Many of Poncelet's ideas in projective geometry were futther developed
gy the Swiss geometer Jacob Steiner, one of the greatest synthetic geometers
the world has ever known. Steiner was born at Utzensdorf in 1796 and did not
learn to write until he was fourteen. At seventeen, he became a pupil of johann
Heinrich Pestalozzi (1746-1827), the famous Swiss educator, who instilled in the boy a love for mathematics. Later, in 1818, Steiner matriculated at Heidelberg,
where he quickly exhibited his ability in mathematics.
In 1821, he started
giving private lessons in mathematics in Berlin, and soon was appointed a
teacher in the Gewerbeakademi.
His name became well known through his
articles published in the niwly founded Crelle's Journal; he and Abel were
leading contributors to the journal. In 1834, throuhg the influence of Jacobi,
Crelle, and von Humbolt, a chair was founded for him at the University of
Berlin, where he remained for the rest of his teaching career His final years
were spent in poor health in Switzerland. He died at Bern in 1863.
described as "the greatest geometrician since the time of Apollonius,"
Steiner possessed incredible power in the synthetic treatment of geometry. He
became a prolific contributor in the field and wrote a number of treatises of the
highest rank. It is said that he loathed the analytical method in geometry,
regarding it as a crutch for the geometrically feeble-minded. He created new
geometry at such a prodigious rate that often he had no time to record his
proofs, with the result that many of his findings remained for years as riddles to
those seeking demonstrations. His Systematische Entwicklungen, published in
1832, immediately made his reputation. This work contains a complete discussion
of reciprocation, the principle of duality, homothetic ranges and pencils,
harmonic division, and the projective geometry of the conic sections based
upon the highly fruitful definition of a conic as the locus of the points of
intersection of corresponding lines of two homographic pencils with distinct
vertices. He contributed to the study of the n-gon in space, the theory of curves
and surfaces, pedal curves, foulettes, and the twenty-seven straight lines on a
surface of the third order. He attacked by synthetic geometry problems in
maxima and minima that in the hands of others required the paraphernalia of
the calculus of variations. His name in met in many places in geometry, as in
the Steiner solution and generalization of the Malfattl problem, Steiner chains,
Steiner's porism, and the Steiner points of the mystic hexagram configuration.