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2|Introduction|5
2|Applications diverses de la th&amp;#233;orie des pseudo-surfaces|7
2|Application I. La vraie g&amp;#233;n&amp;#232;se des formules de Lelieuvre|7
2|Application II. Extension aux pseudo-surfaces des formules de M. Darboux, comprenant celles de Lelieuvre|12
2|Application III. G&amp;#233;n&amp;#233;ralisation d'une expression gaussienne du rayon de courbure g&amp;#233;od&amp;#233;sique, d&amp;#251;e &amp;#224; O. Bonnet.|19
2|Application IV. Pseudo-surfaces et n&amp;#233;o-surfaces minima adjointes, g&amp;#233;n&amp;#233;ralisant les surfaces similaires d'O. Bonnet et de Schwarz|21
2|Application V. Th&amp;#233;or&amp;#232;me g&amp;#233;n&amp;#233;ral relatif &amp;#224; la &amp;quot;d&amp;#233;formation infiniment petite&amp;quot; d'une pseudo-surface|26
2|Application VI. Etude de la d&amp;#233;velopp&amp;#233;e optique d'une pseudo-surface|28
2|Application VII. Etude (corr&amp;#233;lative) de la d&amp;#233;velopp&amp;#233;e anoptique d'une pseudo-surface|33
2|Application VIII. De la variation totale ou partielle de l'angle des lignes coordonn&amp;#233;es, dans la g&amp;#233;n&amp;#233;ration des pseudo-surfaces ou des surfaces|38
2|Application IX. Exemple choisi o&amp;#249; les pseudo-surfaces mettent en d&amp;#233;faut une formule visuelle du calcul des variations|41
2|Application X. G&amp;#233;od&amp;#233;siques vraies et simili-g&amp;#233;od&amp;#233;siques d'une pseudo-surface. - Leur transformation commune en g&amp;#233;od&amp;#233;siques de surface|45
2|Application XI. Extension aux pseudo-surfaces du principe &amp;quot; de la moindre action&amp;quot;|49
2|Application XII. Retour &amp;#224; l'interpr&amp;#233;tation rationnelle des ph&amp;#233;nom&amp;#232;nes d'optique, au moyen des pseudo-surfaces|51
2|Appendice|55
1|Table des mati&amp;#232;res|59
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2|Introduction|5
2|Applications nouvelles de la th&amp;#233;orie des pseudo-surfaces|7
2|Application I. Condition du maximum et du minimum d'une int&amp;#233;grale d&amp;#233;finie tr&amp;#232;s g&amp;#233;n&amp;#233;rale, relevant des pseudo-surfaces|7
2|Application II. Sur l'orthogonalit&amp;#233; et l'&amp;#233;galit&amp;#233; des &amp;#233;l&amp;#233;ments lin&amp;#233;aires de deux pseudo-surfaces|12
2|Application III. Exemple de deux pseudo-surfaces transform&amp;#233;es en surfaces, avec orthogonalit&amp;#233; de leurs &amp;#233;l&amp;#233;ments lin&amp;#233;aires correspondants|16
2|Application IV. Autre exemple, analogue au pr&amp;#233;c&amp;#233;dent|19
2|Application V. Formes g&amp;#233;n&amp;#233;rales diverses des &amp;#233;quations qui d&amp;#233;finissent les ombilics d'une pseudo-surface|24
2|Application VI. De l'intersection de deux pseudo-surfaces, dans des conditions particuli&amp;#232;res donn&amp;#233;es|30
2|Application VII. Le pseudo-h&amp;#233;lico&amp;#239;de g&amp;#233;n&amp;#233;ral, successivement transform&amp;#233; en pseudo-surface minima et en pseudo-surface &amp;#224; courbure totale nulle|34
2|Application VIII. Points singuliers d'une pseudo-courbe|37
2|Application IX. Solutions g&amp;#233;n&amp;#233;ralis&amp;#233;es de quelques probl&amp;#232;mes classiques, d&amp;#233;pendant du calcul des variations|40
2|Application X. Interpr&amp;#233;tation g&amp;#233;om&amp;#233;trique et g&amp;#233;n&amp;#233;ralisation des &amp;#233;quations (dynamiques) de Lagrange, au moyen des pseudo-surfaces|45
2|Application XI. Retour &amp;#224; l'&amp;#233;l&amp;#233;ment lin&amp;#233;aire d'une pseudo-surface ou d'une surface|51
2|Application XII. Distance maximum ou minimum d'un point &amp;#224; une pseudo-surface|54
1|Table des mati&amp;#232;res|59
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2|III.|15
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2|VIII.|35
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2|XI. L'int&amp;#233;gration de l'&amp;#233;quation g&amp;#233;n&amp;#233;ralis&amp;#233;e de Monge-Amp&amp;#232;re, dans ses rapports avec les caract&amp;#233;ristiques et les semi-caract&amp;#233;ristiques d'une pseudo-surface|47
2|XII. Observations critiques diverses|50
2|Note sur un &amp;quot;th&amp;#233;or&amp;#232;me fondamental&amp;quot; relatif &amp;#224; l'int&amp;#233;gration d'un syst&amp;#232;me d'&amp;#233;quations diff&amp;#233;rentielles du premier ordre, et sur l'&amp;#233;quation int&amp;#233;grale de Freidholen|54
1|Table des mati&amp;#232;res|59
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                    <text>1|Les Probl&amp;#232;mes de Plateau, de Dirichlet, de Gauss, etc., et autres questions choisies, servant d'applications &amp;#224; la Th&amp;#233;orie des pseudo-surfaces : cinqui&amp;#232;me ouvrage (in&amp;#233;dit) de l'auteur sur les pseudo-surfaces|3
2|Ouvrages du m&amp;#234;me auteur sur les pseudo-surfaces|4
2|Introduction|5
2|Section I. Les probl&amp;#232;mes annonc&amp;#233;s|8
3|&amp;#167; I. Le probl&amp;#232;me de Plateau, g&amp;#233;n&amp;#233;ralis&amp;#233; et r&amp;#233;solu &amp;#224; l'aide des pseudo-surfaces minima|8
3|&amp;#167; II. Le probl&amp;#232;me de Derichlet, g&amp;#233;n&amp;#233;ralis&amp;#233; et r&amp;#233;solu &amp;#224; l'aide des pseudo-surfaces harmoniques|21
3|&amp;#167; III.  Condition particuli&amp;#232;re &amp;#224; laquelle la solution des probl&amp;#232;mes pr&amp;#233;c&amp;#233;dents se trouve assujettie|28
3|&amp;#167; IV. Probl&amp;#232;me compl&amp;#233;mentaire de celui de Dirichlet|33
3|&amp;#167; V. Le probl&amp;#232;me de Gauss, g&amp;#233;n&amp;#233;ralis&amp;#233; et r&amp;#233;solu &amp;#224; l'aide des pseudo-surface &amp;#224; courbure totale quelconque|36
3|&amp;#167; VI. Nouveaux probl&amp;#232;mes, impliquant, comme ceux qui pr&amp;#233;c&amp;#232;dent, un contour donn&amp;#233;|43
2|Section II. Autres questions g&amp;#233;n&amp;#233;ralis&amp;#233;es et r&amp;#233;solues &amp;#224; l'aide des pseudo-surfaces|49
3|&amp;#167; I. Condition du maximum ou du minimum d'une int&amp;#233;grale d&amp;#233;finie remarquable, relevant des pseudo-surfaces|49
3|&amp;#167; II. Sur un &amp;quot;th&amp;#233;or&amp;#232;me fondamental&amp;quot; d'analyse|54
3|&amp;#167; III. Pseudo-surfaces et n&amp;#233;o-surfaces minima adjointes g&amp;#233;n&amp;#233;ralisant les surfaces similaires d'O. Bonnet et de Schwartz|58
3|&amp;#167; IV. Le pseudo-h&amp;#233;lico&amp;#239;de g&amp;#233;n&amp;#233;ral, successivement transform&amp;#233; en pseudo-surface minima et pseudo-surface &amp;#224; courbure totale nulle|63
3|&amp;#167; V. Sur la d&amp;#233;velopp&amp;#233;e optique d'une pseudo-surface|67
4|Correction au texte du manuscrit de l'auteur|69
3|&amp;#167; VI. Interpr&amp;#233;tation g&amp;#233;om&amp;#233;trique et g&amp;#233;n&amp;#233;ralisation des &amp;#233;quations (dynamiques) de Lagrange, au moyen des pseudo-surfaces|75
3|&amp;#167; VII. Extension aux pseudo-surfaces du principe &amp;quot;de la moindre action&amp;quot;|81
3|&amp;#167; VIII. Retour &amp;#224; l'interpr&amp;#233;tation rationnelle des ph&amp;#233;nom&amp;#232;nes d'optique, au moyen des pseudo-surfaces|84
2|Appendice|87
1|Table des mati&amp;#232;res|91
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