## Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids; to which are Added, Elements of Plane and Spherical Trigonometry |

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Resultat 1-5 av 31

Side 55

A straight line is said to touch a circle , when it meets the circle , and being

produced does not cut it . And that line which has but . one point in common with

the circumference , is called a

contact .

A straight line is said to touch a circle , when it meets the circle , and being

produced does not cut it . And that line which has but . one point in common with

the circumference , is called a

**tangent**, and the point in common , the point ofcontact .

Side 68

Hence , a perpendicular at the extremity of a diameter is a

and , conversely , a

follows , likewise , that

Cor .

Hence , a perpendicular at the extremity of a diameter is a

**tangent**to the circle ;and , conversely , a

**tangent**to a circle is perpendicular to the diameter ... Itfollows , likewise , that

**tangents**at each extremity of the diameter are parallel (Cor .

Side 69

to its chord GH : it is also perpendicular to the

parallel If both lines cut the circle , as GH , JK , and intercept equal arcs GJ , let

the diameter FE bisect one of the chords , as GH : it will also bisect the arc GEH ...

to its chord GH : it is also perpendicular to the

**tangent**AB ; therefore AB , GH areparallel If both lines cut the circle , as GH , JK , and intercept equal arcs GJ , let

the diameter FE bisect one of the chords , as GH : it will also bisect the arc GEH ...

Side 78

It follows , moreover , that two

. 3. And since a radius drawn to the point of contact is perpendicular to the

same ...

It follows , moreover , that two

**tangents**drawn from the same point are equal . Cor. 3. And since a radius drawn to the point of contact is perpendicular to the

**tangent**, C it follows that the angle included by two**tangents**, B drawn from thesame ...

Side 81

When the point A lies without the circle , there will evidently be always two equal

meets the circumference AG , and joining E and the point of intersection , and

also A ...

When the point A lies without the circle , there will evidently be always two equal

**tangents**passing through the point A. For , by producing the**tangent**FD till itmeets the circumference AG , and joining E and the point of intersection , and

also A ...

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### Vanlige uttrykk og setninger

ABCD altitude angle ABC angle BAC base bisected Book called centre chord circle circumference coincide common consequently construction cosine cylinder definition demonstrated described diameter difference distance divided double draw drawn equal equal angles equiangular equilateral Euclid exterior angle extremities fall fore four fourth given given straight line greater half Hence inscribed interior join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism Prob produced PROP proportional proposition proved radius ratio reason rectangle contained rectilineal figure remaining right angles segment shewn sides similar sine solid square straight line taken tangent THEOR third touch triangle ABC wherefore whole