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 162
Suppose that HO and MP are equal to BE and DF . Then , because AE is to EB as CF is to FD , [ Hypothesis . and that GK and LN are equimultiples of AE and CF ; therefore GK is to EB as LN is to FD . [ V. 4 , Cor .
Suppose that HO and MP are equal to BE and DF . Then , because AE is to EB as CF is to FD , [ Hypothesis . and that GK and LN are equimultiples of AE and CF ; therefore GK is to EB as LN is to FD . [ V. 4 , Cor .
Seite 163
[ V. A. Again , suppose that HO and MP are equimultiples of EB and FD . Then , because AE is to EB as CF is to FD ; [ Hypothesis . and that GK and LN are equimultiples of AE and CF , and HO and MP are equi- multiples of EB and FD ...
[ V. A. Again , suppose that HO and MP are equimultiples of EB and FD . Then , because AE is to EB as CF is to FD ; [ Hypothesis . and that GK and LN are equimultiples of AE and CF , and HO and MP are equi- multiples of EB and FD ...
Seite 255
Let the angle ABC be equal to the angle ACB : then the side AB shall be equal to the side A C. For if not , one of them must be greater than the other ; suppose AB greater than AC . Then the angle ACB is greater But this is impossible ...
Let the angle ABC be equal to the angle ACB : then the side AB shall be equal to the side A C. For if not , one of them must be greater than the other ; suppose AB greater than AC . Then the angle ACB is greater But this is impossible ...
Seite 258
Now apply HEG to DAC , so that H may be on D , and HG on DC , and B and F on the same side of DC ; then G will coincide with C , and E with A. Also EF shall coincide with AB ; for if not , suppose , if possible , that it takes a ...
Now apply HEG to DAC , so that H may be on D , and HG on DC , and B and F on the same side of DC ; then G will coincide with C , and E with A. Also EF shall coincide with AB ; for if not , suppose , if possible , that it takes a ...
Seite 261
In the second case also the triangles are not necessarily equal , as may be shewn by an example ; in the figure of I. 11 , suppose the straight line FB drawn ; then in the two triangles FBE , FBD , the side FB and the angle FBC are ...
In the second case also the triangles are not necessarily equal , as may be shewn by an example ; in the figure of I. 11 , suppose the straight line FB drawn ; then in the two triangles FBE , FBD , the side FB and the angle FBC are ...
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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 |