Books 10-13 and appendixThe University Press, 1908 |
Im Buch
Ergebnisse 1-5 von 41
Seite 1
... reference to the length of the diagonal of a square or the hypotenuse of an isosceles right - angled triangle that Pythagoras made his discovery . Plato ( Theaetetus , 147 D ) tells us that Theodorus of Cyrene wrote about square roots ...
... reference to the length of the diagonal of a square or the hypotenuse of an isosceles right - angled triangle that Pythagoras made his discovery . Plato ( Theaetetus , 147 D ) tells us that Theodorus of Cyrene wrote about square roots ...
Seite 4
... reference to it of the binomial can be understood . The connexion between the apotome and the harmonic mean is explained by some propositions in the second book of the Arabic commentary . The 2xy harmonic mean between x , y is and ...
... reference to it of the binomial can be understood . The connexion between the apotome and the harmonic mean is explained by some propositions in the second book of the Arabic commentary . The 2xy harmonic mean between x , y is and ...
Seite 8
... reference to Cossali ( Vol . II . , especially pp . 268-78 and 382-99 ) ; the character of the various odd and even powers of the binomials and apotomes is therein investigated , and Cardano considers in detail of what particular forms ...
... reference to Cossali ( Vol . II . , especially pp . 268-78 and 382-99 ) ; the character of the various odd and even powers of the binomials and apotomes is therein investigated , and Cardano considers in detail of what particular forms ...
Seite 11
... reference to this assumed rational straight line that c called rational or irrational . We should carefully note that the signification of rational in Eucli than in our terminology . With him , not only is a straight line commen length ...
... reference to this assumed rational straight line that c called rational or irrational . We should carefully note that the signification of rational in Eucli than in our terminology . With him , not only is a straight line commen length ...
Seite 16
... reference to the proof of x . 1. Euclid there takes the lesser magnitude and says that it is possible , by multiplying it , to make it some time exceed the greater , and this statement he clearly bases on the 4th definition of Book v ...
... reference to the proof of x . 1. Euclid there takes the lesser magnitude and says that it is possible , by multiplying it , to make it some time exceed the greater , and this statement he clearly bases on the 4th definition of Book v ...
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.