## 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 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 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

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

... and B greater than A , the same construction will again apply , 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 , with the radius EF ... Page 65

Now , if from the point O as a centre , with the radius OD , a circle be

Now , if from the point O as a centre , with the radius OD , a circle be

**described**, this circle will evidently be inscribed in the triangle ABC ; for the side AB , being perpendicular to the radius at its extremity , is a tangent ...### 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 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