Book 11
26
And, since the two sides KA, AB are equal to the two sides GD, DE respectively, and they contain equal angles, therefore the base KB is equal to the base GE. [I. 4]
26
But KH is also equal to GF, and they contain right angles; therefore HB is also equal to FE. [I. 4]
26
Again, since the two sides AK, KH are equal to the two sides DG, GF, and they contain right angles, therefore the base AH is equal to the base FD. [I. 4]
26
But AB is also equal to DE; therefore the two sides HA, AB are equal to the two sides DF, DE.
26
And the base HB is equal to the base FE; therefore the angle BAH is equal to the angle EDF. [I. 8]
26
For the same reason the angle HAL is also equal to the angle FDC.
26
And the angle BAL is also equal to the angle EDC.
26
Therefore on the straight line AB, and at the point A on it, a solid angle has been constructed equal to the given solid angle at D. Q. E. F.
PROPOSITION 27.
27
On a given straight line to describe a parallelepipedal solid similar and similarly situated to a given parallelepipedal solid.
27
Let AB be the given straight line and CD the given parallelepipedal solid; thus it is required to describe on the given straight line AB a parallelepipedal solid similar and similarly situated to the given parallelepipedal solid CD.
