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 23
Ax . ) BG : But it has been shewn that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AŁ is equal to BC .
Ax . ) BG : But it has been shewn that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AŁ is equal to BC .
Σελίδα 33
than the angle B ACB ; but it is not ; therefore the side AC is not less than AB ; and it has been shewn that it is not equal to AB ; therefore AC is greater than AB . Wherefore the greater angle , & c . Q. E. D. 2 PROP . XX . THEOR .
than the angle B ACB ; but it is not ; therefore the side AC is not less than AB ; and it has been shewn that it is not equal to AB ; therefore AC is greater than AB . Wherefore the greater angle , & c . Q. E. D. 2 PROP . XX . THEOR .
Σελίδα 34
... DB ; but it has been shewn that BA , AC are greater that BE , EC ; much more then are BA , AC B greater than BD , DC . Again , because the exterior angle of a triangle ( 16. 1. ) is greater than the interior and opposite angle ...
... DB ; but it has been shewn that BA , AC are greater that BE , EC ; much more then are BA , AC B greater than BD , DC . Again , because the exterior angle of a triangle ( 16. 1. ) is greater than the interior and opposite angle ...
Σελίδα 37
than the base EF ; but it is not ; therefore the angle BAC is not less than the angle EDF ; and it was shewn tbat it is E B not equal to it : therefore F the angle BAC is greater than the angle EDF . Wherefore , if two triaugles , & c .
than the base EF ; but it is not ; therefore the angle BAC is not less than the angle EDF ; and it was shewn tbat it is E B not equal to it : therefore F the angle BAC is greater than the angle EDF . Wherefore , if two triaugles , & c .
Σελίδα 41
to the angle GKD ; and it was shewn that the angle AGK is equal to the angle GHF ; therefore also AGK is equal to GKD ; and they are alternate angles ; therefore AB is parallel ( 27.1 . ) to CD . Wherefore straight lines , & c .
to the angle GKD ; and it was shewn that the angle AGK is equal to the angle GHF ; therefore also AGK is equal to GKD ; and they are alternate angles ; therefore AB is parallel ( 27.1 . ) to CD . Wherefore straight lines , & c .
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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 |