Principles of geometry: Higher geometry

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Multivolume work

Persistent identifier:: 1922041386

Title:: Dictionnaire De L'Académie Française

Type of content:: Wörterbuch

Year of publication:: 1835

Place of publication:: Paris; Hannover

Identifier (digital):: 1922041386

Language:: French

Additional Notes:: Bände 1-2, Complément und Supplement erschienen von 1835-1842

Publisher of the original:: Imprimerie et Librairie de Firmin Didot Frères, Imprimeurs de l'Institut de France.

Printer:: Firmin-Didot, Ambroise

Publisher of the digital copy:: Technische Informationsbibliothek (TIB)

Document type:: Multivolume work

Volume

Persistent identifier:: 192204766X

Title:: Complément De Tous Les Dictionnaires Français, Anciens Et Modernes, Renfermant Cinq ou Six Mille Mots De Plus Qu'Aucun Dictionnaire De La Langue Française Publié Jusqu'a Ce Jour, Tous Reconnus Et Adoptés Par les Savants, Ou Consacrés Par L'Usage

Scope:: XII, 861 Seiten

Type of content:: Wörterbuch

Edition title:: Sixième Édition publiée en 1835

DOI:: 10.14463/KXP:192204766X

Year of publication:: 1836

Place of publication:: Paris

Identifier (digital):: 192204766X

Illustration:: Illustrationen

Signature of the source:: a 3844(Suppl.),6

Language:: French

Publisher of the original:: A La Librairie de Gustave Barba

Usage licence:: Public Domain Mark 1.0

Contributor:: Raymond, François

Publisher of the digital copy:: Technische Informationsbibliothek (TIB)

Place of publication of the digital copy:: Hannover

Year of publication of the original:: 2025

Document type:: Volume

Collection:: General; Literature and language

Section

Title:: M

Document type:: Multivolume work

Structure type:: Section

Contents xi PAGES PAGES Ex. 1. The section oj Veronese’s surface by a fourfold space. 54 25, 26 Ex. 2. The representation in fivefold space of the conics of a plane 54 26 Ex. 3. Statement of some properties of Veronese’s surface . 54, 55 26, 27 Lie’s correspondence between lines and spheres in space of three 28 dimensions .......... 55, 56 28 Ex. 1. Algebraic formulation of the correspondence 56, 57 28 Ex. 2. Comparison with deduction of sphere from fourfold space . 57 28, 29 Ex. 3. The eight pairs of spheres which touch four spheres . 57, 58 29 Ex. 4. The eight spheres touching four planes .... 58 Ex. 5. The double-six theorem expressed in terms of spheres 58 29—31 Generalisation of Wallace’s theorem. The theorem of the double- six. A theorem for six lines with a common transversal 58- -60 31, 32 Exx. 1—5. Proofs of the theorems ...... 60- -64 32 Note. Another proof of Wallace’s theorem, and extensions 64 32—40 CHAPTER II. HART’S THEOREM, FOR CIRCLES IN 32—34 34 A PLANE, OR FOR SECTIONS OF A QUADRIC 34, 35 The sections of a quadric which touch three given sections . 65, 66 35, 36 Ex. 1. A pair of variable sections of a quadric touching one another 36—38 and two fixed sections ........ 66 38 Ex. 2. Construction of the circles touching three given circles 66 38, 39 Ex. 3. A theorem for circles through threes of four special points . 66, 67 39, 40 Ex. 4. Circles cutting three given circles at equal angles 67 40—64 Ex. 5. Circles cutting four given circles at equal angles 67 Ex. 6. Circles cutting three given circles at given angles 67 40—42 Ex. 7. Common tangents, of three circles, which meet in a point . 67, 68 42 Ex. 8. Solution of generalised Malfatti’s problem.... 68, 69 42 Ex. 9. Equations of sections touching three sections of a quadric . 69, 70 42, 43 Exx. 10—15. Various algebraic results ..... 70, 71 43, 44 The Hart circles of three circles when the four have a common orthogonal circle ......... 71, 72 44, 45 The Hart circles of three circles in general ..... 72- 75 45—47 Ex. 1. The various cases ........ 75 47, 48 Ex. 2. The point of contact of the Hart section .... 75, 76 Ex. 3. The bipolar character of the figure obtained 76, 77 48 Ex. 4. Eight sections divided into four pairs .... 77 Ex. 5. Relations with metrical geometry ..... 78 48, 49 Ex. 6. The particular case of the Feuerbach circle 78- -80 49, 50 Ex. 7. The same Hart section arises in different ways . 80 50, 51 Ex. 8. The radius of the Hart section. ..... 80, 81 51 Ex. 9. Four circles arising from the intersections of three circles . 82 The bifocal property is necessary as well as sufficient . 82- -85 52—54 Ex. 1. A particular form of the equation of the quadric 85, 86

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