Proposition Replicated
Proposition I.4
If two triangles have two sides equal to two sides respectively, and have the angles contained by the equal straight lines equal, then they will also have the base equal to the base, the triangle will be equal to the triangle, and the remaining angles will be equal to the remaining angles respectively.
01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:I.4
Euclid's Elements, encoded as an rrxiv paper
Blaise Albis-Burdige \and Claude \\
\small {(translation after Heath, 1908; encoding new, CC-BY-4.0)}·2605.00009·math.HO, math.MG, math.NT
Neighborhood at a glance
Full neighborhood
Required by (dependents) (25)
- 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.6Proposition I.6If in a triangle two angles are equal to one another, the sides which subtend the equal angles will also be equal to…
- I.10Proposition I.10To bisect a given finite straight line.
- I.16Proposition I.16In any triangle, if one of the sides be produced, the exterior angle is greater than either of the interior and…
- I.24Proposition I.24If two triangles have the two sides equal to two sides respectively, but have the one of the angles contained by the…
- I.25Proposition I.25If two triangles have the two sides equal to two sides respectively, but have the one base greater than the other, they…
- I.26Proposition I.26If two triangles have the two angles equal to two angles respectively, and one side equal to one side, namely either…
- I.33Proposition I.33The straight lines joining equal and parallel straight lines (at the extremities which are in the same directions) are…
- I.35Proposition I.35Parallelograms which are on the same base and in the same parallels are equal to one another.
- I.47Proposition I.47In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides…
- 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.17Proposition III.17From a given point to draw a straight line touching a given circle.
- III.24Proposition III.24Similar segments of circles on equal straight lines are equal to one another.
- III.26Proposition III.26In equal circles equal angles stand on equal circumferences, whether they stand at the centres or at the circumferences.
- III.29Proposition III.29In equal circles equal circumferences are subtended by equal straight lines.
- III.30Proposition III.30To bisect a given arc.
- IV.5Proposition IV.5About a given triangle to circumscribe a circle.
- IV.6Proposition IV.6In a given circle to inscribe a square.
- IV.12Proposition IV.12About a given circle to circumscribe an equilateral and equiangular pentagon.
- IV.13Proposition IV.13In a given pentagon, which is equilateral and equiangular, to inscribe a circle.
- IV.14Proposition IV.14About a given pentagon, which is equilateral and equiangular, to circumscribe a circle.
- VI.6Proposition VI.6If two triangles have one angle equal to one angle and the sides about the equal angles proportional, the triangles…
- XI.4Proposition XI.4If a straight line be set up at right angles to two straight lines which cut one another, at their common point of…
- XI.20Proposition XI.20If a solid angle be contained by three plane angles, any two, taken together in any manner, are greater than the…
- XI.35Proposition XI.35If there be two equal plane angles, and on their vertices there be set up elevated straight lines containing equal…
Discussion
No replications, contradictions, or comments registered yet for this claim.