I.45
To construct, in a given rectilineal angle, a parallelogram equal to a given rectilineal figure.
Posts in category 'construct'
I.42
To construct, in a given rectilineal angle, a parallelogram equal to a given triangle.
I.23
On a given straight line and at a point on it to construct a rectilineal angle equal to a given rectilineal angle.
I.22
Out of three straight lines, which are equal to three given straight lines, to construct a triangle: thus it is necessary that two of the straight lines taken together in any manner should be greater than the remaining one.
I.21
If on one of the sides of a triangle, from its extremities, there be constructed two straight lines meeting within the triangle, the straight lines so constructed will be less than the remaining two sides of the triangle, but will contain a greater angle.
XI.26
On a given straight line, and at a given point on it, to construct a solid angle equal to a given solid angle.
XI.23
To construct a solid angle out of three plane angles two of which, taken together in any manner, are greater than the remaining one: thus the three angles must be less than four right angles.
XI.22
If there be three plane angles of which two, taken together in any manner, are greater than the remaining one, and they are contained by equal straight lines, it is possible to construct a triangle out of the straight lines joining the extremities of the equal straight lines.
I.7
Given two straight lines constructed on a straight line (from its extremities) and meeting in a point, there cannot be constructed on the same straight line (from its extremities), and on the same side of it, two other straight lines meeting in another point and equal to the former two respectively, namely each to that which has the same extremity with it.
III.23
On the same straight line there cannot be constructed two similar and unequal segments of circles on the same side.
I.1
On a given finite straight line to construct an equilateral triangle.
VI.25
To construct one and the same figure similar to a given rectilineal figure and equal to another given rectilineal figure.
IV.10
To construct an isosceles triangle having each of the angles at the base double of the remaining one.
XIII.17
To construct a dodecahedron and comprehend it in a sphere, like the aforesaid figures, and to prove that the side of the dodecahedron is the irrational straight line called apotome.
II.14
To construct a square equal to a given rectilineal figure.
XIII.16
To construct an icosahedron and comprehend it in a sphere, like the aforesaid figures; and to prove that the side of the icosahedron is the irrational straight line called minor.
XIII.15
To construct a cube and comprehend it in a sphere, like the pyramid; and to prove that the square on the diameter of the sphere is triple of the square on the side of the cube.
XIII.14
To construct an octahedron and comprehend it in a sphere, as in the preceding case; and to prove that the square on the diameter of the sphere is double of the square on the side of the octahedron.
XIII.13
To construct a pyramid, to comprehend it in a given sphere, and to prove that the square on the diameter of the sphere is one and a half times the square on the side of the pyramid.
XI.def.12
A pyramid is a solid figure, contained by planes, which is constructed from one plane to one point.
III.def.10
A sector of a circle is the figure which, when an angle is constructed at the centre of the circle, is contained by the straight lines containing the angle and the circumference cut off by them.