LEADER 03018nam 22005295 450 001 9910484217103321 005 20200930134825.0 010 $a3-030-46287-0 024 7 $a10.1007/978-3-030-46287-1 035 $a(CKB)4100000011413814 035 $a(DE-He213)978-3-030-46287-1 035 $a(MiAaPQ)EBC6331628 035 $a(PPN)250222655 035 $a(EXLCZ)994100000011413814 100 $a20200901d2020 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aCollineations and Conic Sections $eAn Introduction to Projective Geometry in its History /$fby Christopher Baltus 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (XI, 187 p.) 311 $a3-030-46286-2 320 $aIncludes bibliographical references and index. 327 $aPreface -- 1. Introduction -- 2. Central Collineations -- 3. The Geometry of Euclid's Elements -- 4. Conics in Greek Geometry -- 5. Conic Sections in Early Modern Europe -- 6. Conic Sections in Early Modern Europe -- 7. Central Collineations -- 8. Nineteenth Century -- 9. Foci -- 10. Steiner. 11. Desargues and Involution -- 12. Looking Ahead -- 13. Matrices and Homogeneous Coordinates -- 14. Some Applications of Conics in History -- 15. Vertical Stretch and Isaac Newton's Conics -- 16. Three Appendices -- Bibliography. 330 $aThis volume combines an introduction to central collineations with an introduction to projective geometry, set in its historical context and aiming to provide the reader with a general history through the middle of the nineteenth century. Topics covered include but are not limited to: The Projective Plane and Central Collineations The Geometry of Euclid's Elements Conic Sections in Early Modern Europe Applications of Conics in History With rare exception, the only prior knowledge required is a background in high school geometry. As a proof-based treatment, this monograph will be of interest to those who enjoy logical thinking, and could also be used in a geometry course that emphasizes projective geometry. 606 $aProjective geometry 606 $aMathematics 606 $aHistory 606 $aProjective Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21050 606 $aHistory of Mathematical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M23009 615 0$aProjective geometry. 615 0$aMathematics. 615 0$aHistory. 615 14$aProjective Geometry. 615 24$aHistory of Mathematical Sciences. 676 $a516.5 700 $aBaltus$b Christopher$4aut$4http://id.loc.gov/vocabulary/relators/aut$0879371 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910484217103321 996 $aCollineations and Conic Sections$91963628 997 $aUNINA