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Required by (dependents) (26)
- I.1Proposition I.1On a given finite straight line to construct an equilateral triangle.
- I.2Proposition I.2To place at a given point (as an extremity) a straight line equal to a given straight line.
- I.3Proposition I.3Given two unequal straight lines, to cut off from the greater a straight line equal to the less.
- III.1Proposition III.1To find the centre of a given circle.
- III.2Proposition III.2If on the circumference of a circle two points be taken at random, the straight line joining the points will fall…
- III.3Proposition III.3If in a circle a straight line through the centre bisect a straight line not through the centre, it also cuts it at…
- III.5Proposition III.5If two circles cut one another, they will not have the same centre.
- III.6Proposition III.6If two circles touch one another, they will not have the same centre.
- III.7Proposition III.7If on the diameter of a circle a point be taken which is not the centre, and from the point straight lines fall upon…
- III.8Proposition III.8If a point be taken outside a circle and from the point straight lines be drawn through to the circle, one of which is…
- III.9Proposition III.9If a point be taken within a circle, and more than two equal straight lines fall from the point on the circle, the…
- III.11Proposition III.11If two circles touch one another internally, and their centres be taken, the straight line joining their centres, if…
- III.17Proposition III.17From a given point to draw a straight line touching a given circle.
- III.18Proposition III.18If a straight line touch a circle, and a straight line be joined from the centre to the point of contact, the straight…
- III.20Proposition III.20In a circle the angle at the centre is double of the angle at the circumference, when the angles have the same…
- III.25Proposition III.25Given a segment of a circle, to describe the complete circle of which it is a segment.
- III.26Proposition III.26In equal circles equal angles stand on equal circumferences, whether they stand at the centres or at the circumferences.
- III.31Proposition III.31In a circle the angle in the semicircle is right, that in a greater segment less than a right angle, and that in a less…
- III.35Proposition III.35If in a circle two straight lines cut one another, the rectangle contained by the segments of the one is equal to the…
- III.36Proposition III.36If a point be taken outside a circle and from it there fall on the circle two straight lines, and if one of them cut…
- IV.1Proposition IV.1Into a given circle to fit a straight line equal to a given straight line which is not greater than the diameter of the…
- IV.5Proposition IV.5About a given triangle to circumscribe a circle.
- IV.6Proposition IV.6In a given circle to inscribe a square.
- IV.9Proposition IV.9About a given square to circumscribe a circle.
- IV.14Proposition IV.14About a given pentagon, which is equilateral and equiangular, to circumscribe a circle.
- IV.15Proposition IV.15In a given circle to inscribe an equilateral and equiangular hexagon.
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