## Elements of Geometry and Trigonometry |

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Page 46

... are equal ; therefore the circumference

... are equal ; therefore the circumference

**described**from the centre O , with the radius OB , will pass through the three given points A ... not in the same straight line : we say farther , that but one can be**described**through them . Page 49

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

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

**described**from the centres C and D , will cut each other in A and B. E D 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 ACD ... Page 53

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

It is only necessary that , in the comparison 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

But if the angle C is acute , and the side B less than A , then the arc

But if the angle C is acute , and the side B less than A , then the arc

**described**from the centre E , with the radius EF = B , will cut the side DF in two points F and G , lying on the same side of D : hence there will be two triangles ...### 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