## Books 10-13 and appendixThe University Press, 1908 - Mathematics, Greek |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Common terms and phrases

area a medial base binomial straight line bisected circle ABCD circle EFGH commensurable in length commensurable in square cone cube cut in extreme cylinder decagon diameter dodecahedron equiangular equilateral Eucl Euclid extreme and mean greater segment height Hence icosahedron inscribed irrational straight line Lemma let the square magnitudes mean ratio measure medial area medial straight line medial whole parallelepipedal solid parallelogram pentagon perpendicular plane of reference polygon prism Proposition proved ratio triplicate rational and incommensurable rational area rational straight line rectangle AC rectangle contained right angles second apotome side similar Similarly sixth binomial solid angle sphere square number square on AB squares on AC straight lines commensurable surable theorem triangle twice the rectangle vertex whence

### Popular passages

Page 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.

Page 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?

Page 260 - The inclination of a plane to a plane is the acute angle contained by two straight lines drawn from any the...

Page 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.

Page 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.

Page 389 - The upper end of the frustum of a pyramid or cone is called the upper base...

Page 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...

Page 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.

Page 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...

Page 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.