Books 10-13 and appendix |
Im Buch
Ergebnisse 1-5 von 100
Seite 260
I. 2 . a A solid is that which has length , breadth , and depth . An extremity of a solid is a surface . 3 . A straight line is at right angles to a plane , when it makes right angles with all the straight lines which meet it and are in ...
I. 2 . a A solid is that which has length , breadth , and depth . An extremity of a solid is a surface . 3 . A straight line is at right angles to a plane , when it makes right angles with all the straight lines which meet it and are in ...
Seite 261
Similar solid figures are those contained by similar planes equal in multitude . ... A solid angle is the inclination constituted by more than two lines which meet one another and are not in the same surface , towards all the lines .
Similar solid figures are those contained by similar planes equal in multitude . ... A solid angle is the inclination constituted by more than two lines which meet one another and are not in the same surface , towards all the lines .
Seite 262
A cube is a solid figure contained by six equal squares . 26 . An octahedron is a solid figure contained by eight equal and equilateral triangles . 27 . An icosahedron is a solid figure contained by twenty equal and equilateral ...
A cube is a solid figure contained by six equal squares . 26 . An octahedron is a solid figure contained by eight equal and equilateral triangles . 27 . An icosahedron is a solid figure contained by twenty equal and equilateral ...
Seite 263
A solid body is that which has length , breadth , and depth : or that which possesses the three dimensions . " ( Def . 13. ) Similarly Theon of Smyrna ( p . 111 , 19 , ed . Hiller ) : “ that which is extended ( diaotatóv ) and divisible ...
A solid body is that which has length , breadth , and depth : or that which possesses the three dimensions . " ( Def . 13. ) Similarly Theon of Smyrna ( p . 111 , 19 , ed . Hiller ) : “ that which is extended ( diaotatóv ) and divisible ...
Seite 264
This dihedral angle is an “ angle ” altogether different in kind from a plane angle , as again it is different from a solid angle as defined by Euclid ( i.e. a trihedral , tetrahedral , etc. angle ) . Adopting for the moment Apollonius ...
This dihedral angle is an “ angle ” altogether different in kind from a plane angle , as again it is different from a solid angle as defined by Euclid ( i.e. a trihedral , tetrahedral , etc. angle ) . Adopting for the moment Apollonius ...
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 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 |