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 40
... they are equal F to one another . Now , the angle EGB is equal to AGH ( 15. 1. ) ; and AGH is proved to be equal to GHD ; therefore EGB is likewise equal to GHD ; add to each of these tbe angle BGH ; therefore the angles ÉGB .
... they are equal F to one another . Now , the angle EGB is equal to AGH ( 15. 1. ) ; and AGH is proved to be equal to GHD ; therefore EGB is likewise equal to GHD ; add to each of these tbe angle BGH ; therefore the angles ÉGB .
Página 87
3. ) to two right angles ; therefore the angles DBF , DBE , being likewise equal ( 1 : 3 . 1. ) to two right angles , are equal to the angles BAD , BCD ; and DBF has been proved equal to BAD : therefore the remaining angle OF GEOMETRY .
3. ) to two right angles ; therefore the angles DBF , DBE , being likewise equal ( 1 : 3 . 1. ) to two right angles , are equal to the angles BAD , BCD ; and DBF has been proved equal to BAD : therefore the remaining angle OF GEOMETRY .
Página 88
been proved equal to BAD : therefore the remaining angle DBE is equal to the angle BCD in the alternate segment of the circle . Wherefore , if a straight line , & c . Q. E. D. PROP . XXXIII . PROB . a G Upon a given straight line to ...
been proved equal to BAD : therefore the remaining angle DBE is equal to the angle BCD in the alternate segment of the circle . Wherefore , if a straight line , & c . Q. E. D. PROP . XXXIII . PROB . a G Upon a given straight line to ...
Página 115
A : C :: B : C. Again , if A = B , C : A :: C : B ; for , as has been proved , A : C :: B : C , and inversely ( A. 5. ) , C : A :: C : B. Therefore , & c . Q. E. D. > : : PROP . VIII . THEOR . Of unequal magnitudes , the greater has a ...
A : C :: B : C. Again , if A = B , C : A :: C : B ; for , as has been proved , A : C :: B : C , and inversely ( A. 5. ) , C : A :: C : B. Therefore , & c . Q. E. D. > : : PROP . VIII . THEOR . Of unequal magnitudes , the greater has a ...
Página 118
In the same manner , it is proved , that if A = C , B = D ; and if AXC , BLD . Therefore , & c . Q. E. D. : : PROP . XV . THEOR . 1 Magnitudes have the same ratio to one another which their equimulteples have .
In the same manner , it is proved , that if A = C , B = D ; and if AXC , BLD . Therefore , & c . Q. E. D. : : PROP . XV . THEOR . 1 Magnitudes have the same ratio to one another which their equimulteples have .
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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 |