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Source — Euclid's Elements, encoded as an rrxiv paper — rrxiv
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Euclid's Elements, encoded as an rrxiv paper
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Source —
Euclid's Elements, encoded as an rrxiv paper
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I.7
Proposition I.7
Given two straight lines constructed on a straight line and meeting in a point, there…
I.8
Proposition I.8
If two triangles have the two sides equal to two sides respectively, and have also the…
I.9
Proposition I.9
To bisect a given rectilineal angle.
I.10
Proposition I.10
To bisect a given finite straight line.
I.11
Proposition I.11
To draw a straight line at right angles to a given straight line from a given point on it.
I.12
Proposition I.12
To draw a perpendicular straight line to a given infinite straight line from a given…
I.13
Proposition I.13
If a straight line set up on a straight line make angles, it will make either two right…
I.14
Proposition I.14
If with any straight line, and at a point on it, two straight lines not lying on the same…
I.15
Proposition I.15
If two straight lines cut one another, they make the vertical angles equal to one another.
I.16
Proposition I.16
In any triangle, if one of the sides be produced, the exterior angle is greater than…
I.17
Proposition I.17
In any triangle two angles taken together in any manner are less than two right angles.
I.18
Proposition I.18
In any triangle the greater side subtends the greater angle.
I.19
Proposition I.19
In any triangle the greater angle is subtended by the greater side.
I.20
Proposition I.20
In any triangle two sides taken together in any manner are greater than the remaining one.
I.21
Proposition I.21
If on one of the sides of a triangle, from its extremities, there be constructed two…
I.22
Proposition I.22
Out of three straight lines, which are equal to three given straight lines, to construct…
I.23
Proposition I.23
On a given straight line and at a point on it to construct a rectilineal angle equal to a…
I.24
Proposition I.24
If two triangles have the two sides equal to two sides respectively, but have the one of…
I.25
Proposition I.25
If two triangles have the two sides equal to two sides respectively, but have the one…
I.26
Proposition I.26
If two triangles have the two angles equal to two angles respectively, and one side equal…
I.27
Proposition I.27
If a straight line falling on two straight lines make the alternate angles equal to one…
I.28
Proposition I.28
If a straight line falling on two straight lines make the exterior angle equal to the…
I.29
Proposition I.29
A straight line falling on parallel straight lines makes the alternate angles equal to…
I.30
Proposition I.30
Straight lines parallel to the same straight line are also parallel to one another.
I.31
Proposition I.31
Through a given point to draw a straight line parallel to a given straight line.
I.32
Proposition I.32
In any triangle, if one of the sides be produced, the exterior angle is equal to the two…
I.33
Proposition I.33
The straight lines joining equal and parallel straight lines (at the extremities which…
I.34
Proposition I.34
In parallelogrammic areas the opposite sides and angles are equal to one another, and the…
I.35
Proposition I.35
Parallelograms which are on the same base and in the same parallels are equal to one…
I.36
Proposition I.36
Parallelograms which are on equal bases and in the same parallels are equal to one…
I.37
Proposition I.37
Triangles which are on the same base and in the same parallels are equal to one another.
I.38
Proposition I.38
Triangles which are on equal bases and in the same parallels are equal to one another.
I.39
Proposition I.39
Equal triangles which are on the same base and on the same side are also in the same…
I.40
Proposition I.40
Equal triangles which are on equal bases and on the same side are also in the same…
I.41
Proposition I.41
If a parallelogram have the same base with a triangle and be in the same parallels, the…
I.42
Proposition I.42
To construct, in a given rectilineal angle, a parallelogram equal to a given triangle.
I.43
Proposition I.43
In any parallelogram the complements of the parallelograms about the diameter are equal…
I.44
Proposition I.44
To a given straight line to apply, in a given rectilineal angle, a parallelogram equal to…
I.45
Proposition I.45
To construct, in a given rectilineal angle, a parallelogram equal to a given rectilineal…
I.46
Proposition I.46
On a given straight line to describe a square.
I.47
Proposition I.47
In right-angled triangles the square on the side subtending the right angle is equal to…
I.48
Proposition I.48
If in a triangle the square on one of the sides be equal to the squares on the remaining…
II.1
Proposition II.1
If there be two straight lines, and one of them be cut into any number of segments…
II.2
Proposition II.2
If a straight line be cut at random, the rectangle contained by the whole and both of the…
II.3
Proposition II.3
If a straight line be cut at random, the rectangle contained by the whole and one of the…
II.4
Proposition II.4
If a straight line be cut at random, the square on the whole is equal to the squares on…
II.5
Proposition II.5
If a straight line be cut into equal and unequal segments, the rectangle contained by the…
II.6
Proposition II.6
If a straight line be bisected and a straight line be added to it in a straight line, the…
II.7
Proposition II.7
If a straight line be cut at random, the square on the whole and that on one of the…
II.8
Proposition II.8
If a straight line be cut at random, four times the rectangle contained by the whole and…
II.9
Proposition II.9
If a straight line be cut into equal and unequal segments, the squares on the unequal…
II.10
Proposition II.10
If a straight line be bisected and a straight line be added to it in a straight line, the…
II.11
Proposition II.11
To cut a given straight line so that the rectangle contained by the whole and one of the…
II.12
Proposition II.12
In obtuse-angled triangles the square on the side subtending the obtuse angle is greater…
II.13
Proposition II.13
In acute-angled triangles the square on the side subtending the acute angle is less than…
II.14
Proposition II.14
To construct a square equal to a given rectilineal figure.
III.1
Proposition III.1
To find the centre of a given circle.
III.2
Proposition III.2
If on the circumference of a circle two points be taken at random, the straight line…
III.3
Proposition III.3
If in a circle a straight line through the centre bisect a straight line not through the…
III.4
Proposition III.4
If in a circle two straight lines cut one another which are not through the centre, they…
III.5
Proposition III.5
If two circles cut one another, they will not have the same centre.
III.6
Proposition III.6
If two circles touch one another, they will not have the same centre.
III.7
Proposition III.7
If on the diameter of a circle a point be taken which is not the centre, and from the…
III.8
Proposition III.8
If a point be taken outside a circle and from the point straight lines be drawn through…
III.9
Proposition III.9
If a point be taken within a circle, and more than two equal straight lines fall from the…
III.10
Proposition III.10
A circle does not cut a circle at more points than two.
III.11
Proposition III.11
If two circles touch one another internally, and their centres be taken, the straight…
III.12
Proposition III.12
If two circles touch one another externally, the straight line joining their centres will…
III.13
Proposition III.13
A circle does not touch a circle at more points than one, whether it touch it internally…
III.14
Proposition III.14
In a circle equal straight lines are equally distant from the centre, and those which are…
III.15
Proposition III.15
Of straight lines in a circle the diameter is greatest, and of the rest the nearer to the…
III.16
Proposition III.16
The straight line drawn at right angles to the diameter of a circle from its extremity…
III.17
Proposition III.17
From a given point to draw a straight line touching a given circle.
III.18
Proposition III.18
If a straight line touch a circle, and a straight line be joined from the centre to the…
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