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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Σελίδα 24
... AC be produced to D and E , the angle ABC shall be equal to the angle ACB , and the angle CBD to the angle BCE . In BD take any point F , and from AE the greater cut off AG equal ( 3. 1. ) to AF , the less , and join FC , GB .
... AC be produced to D and E , the angle ABC shall be equal to the angle ACB , and the angle CBD to the angle BCE . In BD take any point F , and from AE the greater cut off AG equal ( 3. 1. ) to AF , the less , and join FC , GB .
Σελίδα 25
off DB equal to AC the less , and join DC ; therefore , beΑ . cause in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are equal to the two AC , D CB , each to each ; but the angle DBC is also ...
off DB equal to AC the less , and join DC ; therefore , beΑ . cause in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are equal to the two AC , D CB , each to each ; but the angle DBC is also ...
Σελίδα 26
Join CD , and if possible let CB be equal to DB ; then , in the case D in which the vertex of each of the triangles is without the other triangle , because AC is equal to AD , the angle ACD is equal ( 5. 1. ) to the angle ADC : But the ...
Join CD , and if possible let CB be equal to DB ; then , in the case D in which the vertex of each of the triangles is without the other triangle , because AC is equal to AD , the angle ACD is equal ( 5. 1. ) to the angle ADC : But the ...
Σελίδα 29
FG in H , and D join CF , CH , CG ; the straight line CH , drawn from the given point C , is perpendicular to the given straight line AB . Because FH is equal to HG , and HC common to the two triangles FHC , GHC , the two sides FH ...
FG in H , and D join CF , CH , CG ; the straight line CH , drawn from the given point C , is perpendicular to the given straight line AB . Because FH is equal to HG , and HC common to the two triangles FHC , GHC , the two sides FH ...
Σελίδα 33
AD equal to AC ; and join DC . Because DA is equal to AC , the angle ADC is likewise equal ( 5. 1. ) to ACD ; but the angle BCD is greater than the angle ACD ; therefore the angle BCD B is greater than the angle ADC ; and because the ...
AD equal to AC ; and join DC . Because DA is equal to AC , the angle ADC is likewise equal ( 5. 1. ) to ACD ; but the angle BCD is greater than the angle ACD ; therefore the angle BCD B is greater than the angle ADC ; and because 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
Πληροφορίες βιβλιογραφίας
| Τίτλος | 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 |
| Συγγραφέας | John Playfair |
| Εκδότης | E. Duyckinck, and George Long, 1824 |
| Πρωτότυπο από | Πανεπιστήμιο της Ιντιάνα |
| Ψηφιοποιήθηκε στις | 15 Ιαν. 2009 |
| Μέγεθος | 333 σελίδες |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |