equal , each to each , and the triangles themselves will be equal . Let the side ED = BA , the side EF

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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