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 85
them , wbich cut off the two greater arches BAC , EDF , and the two less BGC , EHF : the greater BAC is equal to the greater EDF , and the ... arches , when they are at the centres ; therefore the arch BGC is equal to the arch EHF .
them , wbich cut off the two greater arches BAC , EDF , and the two less BGC , EHF : the greater BAC is equal to the greater EDF , and the ... arches , when they are at the centres ; therefore the arch BGC is equal to the arch EHF .
Página 86
3 1 To bisect a given arch , that is , to divide it into two equal parts , Let ADB be the given arch ; it is required to bisect it . Join AB , and bisect ( 10. 1. ) it in C ; from the point C draw CD at right angles to AB , and joio AD ...
3 1 To bisect a given arch , that is , to divide it into two equal parts , Let ADB be the given arch ; it is required to bisect it . Join AB , and bisect ( 10. 1. ) it in C ; from the point C draw CD at right angles to AB , and joio AD ...
Página 87
BA at right angles to EF , and take any point C in the arch BD , and join AD , DC , CB ; and because the straight line EF touches the circle ABCD in the point B , and BA is drawn at right angles to the touching line , from the point of ...
BA at right angles to EF , and take any point C in the arch BD , and join AD , DC , CB ; and because the straight line EF touches the circle ABCD in the point B , and BA is drawn at right angles to the touching line , from the point of ...
Página 101
... and may therefore be divided “ into ten parts each equal to BAD . And as these ten equal angles at " the centre , must stand on ten equal arches , therefore the arch BD " is one - tenth of the circumference ; and the ...
... and may therefore be divided “ into ten parts each equal to BAD . And as these ten equal angles at " the centre , must stand on ten equal arches , therefore the arch BD " is one - tenth of the circumference ; and the ...
Página 102
“ each of the arches eut off will be one - tenth of the circumference , and " therefore the arch made up of both will be one - fifth of the circum“ ference ; and if the straight line subtending this arch be drawn it “ will ...
“ each of the arches eut off will be one - tenth of the circumference , and " therefore the arch made up of both will be one - fifth of the circum“ ference ; and if the straight line subtending this arch be drawn it “ will ...
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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 |