## Elements of Geometry and Trigonometry |

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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 . Planes and Solid Angles , Polyedrons , 400mm The Proportions of Figures and the Measurement of Areas , -**Problems**relating to the ... Page 12

A lemma is a subsidiary truth , employed for the demonstration of a theorem , or the solution of a

A lemma is a subsidiary truth , employed for the demonstration 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

H D

H D

**PROBLEM**I.**PROBLEMS**RELATING TO THE FIRST AND THIRD BOOKS 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 . · Take the points B and C at equal distances from A ; then from the points B and C as ... Page 59

... describe an arc cutting the indefinite arc BO , in D ; draw AD ; and the angle DAB will be equal to the given angle K.

... describe an arc cutting the indefinite arc BO , in D ; draw AD ; and the angle DAB will be equal to the given angle K.

**PROBLEM**V. J B For , the two arcs BD , LI , have equal radii , and equal chords ; hence they are equal ( Prop .### What people are saying - Write a review

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### Common terms and phrases

ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently contained Cosine Cotang cylinder described determine diameter difference distance divided draw drawn equal equations equivalent expressed extremities faces feet figure follows formed four frustum give given gles greater half hence homologous hypothenuse included inscribed intersection less let fall logarithm manner means measured meet middle multiplied number of sides opposite parallel parallelogram pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quadrant quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment sides similar Sine solid solid angle sphere spherical triangle square straight line suppose taken Tang tangent THEOREM third triangle triangle ABC unit vertex whole