Books 10-13 and appendixThe University Press, 1908 |
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Ergebnisse 6-10 von 38
Seite 270
... cones only by sections always perpendicular to an edge . With this system the parabola was a section of a right - angled cone , the hyperbola a section of an obtuse - angled cone , and the ellipse a section of an acute - angled cone ...
... cones only by sections always perpendicular to an edge . With this system the parabola was a section of a right - angled cone , the hyperbola a section of an obtuse - angled cone , and the ellipse a section of an acute - angled cone ...
Seite 350
... cones and cylinders [ XII . 15 ] , he begins by supposing the heights equal , inferring by xII . 11 ( corresponding to XI . 32 ) that , the solids being equal , the bases are also equal , and then proceeds to the case where the heights ...
... cones and cylinders [ XII . 15 ] , he begins by supposing the heights equal , inferring by xII . 11 ( corresponding to XI . 32 ) that , the solids being equal , the bases are also equal , and then proceeds to the case where the heights ...
Seite 365
... cone is one third part of the cylinder which has base with the cone and equal height [ i.e. Eucl . XII . 10 ] . For , thou properties also were naturally inherent in the figures all along , yet th in fact unknown to all the many able ...
... cone is one third part of the cylinder which has base with the cone and equal height [ i.e. Eucl . XII . 10 ] . For , thou properties also were naturally inherent in the figures all along , yet th in fact unknown to all the many able ...
Seite 366
... cone and the pyramid , that the cone is one third part of the cylinder , and the pyramid one third part of the prism , having the same base and equal height , no small part of the credit will naturally be assigned to Democritus , who ...
... cone and the pyramid , that the cone is one third part of the cylinder , and the pyramid one third part of the prism , having the same base and equal height , no small part of the credit will naturally be assigned to Democritus , who ...
Seite 368
... cone irregular , as having many indentations , like steps , and uneven- nesses ; but , if they are equal , the sections will be equal , and the cone will appear to have the property of the cylinder and to be made up of equal , not ...
... cone irregular , as having many indentations , like steps , and uneven- nesses ; but , if they are equal , the sections will be equal , and the cone will appear to have the property of the cylinder and to be made up of equal , not ...
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.