Books 10-13 and appendix |
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Seite 8
Consequently the summaries which have been given of Eucl . x . by various writers differ much in appearance while expressing the same thing in substance . The first summary in algebraical form ( and a very elaborate one ) seems to have ...
Consequently the summaries which have been given of Eucl . x . by various writers differ much in appearance while expressing the same thing in substance . The first summary in algebraical form ( and a very elaborate one ) seems to have ...
Seite 10
... given by Apollonius may have been . See note at end of Book . DEFINITIONS . 1 . Those magnitudes are said to be commensurable which are measured by the same measure , and those incommensurable which cannot have any common measure .
... given by Apollonius may have been . See note at end of Book . DEFINITIONS . 1 . Those magnitudes are said to be commensurable which are measured by the same measure , and those incommensurable which cannot have any common measure .
Seite 16
It is required to prove that , given two straight lines , there always exists a multiple of the smaller which is greater than the other . Let the straight lines be so placed that they have a common extremity and the smaller lies along ...
It is required to prove that , given two straight lines , there always exists a multiple of the smaller which is greater than the other . Let the straight lines be so placed that they have a common extremity and the smaller lies along ...
Seite 19
This method is given in Chrystal's Textbook of Algebra ( 1. p . 270 ) . Let d , a be the a A diagonal and side respectively of a square ABCD . Mark off AF along AC equal to a . Draw FE at right angles to AC meeting BC in E. E It is ...
This method is given in Chrystal's Textbook of Algebra ( 1. p . 270 ) . Let d , a be the a A diagonal and side respectively of a square ABCD . Mark off AF along AC equal to a . Draw FE at right angles to AC meeting BC in E. E It is ...
Seite 20
Given two commensurable magnitudes , to find their greatest common measure . Let the two given commensurable magnitudes be AB , CD of which AB is the less ; thus it is required to find the greatest common measure of AB , CD .
Given two commensurable magnitudes , to find their greatest common measure . Let the two given commensurable magnitudes be AB , CD of which AB is the less ; thus it is required to find the greatest common measure of AB , CD .
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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 |