## Elements of Geometry and Trigonometry |

### From inside the book

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Page 5

The Circle and the Measurement of Angles ,

The Circle and the Measurement of Angles ,

**Problems**relating to the First and Third Books , BOOK IV . The Proportions of Figures and the Measurement of Areas , -**Problems**relating to the Fourth Book , 41 57 98 88888 68 BOOK V. Regular ... Page 12

A lemma is a subsidiary truth , employed for the demonstra- tion of a theorem , or the solution of a

A lemma is a subsidiary truth , employed for the demonstra- tion of a theorem , or the solution of a

**problem**. The common name , proposition , is applied indifferently , to theorems ,**problems**, and lemmas . A corollary is an obvious ... Page 57

**PROBLEMS**RELATING TO THE FIRST AND THIRD BOOKS .**PROBLEM**I. To divide a given straight line into two equal parts . Let AB be the given straight line . From the points A and B as centres , with a radius greater than the half of AB ... Page 58

**PROBLEM**II . At a given point , in a given straight line , to erect a perpendicu- lar to this line . Let A be the given point , and BC the given line . A Take the points B and C at equal dis- tances from A ; then from the points B and ... Page 59

**PROBLEM**V. To divide a given arc , or a given angle , into two equal parts . First . Let it be required to divide the arc AEB into two equal parts . From the points A and B , as centres , with the same radius , describe two arcs cutting ...### 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