## Elements of Geometry and Trigonometry |

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Page 46

and since the same point O lies in the perpen- dicular FG , it is also equally distant from the two points B and C : hence the three distances OA , OB , OC , are equal ; there- fore the circumference

and since the same point O lies in the perpen- dicular FG , it is also equally distant from the two points B and C : hence the three distances OA , OB , OC , are equal ; there- fore the circumference

**described**from the centre O ... Page 49

And , whenever the triangle CAD can be constructed , it is plain D that the circles

And , whenever the triangle CAD can be constructed , it is plain D that the circles

**described**from the centres C and D , will cut each other in A and B. 7 E PROPOSITION XIII . THEOREM . If the distance between the BOOK III . 49. Page 52

Whatever be the ratio of two angles , they will always be to each other as the arcs intercepted between their sides ; the arcs being

Whatever be the ratio of two angles , they will always be to each other as the arcs intercepted between their sides ; the arcs being

**described**from the vertices of the angles as centres , with equal radii . Let ACB be the greater and ... Page 53

It is only necessary that , in the com- parison of angles with each other , the arcs which serve to measure them , be

It is only necessary that , in the com- parison of angles with each other , the arcs which serve to measure them , be

**described**with equal radii , as is implied in all the foregoing propositions . Scholium 1. It appears most natural to ... Page 62

If the angle C is acute , and B greater than A , the same construction will again ap- ply , and DEF will be the triangle required . But if the angle C is acute , and the side B less than A , then the arc

If the angle C is acute , and B greater than A , the same construction will again ap- ply , and DEF will be the triangle required . But if the angle C is acute , and the side B less than A , then the arc

**described**from the centre E ...### 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