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 82
coincide with the segment CFD , and therefore is equal to it . Wherefore , similar segments , & c . Q. E. D. PROP . XXV . PROB . A segment of a circle being given , to describe the circle of which it is the segment .
coincide with the segment CFD , and therefore is equal to it . Wherefore , similar segments , & c . Q. E. D. PROP . XXV . PROB . A segment of a circle being given , to describe the circle of which it is the segment .
Página 197
the point N coinciding with the point D , K with A , L with B , and so on . And because the plane KM coincides with the plane AC , and , by hypothesis , the inclination of KR to KM is the same with the inclination of AH , to AC ...
the point N coinciding with the point D , K with A , L with B , and so on . And because the plane KM coincides with the plane AC , and , by hypothesis , the inclination of KR to KM is the same with the inclination of AH , to AC ...
Página 213
Therefore , when in the revolution of the rectangle AH , the straight line AG coincides with EG , the two rectangles AĦ and EH will coincide , and the straight line AD will coincide with the straight line EF .
Therefore , when in the revolution of the rectangle AH , the straight line AG coincides with EG , the two rectangles AĦ and EH will coincide , and the straight line AD will coincide with the straight line EF .
Página 241
Hence , if the point B coincide with A , R : cos . BC :: sin . BC : 1 sio . BD , that is the radius is to the cosine of any arch , as the sine of the arch is to half the sine of twice the any arch = A , sin . ? A = sin . A Xcos .
Hence , if the point B coincide with A , R : cos . BC :: sin . BC : 1 sio . BD , that is the radius is to the cosine of any arch , as the sine of the arch is to half the sine of twice the any arch = A , sin . ? A = sin . A Xcos .
Página 282
The former of these coincides with the cor . to the 20th ; and the latter with the 22d . To apply the foregoing general proposition , to resolve any case of a right angled spherical triangle , consider which of the three quantities ...
The former of these coincides with the cor . to the 20th ; and the latter with the 22d . To apply the foregoing general proposition , to resolve any case of a right angled spherical triangle , consider which of the three quantities ...
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Términos y frases comunes
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 |