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 67
Similar segments of a circle , are those in which the an : gles are equal , or which contain equal angles . PROP . I. PROB . To find the centre of a given circle . Let ABC be the given circle ; it is required to find its centre .
Similar segments of a circle , are those in which the an : gles are equal , or which contain equal angles . PROP . I. PROB . To find the centre of a given circle . Let ABC be the given circle ; it is required to find its centre .
Página 81
Upon the same straight line , and upon the same side of it , there cannot bé two similar segments of circles , not coinciding with one another . If it be possible , let the two similar segments of circles , viz .
Upon the same straight line , and upon the same side of it , there cannot bé two similar segments of circles , not coinciding with one another . If it be possible , let the two similar segments of circles , viz .
Página 82
one of the segments must therefore fall within the other : let ACB fall within ADB , draw the straight line BCD , and join CA , DA : and because the segment ACB is similar to the segment ADB , and similar segments of circles contain ...
one of the segments must therefore fall within the other : let ACB fall within ADB , draw the straight line BCD , and join CA , DA : and because the segment ACB is similar to the segment ADB , and similar segments of circles contain ...
Página 84
to the base EF : and because the angle at A is equal to the angle at D , the segment BAC is similar ( 9. def . 3. ) to the segment EDF ; and they ; are upon equal straight lines BC , EF ; but similar segments of circles upon equal ...
to the base EF : and because the angle at A is equal to the angle at D , the segment BAC is similar ( 9. def . 3. ) to the segment EDF ; and they ; are upon equal straight lines BC , EF ; but similar segments of circles upon equal ...
Página 132
THEOR , In a right angled triangle if a perpendicular be drawn from the right angle to the base ; the triangles on each side of it are similar to the whole triangle , and to one another . Let ABC be a right angled triangle , having the ...
THEOR , In a right angled triangle if a perpendicular be drawn from the right angle to the base ; the triangles on each side of it are similar to the whole triangle , and to one another . Let ABC be a right angled triangle , having the ...
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ABC is equal ABCD altitude angle ABC angle BAC arch base bisected Book called centre circle circle ABC circumference coincide common cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular Euclid exterior angle extremity fall fore four fourth given given straight line greater half inscribed interior join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism produced PROP proportionals proposition proved radius ratio reason rectangle contained rectilineal figure right angles segment shewn sides similar sine solid square straight line taken tangent THEOR thing third touches 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 | E. Duyckinck, and George Long, 1824 |
| Procedencia del original | Universidad de Indiana |
| Digitalizado | 15 Ene. 2009 |
| Largo | 333 páginas |
| Exportar cita | BiBTeX EndNote RefMan |