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 1
A plane superficies is that in which any two points being taken , the straight line between them lies wholly in that superficies . 8. A plane angle is the inclination of two lines to one another in a plane , which meet together ...
A plane superficies is that in which any two points being taken , the straight line between them lies wholly in that superficies . 8. A plane angle is the inclination of two lines to one another in a plane , which meet together ...
Seite 6
If equals be taken from equals the remainders are equal . 4. If equals be added to unequals the wholes are unequal . 5. If equals be taken from unequals the remainders are unequal . 6. Things which are double of the same thing are equal ...
If equals be taken from equals the remainders are equal . 4. If equals be added to unequals the wholes are unequal . 5. If equals be taken from unequals the remainders are unequal . 6. Things which are double of the same thing are equal ...
Seite 33
But if a straight line meet two straight lines , so as to make the two interior angles on the same side of it , taken together , less than two right angles , these straight lines being continually produced , shall at length meet on that ...
But if a straight line meet two straight lines , so as to make the two interior angles on the same side of it , taken together , less than two right angles , these straight lines being continually produced , shall at length meet on that ...
Seite 74
If any two points be taken in the circumference of a circle , the straight line which joins them shall fall within the circle . Let ABC be a circle , and A and B any two points in the circumference : the straight line drawn from A to B ...
If any two points be taken in the circumference of a circle , the straight line which joins them shall fall within the circle . Let ABC be a circle , and A and B any two points in the circumference : the straight line drawn from A to B ...
Seite 77
[ I. Definition 15 . [ Axiom 1 . Therefore Fis not the centre of the circles ABC , CDE . Wherefore , if two circles & c . Q.ED. PROPOSITION 7. THEOREM . If any point be taken in BOOK III . 5 , 6 . 77.
[ I. Definition 15 . [ Axiom 1 . Therefore Fis not the centre of the circles ABC , CDE . Wherefore , if two circles & c . Q.ED. PROPOSITION 7. THEOREM . If any point be taken in BOOK III . 5 , 6 . 77.
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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 |