Books 10-13 and appendixThe University Press, 1908 |
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Seite 4
... medial straight line an unlimited number of other irrationals can be derived all different from it and from one another . The connexion between the medial straight line and the geometric mean is obvious , because it is in fact the mean ...
... medial straight line an unlimited number of other irrationals can be derived all different from it and from one another . The connexion between the medial straight line and the geometric mean is obvious , because it is in fact the mean ...
Seite 7
... medial ( μέσης ἀποτομὴ πρώτη ) , which are the positive roots of 3 . k + p + - x2 - 2 √k ( 1 + k ) p2 . x2 + k ( 1 ... straight line ) ( μeíčwv ) and the minor ( irrational straight line ) ( ¿ λáoσwv ) , which are the positive roots of ...
... medial ( μέσης ἀποτομὴ πρώτη ) , which are the positive roots of 3 . k + p + - x2 - 2 √k ( 1 + k ) p2 . x2 + k ( 1 ... straight line ) ( μeíčwv ) and the minor ( irrational straight line ) ( ¿ λáoσwv ) , which are the positive roots of ...
Seite 48
... straight lines commensurable in any of the aforesaid ways . " Now straight ... line , si be either commensurable in length , or commensurable in square on ... medial straight lines commensurable in len enunciation of x . 24. The said ...
... straight lines commensurable in any of the aforesaid ways . " Now straight ... line , si be either commensurable in length , or commensurable in square on ... medial straight lines commensurable in len enunciation of x . 24. The said ...
Seite 50
... medial straight line , now defined for the first time , is so ca it is a mean proportional between two rational straight lines co in square only . Such straight lines can be denoted by p , p straight line is therefore of the form p√k ...
... medial straight line , now defined for the first time , is so ca it is a mean proportional between two rational straight lines co in square only . Such straight lines can be denoted by p , p straight line is therefore of the form p√k ...
Seite 51
... a , b be two straight lines , a : b = a2 : ab . PROPOSITION 22 . The square on a medial straight line , if appli rational straight line , produces as breadth a stra rational and incommensurable in length with that to is applied . Let A be ...
... a , b be two straight lines , a : b = a2 : ab . PROPOSITION 22 . The square on a medial straight line , if appli rational straight line , produces as breadth a stra rational and incommensurable in length with that to is applied . Let A be ...
Häufige Begriffe und Wortgruppen
area a medial base bimedial binomial straight line bisected circle ABCD commensurable in length commensurable in square cone cut in extreme cylinder decagon diameter dihedral angle dodecahedron equal equilateral Euclid extreme and mean greater segment height icosahedron inscribed irrational straight line kp² Lemma let the square magnitudes mean ratio medial area medial straight line medial whole parallel parallelepipedal solids parallelogram pentagon perpendicular plane of reference polygon prism Proclus PROPOSITION proved rational and incommensurable rational area rational straight line rectangle AC rectangle contained right angles second apotome side Similarly solid angle sphere square number square on AB squares on AC straight lines commensurable surable triangle twice the rectangle vertex whence
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.