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 31
AC in E , join E BE and produce it to F , and make EF equal to BE ; join also FC , and produce AC to G. Because AE is equal to EC , and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the angle AEB is equal ( 15 . 1. ) ...
AC in E , join E BE and produce it to F , and make EF equal to BE ; join also FC , and produce AC to G. Because AE is equal to EC , and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the angle AEB is equal ( 15 . 1. ) ...
Σελίδα 32
AD equal to AB and join BD ; and because ADB is the exterior angle of the triangle B BDC , it is greater ( 16. 1. ) than the interior and opposite angle DCB ; but ADB is equal ( 5. 1. ) to ABD because the side AB is equal to the side AD ...
AD equal to AB and join BD ; and because ADB is the exterior angle of the triangle B BDC , it is greater ( 16. 1. ) than the interior and opposite angle DCB ; but ADB is equal ( 5. 1. ) to ABD because the side AB is equal to the side AD ...
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 ...
Σελίδα 35
another circle HLK ; A and join KF , KG ; the triB angle KFG has its sides equal to the three straight lines , A , B , C. Because the point F is the centre of the circle DKL , FD is equal ( 11. Def . ) to FK ; but FD is equal to the ...
another circle HLK ; A and join KF , KG ; the triB angle KFG has its sides equal to the three straight lines , A , B , C. Because the point F is the centre of the circle DKL , FD is equal ( 11. Def . ) to FK ; but FD is equal to the ...
Σελίδα 36
to AC or DF , and join EG , GF . Because AB is equal to DE , and AC to DG , the two sides BA , AC are equal to the two ED , DG , each to each , and the angle BAC iş equal to the angle А. D EDG , therefore the base BC is equal ( 4. 1. ) ...
to AC or DF , and join EG , GF . Because AB is equal to DE , and AC to DG , the two sides BA , AC are equal to the two ED , DG , each to each , and the angle BAC iş equal to the angle А. D EDG , therefore the base BC is equal ( 4. 1. ) ...
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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 |