Books 10-13 and appendix |
Im Buch
Seite 1
... Cyrene wrote about square roots ( dvváμes ) , proving that the square roots of 1 I have already noted ( Vol . I. p . 351 ) that G. Junge ( Wann haben die Griechen das Irrationale entdeckt ? ) disputes this , maintaining that it was ...
... Cyrene wrote about square roots ( dvváμes ) , proving that the square roots of 1 I have already noted ( Vol . I. p . 351 ) that G. Junge ( Wann haben die Griechen das Irrationale entdeckt ? ) disputes this , maintaining that it was ...
Seite 2
three square feet and five square feet are not commensurable with that of one square foot , and so on , selecting each such square root up to that of 17 square feet , at which for some reason he stopped . No mention is here made of √2 ...
three square feet and five square feet are not commensurable with that of one square foot , and so on , selecting each such square root up to that of 17 square feet , at which for some reason he stopped . No mention is here made of √2 ...
Seite 3
The idea occurred to me , seeing that square roots ( dvváμeis ) appeared to be unlimited in multitude , to try to arrive at one collective term by which we could designate all these square roots .... I divided number in general into two ...
The idea occurred to me , seeing that square roots ( dvváμeis ) appeared to be unlimited in multitude , to try to arrive at one collective term by which we could designate all these square roots .... I divided number in general into two ...
Seite 4
56 ) " Since such roots of equations of the second degree as are incommensurable with the given magnitudes cannot be expressed by means of the latter and of numbers , it is conceivable that the Greeks , in exact investigations ...
56 ) " Since such roots of equations of the second degree as are incommensurable with the given magnitudes cannot be expressed by means of the latter and of numbers , it is conceivable that the Greeks , in exact investigations ...
Seite 5
Now the positive roots of the quadratic equations x2 + 2ax . p + B. p2 = 0 can only have the following forms . x1 = p ( a + √ a2 ... x2 = p ( √ a2 + B - a ) 66 } The negative roots do not come in , since x must be a straight line .
Now the positive roots of the quadratic equations x2 + 2ax . p + B. p2 = 0 can only have the following forms . x1 = p ( a + √ a2 ... x2 = p ( √ a2 + B - a ) 66 } The negative roots do not come in , since x must be a straight line .
Was andere dazu sagen - Rezension schreiben
Es wurden keine Rezensionen gefunden.
Häufige Begriffe und Wortgruppen
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 reference remainder respectively right angles segment side similar Similarly solid sphere square number squares on AC straight lines commensurable Suppose Take 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 |