I.46
On a given straight line to describe a square.
Posts in category 'describe'
XI.37
If four straight lines be proportional, the parallelepipedal solids on them which are similar and similarly described will also be proportional; and, if the parallelepipedal solids on them which are similar and similarly described be proportional, the straight lines will themselves also be proportional.
XI.27
On a given straight line to describe a parallelepipedal solid similar and similarly situated to a given parallelepipedal solid.
III.33
On a given straight line to describe a segment of a circle admitting an angle equal to a given rectilineal angle.
III.25
Given a segment of a circle, to describe the complete circle of which it is a segment.
VI.31
In right-angled triangles the figure on the side subtending the right angle is equal to the similar and similarly described figures on the sides containing the right angle.
VI.28
To a given straight line to apply a parallelogram equal to a given rectilineal figure and deficient by a parallelogrammic figure similar to a given one : thus the given rectilineal figure must not be greater than the parallelogram described on the half of the straight line and similar to the defect.
VI.27
Of all the parallelograms applied to the same straight line and deficient by parallelogrammic figures similar and similarly situated to that described on the half of the straight line, that parallelogram is greatest which is applied to the half of the straight line and is similar to the defect.
VI.22
If four straight lines be proportional, the rectilineal figures similar and similarly described upon them will also be proportional; and, if the rectilineal figures similar and similarly described upon them be proportional, the straight lines will themselves also be proportional.
I.post.3
To describe a circle with any centre and distance.
VI.18
On a given straight line to describe a rectilineal figure similar and similarly situated to a given rectilineal figure.
XI.def.23
And the bases are the circles described by the two sides opposite to one another which are carried round.
XI.def.20
And the base is the circle described by the straight line which is carried round.
II.10
If a straight line be bisected, and a straight line be added to it in a straight line, the square on the whole with the added straight line and the square on the added straight line both together are double of the square on the half and of the square described on the straight line made up of the half and the added straight line as on one straight line.
II.8
If a straight line be cut at random, four times the rectangle contained by the whole and one of the segments together with the square on the remaining segment is equal to the square described on the whole and the aforesaid segment as on one straight line.
X.def.4
And let the square on the assigned straight line be called rational and those areas which are commensurable with it rational, but those which are incommensurable with it irrational, and the straight lines which produce them irrational, that is, in case the areas are squares, the sides themselves, but in case they are any other rectilineal figures, the straight lines on which are described squares equal to them.