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 xv
If , for example , it be alleged , that it is needless to demonstrate that any two sides of a triangle are greater than the third ; it may be replied , that this is no doubt a truth which , without proof , most men will be inclined to ...
If , for example , it be alleged , that it is needless to demonstrate that any two sides of a triangle are greater than the third ; it may be replied , that this is no doubt a truth which , without proof , most men will be inclined to ...
Σελίδα 24
Which was to be demonstrated . PROP . V. THEOR . The angles at the base of an Isosceles triangle are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall also be equal .
Which was to be demonstrated . PROP . V. THEOR . The angles at the base of an Isosceles triangle are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall also be equal .
Σελίδα 25
Now , since it has been demonstrated , that the whole angle ABG is equal to the whole ACF , and the part CBG , to the part BCF the remaining angle ABC is therefore equal to the remaining angle ACB , which are the angles at the base of ...
Now , since it has been demonstrated , that the whole angle ABG is equal to the whole ACF , and the part CBG , to the part BCF the remaining angle ABC is therefore equal to the remaining angle ACB , which are the angles at the base of ...
Σελίδα 26
to the angle BCD ; but it has been demonstrated to be greater than it ; which is impossible . But if one of the vertices , as D , be within the other triangle ACB ; produce AC , AD to E , F ; therefore , because AC is equal to AD in the ...
to the angle BCD ; but it has been demonstrated to be greater than it ; which is impossible . But if one of the vertices , as D , be within the other triangle ACB ; produce AC , AD to E , F ; therefore , because AC is equal to AD in 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 |