The Elements of Euclid for the Use of Schools and Colleges: Comprising the First Six Books and Portions of the Eleventh and Twelfth Books |
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Seite 74
Q.E.D. PROPOSITION 3. THEOREM . If a straight line drawn through the centre of a circle , bisect a straight line in it which does not pass through the centre , it shall cut it at right angles ; 74 EUCLID'S ELEMENTS .
Q.E.D. PROPOSITION 3. THEOREM . If a straight line drawn through the centre of a circle , bisect a straight line in it which does not pass through the centre , it shall cut it at right angles ; 74 EUCLID'S ELEMENTS .
Seite 75
Let ABC be a circle ; and let CD , a straight line drawn through the centre , bisect any straight line AB , which does not pass through the centre , at the point F : CD shall cut AB at right angles . Take E the centre of the circle ...
Let ABC be a circle ; and let CD , a straight line drawn through the centre , bisect any straight line AB , which does not pass through the centre , at the point F : CD shall cut AB at right angles . Take E the centre of the circle ...
Seite 76
X If in a circle two straight lines cut one another , which do not both pass through the centre , they do not bisect one another . Let ABCD be a circle , and AC , BD two straight lines in it , which cut one another at the point E ...
X If in a circle two straight lines cut one another , which do not both pass through the centre , they do not bisect one another . Let ABCD be a circle , and AC , BD two straight lines in it , which cut one another at the point E ...
Seite 83
If two circles touch one another internally , the straight line which joins their centres , being produced , shall pass through the point of contact . Let the two circles ABC , ADE touch one another inter- nally at the point A ; and let ...
If two circles touch one another internally , the straight line which joins their centres , being produced , shall pass through the point of contact . Let the two circles ABC , ADE touch one another inter- nally at the point A ; and let ...
Seite 84
If two circles touch one another externally , the straight line which joins their centres shall pass through the point of contact . Let the two circles ABC , ADE touch one another ex- ternally at the point A ; and let F be the centre of ...
If two circles touch one another externally , the straight line which joins their centres shall pass through the point of contact . Let the two circles ABC , ADE touch one another ex- ternally at the point A ; and let F be the centre of ...
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ABCD AC is equal angle ABC angle BAC Axiom base bisected Book centre chord circle ABC circumference common Construction Corollary Definition demonstration describe a circle described diameter difference divided double draw drawn equal equal angles equiangular equilateral equimultiples Euclid extremities fall figure fixed formed four fourth given circle given point given straight line greater half Hypothesis inscribed intersect join less Let ABC magnitudes manner meet multiple namely opposite sides parallel parallelogram pass perpendicular plane polygon PROBLEM produced proportionals PROPOSITION Q.E.D. PROPOSITION quadrilateral radius ratio reason rectangle contained rectilineal figure remaining respectively right angles segment shew shewn sides similar square square on AC straight line drawn suppose Take taken tangent THEOREM third triangle ABC twice Wherefore whole
Bibliografische Informationen
| Titel | The Elements of Euclid for the Use of Schools and Colleges: Comprising the First Six Books and Portions of the Eleventh and Twelfth Books Cambridge school class books Macmillan's school class books |
| Autoren | Euclid, Isaac Todhunter |
| Herausgeber | Isaac Todhunter, Robert Simson |
| Ausgabe | Neuauflage |
| Verlag | Macmillan, 1886 |
| Original von | Princeton University |
| Digitalisiert | 26. Jan. 2009 |
| Länge | 400 Seiten |
| Zitat exportieren | BiBTeX EndNote RefMan |