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 71
If any point be taken without a circle , and straight lines be drawn from it to the circumference , whereof one passes through the centre ; of those which fall upon the concave circumference , the greatest is thai which passes through ...
If any point be taken without a circle , and straight lines be drawn from it to the circumference , whereof one passes through the centre ; of those which fall upon the concave circumference , the greatest is thai which passes through ...
Σελίδα 72
2 > > straight lines DA , DE , DF , DC be drawn to the circumference , whereof DA passes through the centre . Of those which fall upon the concave part of the circumference AEFC , the greatest is AD which passes through the centre ...
2 > > straight lines DA , DE , DF , DC be drawn to the circumference , whereof DA passes through the centre . Of those which fall upon the concave part of the circumference AEFC , the greatest is AD which passes through the centre ...
Σελίδα 73
Therefore one circumference of a circle canG pot cut another in more than two points . Q. E. D. PROP . XI . THEOR . If two circles touch each other internally , the straight line which joins their centres being produced , will pass ...
Therefore one circumference of a circle canG pot cut another in more than two points . Q. E. D. PROP . XI . THEOR . If two circles touch each other internally , the straight line which joins their centres being produced , will pass ...
Σελίδα 74
point A , and let F be the centre of the circle ABC , and G the centre of the circle ADE ; the straight line wbich joins the centres F , G , being produced , passes through the point A. Н. For , if not , let it fall otherwise , if D ...
point A , and let F be the centre of the circle ABC , and G the centre of the circle ADE ; the straight line wbich joins the centres F , G , being produced , passes through the point A. Н. For , if not , let it fall otherwise , if D ...
Σελίδα 75
in the straight line GH which bisects BD at right angles : Therefore GH passes through the point of contact ( 11. 3. ) ; but it does not pass through it , because the points B , D are without the straight line GH , which is absurd ...
in the straight line GH which bisects BD at right angles : Therefore GH passes through the point of contact ( 11. 3. ) ; but it does not pass through it , because the points B , D are without the straight line GH , which is absurd ...
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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 |