Death and grieving
Owing to his poor health, Klingenstierna had to give up his position at court in 1764. Even though he was bedridden for long periods of that year, he did not abandon mathematics, especially not geometry. There are many manuscripts preserved in which he attempts to restore theorems that were assumed to have been included in one of Euclid's missing, but talked about books, Porism. A ”definitive” reconstruction of the book was carried out in 1860 by Michel Chasles.
Klingenstierna died on October 26, 1765.
”In the evening when he was about to sit down at the table with his beloved daughters, he cried out, invoked the name of Jesus, his Saviour, and fell into the arms of his elder daughter, who had run to his aid, whereupon this precious and rare life was already ended.”
Porism is a book of geometry that according to ancient Greek sources comprised 171 theorems and 38 corollaries. A corollary is an auxiliary theorem that is needed to prove another ”higher” theorem.
Strömer's commemorative address
Every member of the Royal Swedish Academy of Sciences was to have a commemorative address delivered at a meeting of the Academy after his death. Normally, as in the case of Klingenstierna, it was a close friend that delivered the speech. The address was then published in print by the Academy. To facilitate the composition of these speeches, each member was asked to write his autobiography. We do not know whether Klingenstierna had written one.
The grave of a giant
Queen Lovisa Ulrika showed her gratitude to her son Gustaf's tutors, Olof von Dalin and Samuel Klingenstierna, by erecting an enormous stone column over the two men's graves in 1769. It stands at Lovö Church close to Drottningholm Palace.
An attempt at an Opera Omnia
In the manuscripts Klingenstierna left behind, only mathematical problems are treated, some with applications in physics. They comprise several thousand pages, the overwhelming majority of them written in Latin. These were cataloged by his student Fredric Mallet, who planned to publish them in an Opera Omnia, that is, as Klingenstierna's collected works. As a result of war with Russia, however, there was no money for the printing. In Mallet's catalog, according to a plan from 1788, they are divided into ten main groups, including geometry, algebra, integral computation, differential equations, statistics, mechanics, and optics. These, in turn, are divided into subgroups (a total of 292), each of which contains one or sometimes several propositions in mathematics or physics. The great majority of Klingenstierna's remaining manuscripts are preserved today in the manuscript collection at Uppsala University Library.
Klingenstierna's manuscripts divided into 10 main groups with a total of 292 subgroups with Mallet's categories:
- Geometrica (geometry) G. 1 – 67
- Algebraica (algebra) Alg. 1 – 22
- De Serierum Summatione (on series sums) S.1 – 27
- De Fluentium inventione ex data relatione (on integral computation) F. 1 – 21
- De Æquationibus Fluxionum (on differential equations) N. 1 – 33
- De Mensura Sortis (on statistics and probability) P. 1 – 8
- Mechanica et Physica (mechanics and physics) M. 1 – 41
- De Resistensia Fluidorum (on the resistance of liquids) R. 1 – 8
- Optica et Dioptrica (optics and dioptrics) D. 1 – 58
- Miscellanea (miscellaneous problems) M. 1 – 6