## Elements of Geometry and Trigonometry |

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Page 13

A number placed before a line , or a quantity , serves as a multiplier to that line or quantity ; thus , 3AB signifies that the line AB is taken three times ; A signifies the

A number placed before a line , or a quantity , serves as a multiplier to that line or quantity ; thus , 3AB signifies that the line AB is taken three times ; A signifies the

**half**of the angle A. The square of the line AB is designated ... Page 23

therefore , AB , the

therefore , AB , the

**half**of ABF , is shorter than AC , the**half**of ACF ; hence , the perpendicular is shorter than any oblique line . ~ E Secondly . Let us suppose BC = BE ; then will the triangle CAB be equal to the the triangle BAE ... Page 47

In the right angled triangles CAF , DCG , the hypothenuses CA , CD , are equal ; and the side AF , the

In the right angled triangles CAF , DCG , the hypothenuses CA , CD , are equal ; and the side AF , the

**half**of AB , is equal to the side DG , the**half**of DE : hence the triangles are equal , and CF is equal to CG ( Book I. Prop . XVII . ) ... Page 54

An inscribed angle is measured by

An inscribed angle is measured by

**half**the arc included between its sides . Let BAD be an inscribed angle , and let us first suppose that the centre of the circle lies within the angle BAD . Draw the diameter AE , and the radii CB ... Page 55

All the angles BAC , BDC , BEC , inscribed in the same segment are equal ; because they are all measured by the

All the angles BAC , BDC , BEC , inscribed in the same segment are equal ; because they are all measured by the

**half**of the same arc BOC . B Cor . 2. Every angle BAD , inscribed in a semicircle is a right angle ; because it is measured ...### 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