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 163
Therefore , the polygons ABCDEF and GHIKLM are equiangular to one another ; and since they are equilateral , the sides about the equal angles are proportionals ; the polygon ABCD is therefore similar to the polygon GHIKLM ( def . 1.6 . ) ...
Therefore , the polygons ABCDEF and GHIKLM are equiangular to one another ; and since they are equilateral , the sides about the equal angles are proportionals ; the polygon ABCD is therefore similar to the polygon GHIKLM ( def . 1.6 . ) ...
Página 164
the polygon ABCDEF is to the polygon GHIKLM as the square of AB to the square of GH ; but because the triangles ANB , GOH are equiangular , the square of AB is to the square of GH as the square of AN to the square of GO ( 4. 6. ) ...
the polygon ABCDEF is to the polygon GHIKLM as the square of AB to the square of GH ; but because the triangles ANB , GOH are equiangular , the square of AB is to the square of GH as the square of AN to the square of GO ( 4. 6. ) ...
Página 165
1. ) ; wherefore , the point M is in the circumference of the circle ; and because KMG is a right angle , KM touches the circle . And in the same manner , by joining the centre and the other angular points of the inscribed polygon , and ...
1. ) ; wherefore , the point M is in the circumference of the circle ; and because KMG is a right angle , KM touches the circle . And in the same manner , by joining the centre and the other angular points of the inscribed polygon , and ...
Página 166
Let the polygon described about the circle be called , M and the polygon inscribed be called N ; then , В LF KAM H G D E because these polygons are similar ( Cor . 3. 1. ) , they are as the squarex of the homologous sides HL and AF ...
Let the polygon described about the circle be called , M and the polygon inscribed be called N ; then , В LF KAM H G D E because these polygons are similar ( Cor . 3. 1. ) , they are as the squarex of the homologous sides HL and AF ...
Página 167
1 > has been demonstrated , that the square of AC is to the square of AF as the polygon M to the difference of the polygons ; therefore , since the square of AC is greater than M , the square of AF is greater than the difference of the ...
1 > has been demonstrated , that the square of AC is to the square of AF as the polygon M to the difference of the polygons ; therefore , since the square of AC is greater than M , the square of AF is greater than the difference of the ...
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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 |