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
6. Any portion of the circumference is called an arc . The chord or subtense of an arc is the straight line which joins its two extremities . 7. A straight line is said to be inscribed in a circle , when the extremities of ...
6. Any portion of the circumference is called an arc . The chord or subtense of an arc is the straight line which joins its two extremities . 7. A straight line is said to be inscribed in a circle , when the extremities of ...
Página 56
The angles at the circumference and centre , are both said to be subtended by the chords or arcs which their sides include . 11. The sector of a circle is the figure contained by two straight lines drawn from the centre , and the arc of ...
The angles at the circumference and centre , are both said to be subtended by the chords or arcs which their sides include . 11. The sector of a circle is the figure contained by two straight lines drawn from the centre , and the arc of ...
Página 57
The arc of a circle whose chord is a diameter , is a semi - circumference , and the included segment is a semi - circle . PROP . II . THEOR . If any two points be taken in the circumference of a circle , the straight line which joins ...
The arc of a circle whose chord is a diameter , is a semi - circumference , and the included segment is a semi - circle . PROP . II . THEOR . If any two points be taken in the circumference of a circle , the straight line which joins ...
Página 58
Hence , the perpendicular through the middle of a chord , passes through the centre ; for this perpendicular is the same as the one let fall from the centre on the same chord , since both of them passes through the middle of the chord .
Hence , the perpendicular through the middle of a chord , passes through the centre ; for this perpendicular is the same as the one let fall from the centre on the same chord , since both of them passes through the middle of the chord .
Página 62
AL F It is obvious , that besides this , no other circumference can pass through the same points ; for the centre , lying in the perpendicular DF bisecting the chord AB , and at the same time in the perpendicular EF bisecting the chord ...
AL F It is obvious , that besides this , no other circumference can pass through the same points ; for the centre , lying in the perpendicular DF bisecting the chord AB , and at the same time in the perpendicular EF bisecting the chord ...
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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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