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 vii
A new axiom is also introduced in the room of the 12th , for the purpose of demonstrating more easily some of the properties of parallel lines . In the third Book , the remarks concerning the angles made ...
A new axiom is also introduced in the room of the 12th , for the purpose of demonstrating more easily some of the properties of parallel lines . In the third Book , the remarks concerning the angles made ...
Σελίδα 20
Parallel straight lines , are such as are in the same plane , and which being produced ever so far both ways , do not meet . 2 POSTULATES . I. Let it be granted that a straight 20 ELEMENTS A ...
Parallel straight lines , are such as are in the same plane , and which being produced ever so far both ways , do not meet . 2 POSTULATES . I. Let it be granted that a straight 20 ELEMENTS A ...
Σελίδα 21
Two straight lines which intersect one another , cannot be both “ parallel to the game straight line . " 2 PROPOSITION I. PROBLEM . To describe an equilateral triangle upon OF GEOMETRY . BOOK I. 21.
Two straight lines which intersect one another , cannot be both “ parallel to the game straight line . " 2 PROPOSITION I. PROBLEM . To describe an equilateral triangle upon OF GEOMETRY . BOOK I. 21.
Σελίδα 38
For , if it be not parallel , AB and CD being produced shall meet either towards B , D , or towards A , C ; let them be produced and meet towards B , D in the point G ; therefore GEF is a triangle , and its exterior angle AEF is greater ...
For , if it be not parallel , AB and CD being produced shall meet either towards B , D , or towards A , C ; let them be produced and meet towards B , D in the point G ; therefore GEF is a triangle , and its exterior angle AEF is greater ...
Σελίδα 39
AB therefore is parallel to CD . Wherefore , if a straight line & c . Q. E. D. PROP . XXVIII . THEOR . 1 If a straight line falling upon two other straight lines makes the exterior angle equal to the interior and opposite upon the same ...
AB therefore is parallel to CD . Wherefore , if a straight line & c . Q. E. D. PROP . XXVIII . THEOR . 1 If a straight line falling upon two other straight lines makes the exterior angle equal to the interior and opposite upon the same ...
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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 |