Posts tagged 'rectilineal-figure'
G.12 rectilineal figures
Rectilineal figures are contained by segments: trilateral by three, quadrilateral by four, and multilateral by more than four.
G.74 construct a parallelogram equal to a polygon
Construct, in a given angle, a parallelogram equal in area to a given polygon.
G.97 construct a square equal to a polygon
Construct a square equal in area to a given rectilineal figure.
G.148 polygon inscribed in a circle
A:term:polygon <G.12> is said to be:term:**inscribed in a circle** <inscribed-in-circle> when each:term:angle <G.22> of the inscribed:term:figure <G.9> lies on the arc of the:term:circle <G.10>.
G.150 polygon circumscribed about a circle
A:term:polygon <G.12> is said to be:term:**circumscribed about a circle** <circumscribed-about-circle>, when each side of the circumscribed:term:figure <G.9> touches the arc of the:term:circle <G.10>.
G.152 polygon inscribed in a polygon
A:term:polygon <G.12> is said to be:term:**inscribed in a polygon** <inscribed-in-rectilineal-figure> when the respective:term:angles <G.22> of the inscribed:term:figure <G.9> lie on the respective sides of that in which it is inscribed.
G.229 describe on a given segment a rectilinear figure
Describe on a given segment a rectilinear figure similar and similarly situated to a given rectilinear figure.
G.233 figures similar polygon
Figures which are similar to the same polygon are also similar to one another.
G.234 segments proportional polygons
If four segments be proportional, the polygons similar and similarly described upon them is proportional; and, if the polygons similar and similarly described upon them be proportional, the segments will themselves also be proportional.
G.237 construct one and the same figure similar to
Construct one and the same figure similar to a given polygon and equal to another given polygon.
G.240 segment apply parallelogram
To a given segment to apply a parallelogram equal to a given polygon and deficient by a parallelogrammic figure similar to a given one: thus the given polygon must not be greater than the parallelogram described on the half of the segment and similar to the defect.
G.241 segment apply parallelogram
To a given segment to apply a parallelogram equal to a given polygon and exceeding by a parallelogrammic figure similar to a given one.
G.392 rational and irrational areas
And let the:term:square <G.63> on the assigned:term:segment <G.4> be called:term:**rational** <rational> and those areas which are:term:commensurable <G.372> with it:term:**rational** <rational>, but those which are incommensurable with it:term:**irrational** <G.391>, and the segments which produce them:term:**irrational** <G.391>, that is, in case the areas are squares, the sides themselves, but in case they are any other:term:polygons <G.12>, the segments on which are described squares equal to them.