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 133
gular and similar to the triangle ABC : and the triangles ABD , ADC , being each equiangular and similar to ABC , are equiangular and similar to one another . Therefore , in a right angled , & c . Q. E. D. Cor .
gular and similar to the triangle ABC : and the triangles ABD , ADC , being each equiangular and similar to ABC , are equiangular and similar to one another . Therefore , in a right angled , & c . Q. E. D. Cor .
Σελίδα 138
Upon a given straight line to describe a rectilineal figure similar , and similarly situated to a given rectilineal figure . Let AB be the given straight line , and CDEF the given rectilineal figure of four sides ; it is required upon ...
Upon a given straight line to describe a rectilineal figure similar , and similarly situated to a given rectilineal figure . Let AB be the given straight line , and CDEF the given rectilineal figure of four sides ; it is required upon ...
Σελίδα 139
Next , Let it be required to describe upon a given straight line AB , a rectilineal figure similar , and similarly situated to the rectilineal figure CDKEF . Join DE , and upon the given straight line AB describe the rectilineal figure ...
Next , Let it be required to describe upon a given straight line AB , a rectilineal figure similar , and similarly situated to the rectilineal figure CDKEF . Join DE , and upon the given straight line AB describe the rectilineal figure ...
Σελίδα 140
and have their sides about the equal angles proportionals , they are similar to one another : and in the same manner a rectilineal figure of six , or more , sides may be described upon a given straight line similar to one given , and so ...
and have their sides about the equal angles proportionals , they are similar to one another : and in the same manner a rectilineal figure of six , or more , sides may be described upon a given straight line similar to one given , and so ...
Σελίδα 141
portionals , as the first is to the third , so is any triangle upon the first to a similar , and similarly described triangle upon the second . PROP . XX . THEOR . Similar polygons may be divided into the same number of similar ...
portionals , as the first is to the third , so is any triangle upon the first to a similar , and similarly described triangle upon the second . PROP . XX . THEOR . Similar polygons may be divided into the same number of similar ...
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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 |