Petersen-Shoute Theorem
- 1. If
and 
are two directly similar triangles, while 
, 
, and
are three directly similar triangles, then 
is directly similar to . - 2. When all the points
on 
are related by a Similarity Transformation to all the points 
on 
,the points dividing the segment 
in a given ratio are distant and collinear, or else they coincide.
References
Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 95-100, 1967.
- Sturmian Separation Theorem
- Sturmian Sequence
- Sturm-Liouville Equation
- Sturm-Liouville Theory
- Sturm Theorem
- Stäckel Determinant
- Stérmer Number
- Stöhr Sequence
- Subalgebra
- Subanalytic
- Subfactorial
- Subfield
- Subgraph
- Subgroup
- Sublime Number
- Submanifold
- Submatrix
- Subnormal
- Subordinate Norm
- Subscript
- Subsequence
- Subset
- Subspace
- Substitution Group
- Substitution Map