Books 10-13 and appendixThe University Press, 1908 |
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Seite 1
... commensurable , but those which are not subject to the same measure ... length of the diagonal of a square or the hypotenuse of an isosceles right ... commensurable INTRODUCTORY NOTE.
... commensurable , but those which are not subject to the same measure ... length of the diagonal of a square or the hypotenuse of an isosceles right ... commensurable INTRODUCTORY NOTE.
Seite 3
... length ( μñκos ) , and such as square the oblong square roots ( ovváμeis ) , as not being commensurable with the others in length but only in the plane areas to which their squares are equal . " There is further evidence of the ...
... length ( μñκos ) , and such as square the oblong square roots ( ovváμeis ) , as not being commensurable with the others in length but only in the plane areas to which their squares are equal . " There is further evidence of the ...
Seite 5
... length " commensurable in square only " with the unit of length , or A where A represents a number ( not square ) of units of area . The use therefore of p in our equations makes it unnecessary to multiply different cases according to ...
... length " commensurable in square only " with the unit of length , or A where A represents a number ( not square ) of units of area . The use therefore of p in our equations makes it unnecessary to multiply different cases according to ...
Seite 10
... commensurable and incommensurable respectively , some in length only , and others in square also , with an assigned straight line . Let then the assigned straight line be called rational , and those straight lines which are commensurable ...
... commensurable and incommensurable respectively , some in length only , and others in square also , with an assigned straight line . Let then the assigned straight line be called rational , and those straight lines which are commensurable ...
Seite 11
... Commensurable in square is in the Greek δυνάμει σύμμετρος . translations ( e.g. Williamson's ) dvráμe has been ... length ( pýκei ) , in Euclid's phrase , are commens square also ; but not all straight lines which are commensurable in ...
... Commensurable in square is in the Greek δυνάμει σύμμετρος . translations ( e.g. Williamson's ) dvráμe has been ... length ( pýκei ) , in Euclid's phrase , are commens square also ; but not all straight lines which are commensurable in ...
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.