Books 10-13 and appendixThe University Press, 1908 |
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Ergebnisse 1-5 von 100
Seite 2
Euclid. three square feet and five square feet are not commensurable with that of one ... AC AC2AB , AB a2 : B2 , a2 = 2ẞ2 . EN [ Eucl . 1. 47 ] B Therefore a2 is ... squares , one of which has three times the area of another , an entirely ...
Euclid. three square feet and five square feet are not commensurable with that of one ... AC AC2AB , AB a2 : B2 , a2 = 2ẞ2 . EN [ Eucl . 1. 47 ] B Therefore a2 is ... squares , one of which has three times the area of another , an entirely ...
Seite 19
... AC will then be similarly divided , and so on . Now the greater segment in a ... square that Pythagoras discovered incommensurable magnitudes . But the ... square ABCD . Mark off AF along AC equal to a . Draw FE at right angles to AC ...
... AC will then be similarly divided , and so on . Now the greater segment in a ... square that Pythagoras discovered incommensurable magnitudes . But the ... square ABCD . Mark off AF along AC equal to a . Draw FE at right angles to AC ...
Seite 41
... square figure DB ; I say that AD is equal to the rectangle contained by AC , CB . This is indeed at once manifest ; for , since DB is a square , DC is equal to CB ; and AD is the rectangle AC , CD , that is , the rectang CB . Therefore ...
... square figure DB ; I say that AD is equal to the rectangle contained by AC , CB . This is indeed at once manifest ; for , since DB is a square , DC is equal to CB ; and AD is the rectangle AC , CD , that is , the rectang CB . Therefore ...
Seite 47
... square only . ] PROPOSITION 19 . The rectangle contained by rational straight lines surable in length is rational . For let the rectangle AC be contained by the straight lines AB , BC commensurable in length ; I say that AC is rational ...
... square only . ] PROPOSITION 19 . The rectangle contained by rational straight lines surable in length is rational . For let the rectangle AC be contained by the straight lines AB , BC commensurable in length ; I say that AC is rational ...
Seite 49
... AC be applied to AB , a straight line once more rational in any of the aforesaid ways , producing BC as breadth ; I say that BC is rational and commensurable in length with BA . For on AB let the square AD be described ; therefore AD is ...
... AC be applied to AB , a straight line once more rational in any of the aforesaid ways , producing BC as breadth ; I say that BC is rational and commensurable in length with BA . For on AB let the square AD be described ; therefore AD is ...
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.