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 xvi
The word hypothesis is used in the same sense as supposition . To assist the student in following the steps of the reasoning , references are given to the results already ob- tained which are required in the demonstration .
The word hypothesis is used in the same sense as supposition . To assist the student in following the steps of the reasoning , references are given to the results already ob- tained which are required in the demonstration .
Seite 10
B [ Hypothesis . Therefore also the point C will coincide with the point F , because AC is equal to DF . [ Hypothesis . But the point B was shewn to coincide with the point E , therefore the base BC will coincide with the base EF ...
B [ Hypothesis . Therefore also the point C will coincide with the point F , because AC is equal to DF . [ Hypothesis . But the point B was shewn to coincide with the point E , therefore the base BC will coincide with the base EF ...
Seite 11
[ Hypothesis . and AB to AC , the two sides FA , AC are equal to the two sides GA , AB , each to each ; and they contain the angle FAG common to the two triangles AFC , AGB ; therefore the base FC is equal to the base GB , and the ...
[ Hypothesis . and AB to AC , the two sides FA , AC are equal to the two sides GA , AB , each to each ; and they contain the angle FAG common to the two triangles AFC , AGB ; therefore the base FC is equal to the base GB , and the ...
Seite 13
[ Hypothesis . [ I. 5 . But the angle ACD is greater than the angle BCD , [ Ax . 9 . therefore the angle ADC is also greater than the angle BCD ; much more then is the angle BDC greater than the angle BCD . Again , because BC is equal ...
[ Hypothesis . [ I. 5 . But the angle ACD is greater than the angle BCD , [ Ax . 9 . therefore the angle ADC is also greater than the angle BCD ; much more then is the angle BDC greater than the angle BCD . Again , because BC is equal ...
Seite 16
From the point B draw BE at right angles to AB . E B the angle CBE is equal to the angle EBA . [ Hypothesis . [ Definition 10 . Then , because ABC is a straight line , Also , because ABD is a straight line , the 16 EUCLID'S ELEMENTS .
From the point B draw BE at right angles to AB . E B the angle CBE is equal to the angle EBA . [ Hypothesis . [ Definition 10 . Then , because ABC is a straight line , Also , because ABD is a straight line , the 16 EUCLID'S ELEMENTS .
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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 |