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Required by (dependents) (27)
- I.5Proposition I.5In isosceles triangles the angles at the base are equal to one another; and if the equal straight lines be produced…
- I.15Proposition I.15If two straight lines cut one another, they make the vertical angles equal to one another.
- I.35Proposition I.35Parallelograms which are on the same base and in the same parallels are equal to one another.
- I.43Proposition I.43In any parallelogram the complements of the parallelograms about the diameter are equal to one another.
- II.7Proposition II.7If a straight line be cut at random, the square on the whole and that on one of the segments both together are equal to…
- II.8Proposition II.8If a straight line be cut at random, four times the rectangle contained by the whole and one of the segments together…
- II.9Proposition II.9If a straight line be cut into equal and unequal segments, the squares on the unequal segments of the whole are double…
- II.10Proposition II.10If a straight line be bisected and a straight line be added to it in a straight line, the square on the whole with the…
- II.11Proposition II.11To cut a given straight line so that the rectangle contained by the whole and one of the segments is equal to the…
- II.13Proposition II.13In acute-angled triangles the square on the side subtending the acute angle is less than the squares on the sides…
- II.14Proposition II.14To construct a square equal to a given rectilineal figure.
- III.14Proposition III.14In a circle equal straight lines are equally distant from the centre, and those which are equally distant from the…
- 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.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.32Proposition III.32If a straight line touch a circle, and from the point of contact there be drawn across, in the circle, a straight line…
- V.5Proposition V.5If a magnitude be the same multiple of a magnitude that a subtracted part is of a subtracted part, the remainder also…
- V.6Proposition V.6If two magnitudes be equimultiples of two magnitudes, and any magnitudes subtracted from them be equimultiples of the…
- VII.7Proposition VII.7If a number be the same part of a number that a subtracted number is of a subtracted number, the remainder will also be…
- VII.28Proposition VII.28If two numbers be prime to one another, the sum will also be prime to each of them; and if the sum of two numbers be…
- VII.35Proposition VII.35If two numbers measure any number, the least number measured by them will also measure the same.
- IX.20Proposition IX.20Prime numbers are more than any assigned multitude of prime numbers.
- IX.24Proposition IX.24If from an even number an even number be subtracted, the remainder will be even.
- IX.25Proposition IX.25If from an even number an odd number be subtracted, the remainder will be odd.
- IX.26Proposition IX.26If from an odd number an odd number be subtracted, the remainder will be even.
- IX.27Proposition IX.27If from an odd number an even number be subtracted, the remainder will be odd.
- X.2Proposition X.2If, when the lesser of two unequal magnitudes is continually subtracted in turn from the greater, that which is left…
- X.15Proposition X.15If two commensurable magnitudes be added together, the whole will also be commensurable with each of them; and if the…
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