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 36
Let ABC , DEF be two triangles which have the two sides AB , AC equal to the two DE , DF each to each viz . AB equal to DE , and AC to DF ; but the angle BAC greater than the angle EDF ; the base BC is also greater than the base EF .
Let ABC , DEF be two triangles which have the two sides AB , AC equal to the two DE , DF each to each viz . AB equal to DE , and AC to DF ; but the angle BAC greater than the angle EDF ; the base BC is also greater than the base EF .
Σελίδα 37
Let ABC , DEF be two A D triangles which have the angles ABC , BCA equal G to the angles DEF , EFD , viz . ABC to DEF , and BCA to EFD ; also one ; side equal to one side ; and first let those sides be equal which are adjacent to the ...
Let ABC , DEF be two A D triangles which have the angles ABC , BCA equal G to the angles DEF , EFD , viz . ABC to DEF , and BCA to EFD ; also one ; side equal to one side ; and first let those sides be equal which are adjacent to the ...
Σελίδα 38
... that is , it is equal to it ; and BC is equal to EF ; therefore the two AB , BC are equal to the two DE , EF , each to each ; and the angle ABC is equal to the angle DEF , therefore the base AC is equal ( 4. 1. ) ...
... that is , it is equal to it ; and BC is equal to EF ; therefore the two AB , BC are equal to the two DE , EF , each to each ; and the angle ABC is equal to the angle DEF , therefore the base AC is equal ( 4. 1. ) ...
Σελίδα 41
THEOR , If a side of any triangle be produced , the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles . Let ABC be a triangle , and let one of ...
THEOR , If a side of any triangle be produced , the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles . Let ABC be a triangle , and let one of ...
Σελίδα 42
parallel to CE , and BD falls upon them , the exterior angle ECD is equal to the interior and opposite angle ABC ; but the angle ACE was shewn to be equal to the angle BAC ; therefore the whole exterior angle ACD is equal to the two ...
parallel to CE , and BD falls upon them , the exterior angle ECD is equal to the interior and opposite angle ABC ; but the angle ACE was shewn to be equal to the angle BAC ; therefore the whole exterior angle ACD is equal to the two ...
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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 |