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Required by (dependents) (29)
- I.13Proposition I.13If a straight line set up on a straight line make angles, it will make either two right angles or angles equal to two…
- I.32Proposition I.32In any triangle, if one of the sides be produced, the exterior angle is equal to the two interior and opposite angles,…
- I.34Proposition I.34In parallelogrammic areas the opposite sides and angles are equal to one another, and the diameter bisects the areas.
- I.35Proposition I.35Parallelograms which are on the same base and in the same parallels are equal to one another.
- I.41Proposition I.41If a parallelogram have the same base with a triangle and be in the same parallels, the parallelogram is double of the…
- I.43Proposition I.43In any parallelogram the complements of the parallelograms about the diameter are equal to one another.
- I.45Proposition I.45To construct, in a given rectilineal angle, a parallelogram equal to a given rectilineal figure.
- I.47Proposition I.47In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides…
- II.1Proposition II.1If there be two straight lines, and one of them be cut into any number of segments whatever, the rectangle contained by…
- II.2Proposition II.2If a straight line be cut at random, the rectangle contained by the whole and both of the segments is equal to the…
- II.3Proposition II.3If a straight line be cut at random, the rectangle contained by the whole and one of the segments is equal to the…
- II.4Proposition II.4If a straight line be cut at random, the square on the whole is equal to the squares on the segments and twice the…
- II.5Proposition II.5If a straight line be cut into equal and unequal segments, the rectangle contained by the unequal segments of the whole…
- II.6Proposition II.6If a straight line be bisected and a straight line be added to it in a straight line, the rectangle contained by the…
- 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.12Proposition II.12In obtuse-angled triangles the square on the side subtending the obtuse angle is greater than the squares on the sides…
- 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.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.22Proposition III.22The opposite angles of quadrilaterals in circles are equal to two right angles.
- 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…
- V.1Proposition V.1If there be any number of magnitudes whatever which are, respectively, equimultiples of any magnitudes equal in…
- V.2Proposition V.2If a first magnitude be the same multiple of a second that a third is of a fourth, and a fifth also be the same…
- VII.5Proposition VII.5If a number be a part of a number, and another be the same part of another, the sum will also be the same part of the…
- IX.21Proposition IX.21If as many even numbers as we please be added together, the whole is even.
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