## Elements of Geometry and Trigonometry |

### From inside the book

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Page 5

The Circle and the Measurement of Angles , Problems relating to the First and

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 , - Problems relating to the Fourth ... Page 12

that is to say , when following their perimeters in the same direction , the first side of the one is equal to the first side of the other , the second of the one to the second of the other , the

that is to say , when following their perimeters in the same direction , the first side of the one is equal to the first side of the other , the second of the one to the second of the other , the

**third**to the**third**, and so on . Page 17

DF is equal to AC ; therefore , the point F will fall on C , and the

DF is equal to AC ; therefore , the point F will fall on C , and the

**third**side EF , will coincide with the**third**side BC ( Ax . 11. ) : therefore , the triangle EDF is equal to the triangle BAC ( Ax . 13. ) . Cor . Page 18

Let ABC be a triangle : then will the sum of two of its sides , as AC , CB , be greater than the

Let ABC be a triangle : then will the sum of two of its sides , as AC , CB , be greater than the

**third**side AB . For , the line AB is the shortest distance between the points A and B ( Def . 3. ) ; hence AC + CB is greater than AB . Page 19

... fall on the side BC , it is evident that GC , or its equal EF , will be shorter than BC ( Ax . 8. ) . B

... fall on the side BC , it is evident that GC , or its equal EF , will be shorter than BC ( Ax . 8. ) . B

**Third**Case . Lastly , if the point G fall within the triangle BAC , we shall have , by the preceding theorem , AG + GC < AB + BC ...### 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