# Books 10-13 and appendix (Google eBook)

The University Press, 1908 - Mathematics, Greek

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### Contents

 Definitions 260 Propositions 272 Historical note 365 Historical note 438
 The socalleD Book XIV by Hypsicles 512 AdDenda et Corrigenda 521 Greek 529 English 535

### 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.