The Thirteen Books of Euclid's Elements, Volume 3

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The University Press, 1908 - Mathematics, Greek
 

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This book is missing pages 369-370

Contents

I
1
II
10
III
14
IV
95
V
96
VI
171
VII
172
VIII
247
IX
252
X
264
XI
351
XII
355
XIII
414
XIV
416

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Page 14 - 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. the
Page 254 - 4. A plane is at right angles to a plane when the straight lines drawn, in one of the planes, at right angles to the common section of the planes are at right angles to the remaining plane. 5. The inclination of a straight line to a plane is,
Page 14 - 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 magnitude C. For C if multiplied
Page 335 - Solid parallelepipeds contained by parallelograms equiangular to one another, each to each, that is, of which the solid angles are equal, each to each, have to one another the ratio compounded of the ratios of their sides. The
Page 297 - a plane is at right angles to a plane, when the straight lines drawn, in one of the planes, at right angles to the common section of the planes are at right angles to the remaining plane.
Page 28 - squares on straight lines incommensurable in length have not to one another the ratio which a square number has to a square number; and squares which have not to one another the ratio which a square number has to a square number will not have their sides commensurable in length either.
Page 289 - 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 to one another [xi. 6], which is absurd.
Page 254 - 6. The inclination of a plane to a plane is the acute angle contained by the straight lines drawn at right angles to the common section at the same point, one in each of the planes.
Page 26 - PROPOSITION 6. If two magnitudes have to one another the ratio which a number has to a number, the magnitudes will be commensurable. For let the two magnitudes A, B have to one another the ratio which the number D has to the number E
Page 26 - For let A be divided into as many equal parts as there are units in D, and let C be equal to one of them ; and let F be made up of as many magnitudes equal to C as

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