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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Página 55
And that line which has but . one point in common with the circumference , is called a tangent , and the point in common , the point of contact . 3. Circles are said to touch one another , which meet , but do not cut one another . 4.
And that line which has but . one point in common with the circumference , is called a tangent , and the point in common , the point of contact . 3. Circles are said to touch one another , which meet , but do not cut one another . 4.
Página 68
Hence , a perpendicular at the extremity of a diameter is a tangent to the circle ; and , conversely , a tangent to a circle is ... It follows , likewise , that tangents at each extremity of the diameter are parallel ( Cor . Th.20 .
Hence , a perpendicular at the extremity of a diameter is a tangent to the circle ; and , conversely , a tangent to a circle is ... It follows , likewise , that tangents at each extremity of the diameter are parallel ( Cor . Th.20 .
Página 69
to its chord GH : it is also perpendicular to the tangent AB ; therefore AB , GH are parallel . If both lines cut the circle , as GH , JK , and intercept equal arcs GJ , HK ; let the diameter FE bisect one of the chords , as GH : it ...
to its chord GH : it is also perpendicular to the tangent AB ; therefore AB , GH are parallel . If both lines cut the circle , as GH , JK , and intercept equal arcs GJ , HK ; let the diameter FE bisect one of the chords , as GH : it ...
Página 78
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 , it follows that the angle included by two tangents , B drawn ...
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 , it follows that the angle included by two tangents , B drawn ...
Página 81
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 it meets the circumference AG , and joining E and the point of intersection ...
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 it meets the circumference AG , and joining E and the point of intersection ...
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Términos y frases comunes
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
Información bibliográfica
| Título | 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 |
| Autor | John Playfair |
| Editor | W. E. Dean, 1836 |
| Largo | 311 páginas |
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