Books 10-13 and appendix |
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Seite 2
The proof formerly appeared in the texts of Euclid as X. 117 , but it is undoubtedly an interpolation , and August and Heiberg accordingly relegate it to an Appendix . It is in substance as follows . Suppose AC , the diagonal of a ...
The proof formerly appeared in the texts of Euclid as X. 117 , but it is undoubtedly an interpolation , and August and Heiberg accordingly relegate it to an Appendix . It is in substance as follows . Suppose AC , the diagonal of a ...
Seite 3
... of irrational magnitudes “ had its origin in the school of Pythagoras . considerably developed by Theaetetus the Athenian , who gave proof , in this part of mathematics , as in others , of ability which has been justly admired .
... of irrational magnitudes “ had its origin in the school of Pythagoras . considerably developed by Theaetetus the Athenian , who gave proof , in this part of mathematics , as in others , of ability which has been justly admired .
Seite 8
... published at Berlin an Algebraischer Commentar über das zehente Buch der Elemente des Euklides which gives the contents in algebraical form but fails to give any indication of Euclid's methods , using modern forms of proof only .
... published at Berlin an Algebraischer Commentar über das zehente Buch der Elemente des Euklides which gives the contents in algebraical form but fails to give any indication of Euclid's methods , using modern forms of proof only .
Seite 15
This proposition will be remembered because it is the lemma required in Euclid's proof of xii . 2 to the effect that circles are to one another as the squares on their diameters . Some writers appear to be under the impression that XII ...
This proposition will be remembered because it is the lemma required in Euclid's proof of xii . 2 to the effect that circles are to one another as the squares on their diameters . Some writers appear to be under the impression that XII ...
Seite 16
2 may be explained by reference to the proof of x . I. Euclid there takes the lesser magnitude and says that it is possible , by multiplying it , to make it some time exceed the greater , and this statement he clearly bases on the 4th ...
2 may be explained by reference to the proof of x . I. Euclid there takes the lesser magnitude and says that it is possible , by multiplying it , to make it some time exceed the greater , and this statement he clearly bases on the 4th ...
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ABCD apotome applied base binomial straight line Book breadth called circle commensurable in length commensurable in square common cone construction contained corresponding cylinder definition diameter divided double draw drawn equal Euclid figure follows given greater half height Hence incommensurable inscribed irrational straight line joined Lemma less magnitudes measure medial area medial straight line meet parallel parallelepipedal parallelogram pentagon perpendicular plane polygon prism produces proof proportional PROPOSITION proved pyramid rational straight line reason reference remainder respectively right angles roots segment side similar Similarly solid sphere square number squares on AC straight lines commensurable Suppose Take third triangle twice the rectangle whence whole
Beliebte Passagen
Seite 310 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Seite 372 - Two unequal magnitudes being set out, if from the greater there be subtracted a magnitude greater than its half, and from that which is left a magnitude greater than its half, and if this process be repeated continually, there will be left some magnitude which will be less than the lesser magnitude set out?
Seite 260 - The inclination of a plane to a plane is the acute angle contained by two straight lines drawn from any the...
Seite 295 - BAE; and they are in one plane, which is impossible. Also, from a point above a plane, there can be but one perpendicular to that plane ; for, if there could be two, they would be parallel (6. PI.) to one another, which is absurd. Therefore, from the same point, &c.
Seite 279 - AB, CD. In like manner, it may be proved, that FE makes right angles with every straight line which meets it in that plane. But a straight line is at right angles to a plane when it makes right angles with every straight line which meets it in that plane : (xi. def. 3.) therefore EF is at right angles to the plane in which are AB, CD. Wherefore, if a straight line, &c.
Seite 389 - The upper end of the frustum of a pyramid or cone is called the upper base...
Seite 324 - AE is a parallelogram : join AH, DF ; and because AB is parallel to DC, and BH to CF ; the two straight lines AB, BH, which meet one another, are parallel to DC and CF, which meet one another...
Seite 294 - To erect a straight line at right angles to a given plane, from a point given in the plane. Let A be the point given in the plane.
Seite 304 - And because the plane AB is perpendicular to the third plane, and DE is drawn in the plane AB at right angles to AD their common section...
Seite 345 - N. equiangular to one another, each to each, that is, of which the folid angles are equal, each to each ; have to one another the ratio which is the fame with the ratio compounded of the ratios of their fides.
Bibliografische Informationen
| Titel | Books 10-13 and appendix Band 3 von The Thirteen Books of Euclid's Elements, Sir Thomas Little Heath |
| Autor/in | Euclid |
| Verlag | The University Press, 1908 |
| Zitat exportieren | BiBTeX EndNote RefMan |