Euclid's Elements - Book 1 - Proposition 22
Out of three straight lines, which are equal to three given straight lines, to construct a triangle: thus it is necessary that two of the straight lines taken together in any manner should be greater than the remaining one.
In other words, when you construct a triangle, the sum of any two sides must be greater than the remaining one.
Steps:
1. Given three straight lines, A, B, and C where the sum of any two are greater than the remaining one.
2. Construct a ray DE of sufficient length such that its length is greater than the sum of A, B, and C.
3. Define a point F such that DF is equal in length to A (I.3).
4. Define a point G such that FG is equal in length to B (I.3).
5. Define a point H such that GH is equal in length to C (I.3).
6. Draw a circle with center F, and radius DF.
7. Draw a circle with center G, and radius GH.
8. Draw point K where two circles intersect.
9. From the intersection point K, construct two lines KF
10. and KG.
Therefore out of the three straight lines KF, FG, GK, which are equal to the three given straight lines A, B, C, the triangle KFG has been constructed.
Q.E.F.