added several fonts

- added symlinks for the old name for AGaramondPro
- add times new roman

fonts/AGaramondPro/AGaramondPro-Bd.otf

@@ -0,0 +1 @@
+../Garamond/GaramondPremrPro-Bd.otf

fonts/AGaramondPro/AGaramondPro-BdCapt.otf

@@ -0,0 +1 @@
+../Garamond/GaramondPremrPro-BdCapt.otf

fonts/AGaramondPro/AGaramondPro-BdDisp.otf

@@ -0,0 +1 @@
+../Garamond/GaramondPremrPro-BdDisp.otf

fonts/AGaramondPro/AGaramondPro-BdIt.otf

@@ -0,0 +1 @@
+../Garamond/GaramondPremrPro-BdIt.otf

fonts/AGaramondPro/AGaramondPro-BdItCapt.otf

@@ -0,0 +1 @@
+../Garamond/GaramondPremrPro-BdItCapt.otf

fonts/AGaramondPro/AGaramondPro-BdItDisp.otf

@@ -0,0 +1 @@
+../Garamond/GaramondPremrPro-BdItDisp.otf

fonts/AGaramondPro/AGaramondPro-BdItSubh.otf

@@ -0,0 +1 @@
+../Garamond/GaramondPremrPro-BdItSubh.otf

fonts/AGaramondPro/AGaramondPro-BdSubh.otf

@@ -0,0 +1 @@
+../Garamond/GaramondPremrPro-BdSubh.otf

fonts/AGaramondPro/AGaramondPro-Capt.otf

@@ -0,0 +1 @@
+../Garamond/GaramondPremrPro-Capt.otf

fonts/AGaramondPro/AGaramondPro-Disp.otf

@@ -0,0 +1 @@
+../Garamond/GaramondPremrPro-Disp.otf

fonts/AGaramondPro/AGaramondPro-It.otf

@@ -0,0 +1 @@
+../Garamond/GaramondPremrPro-It.otf

fonts/AGaramondPro/AGaramondPro-ItCapt.otf

@@ -0,0 +1 @@
+../Garamond/GaramondPremrPro-ItCapt.otf

fonts/AGaramondPro/AGaramondPro-ItDisp.otf

@@ -0,0 +1 @@
+../Garamond/GaramondPremrPro-ItDisp.otf

fonts/AGaramondPro/AGaramondPro-ItSubh.otf

@@ -0,0 +1 @@
+../Garamond/GaramondPremrPro-ItSubh.otf

fonts/AGaramondPro/AGaramondPro-LtDisp.otf

@@ -0,0 +1 @@
+../Garamond/GaramondPremrPro-LtDisp.otf

fonts/AGaramondPro/AGaramondPro-LtItDisp.otf

@@ -0,0 +1 @@
+../Garamond/GaramondPremrPro-LtItDisp.otf

fonts/AGaramondPro/AGaramondPro-Med.otf

@@ -0,0 +1 @@
+../Garamond/GaramondPremrPro-Med.otf

fonts/AGaramondPro/AGaramondPro-MedCapt.otf

@@ -0,0 +1 @@
+../Garamond/GaramondPremrPro-MedCapt.otf

fonts/AGaramondPro/AGaramondPro-MedDisp.otf

@@ -0,0 +1 @@
+../Garamond/GaramondPremrPro-MedDisp.otf

fonts/AGaramondPro/AGaramondPro-MedIt.otf

@@ -0,0 +1 @@
+../Garamond/GaramondPremrPro-MedIt.otf

fonts/AGaramondPro/AGaramondPro-MedItCapt.otf

@@ -0,0 +1 @@
+../Garamond/GaramondPremrPro-MedItCapt.otf

fonts/AGaramondPro/AGaramondPro-MedItDisp.otf

@@ -0,0 +1 @@
+../Garamond/GaramondPremrPro-MedItDisp.otf

fonts/AGaramondPro/AGaramondPro-MedItSubh.otf

@@ -0,0 +1 @@
+../Garamond/GaramondPremrPro-MedItSubh.otf

fonts/AGaramondPro/AGaramondPro-MedSubh.otf

@@ -0,0 +1 @@
+../Garamond/GaramondPremrPro-MedSubh.otf

fonts/AGaramondPro/AGaramondPro-Regular.otf

@@ -0,0 +1 @@
+../Garamond/GaramondPremrPro.otf

fonts/AGaramondPro/AGaramondPro-Smbd.otf

@@ -0,0 +1 @@
+../Garamond/GaramondPremrPro-Smbd.otf

fonts/AGaramondPro/AGaramondPro-SmbdCapt.otf

@@ -0,0 +1 @@
+../Garamond/GaramondPremrPro-SmbdCapt.otf

fonts/AGaramondPro/AGaramondPro-SmbdDisp.otf

@@ -0,0 +1 @@
+../Garamond/GaramondPremrPro-SmbdDisp.otf

fonts/AGaramondPro/AGaramondPro-SmbdIt.otf

@@ -0,0 +1 @@
+../Garamond/GaramondPremrPro-SmbdIt.otf

fonts/AGaramondPro/AGaramondPro-SmbdItCapt.otf

@@ -0,0 +1 @@
+../Garamond/GaramondPremrPro-SmbdItCapt.otf

fonts/AGaramondPro/AGaramondPro-SmbdItDisp.otf

@@ -0,0 +1 @@
+../Garamond/GaramondPremrPro-SmbdItDisp.otf

fonts/AGaramondPro/AGaramondPro-SmbdItSubh.otf

@@ -0,0 +1 @@
+../Garamond/GaramondPremrPro-SmbdItSubh.otf

fonts/AGaramondPro/AGaramondPro-SmbdSubh.otf

@@ -0,0 +1 @@
+../Garamond/GaramondPremrPro-SmbdSubh.otf

fonts/AGaramondPro/AGaramondPro-Subh.otf

@@ -0,0 +1 @@
+../Garamond/GaramondPremrPro-Subh.otf

fonts/AGaramondPro/AGaramondPro.otf

@@ -0,0 +1 @@
+../Garamond/GaramondPremrPro.otf

fonts/Times New Roman/fonts.dir

@@ -0,0 +1,101 @@
+100
+Times new roman bold italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-adobe-standard
+Times new roman bold italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-ascii-0
+Times new roman bold italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-ibm-cp437
+Times new roman bold italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-ibm-cp850
+Times new roman bold italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-ibm-cp852
+Times new roman bold italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-ibm-cp866
+Times new roman bold italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-iso10646-1
+Times new roman bold italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-iso8859-1
+Times new roman bold italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-iso8859-10
+Times new roman bold italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-iso8859-13
+Times new roman bold italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-iso8859-15
+Times new roman bold italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-iso8859-16
+Times new roman bold italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-iso8859-2
+Times new roman bold italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-iso8859-3
+Times new roman bold italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-iso8859-4
+Times new roman bold italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-iso8859-5
+Times new roman bold italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-iso8859-8
+Times new roman bold italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-iso8859-9
+Times new roman bold italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-koi8-e
+Times new roman bold italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-koi8-r
+Times new roman bold italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-koi8-ru
+Times new roman bold italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-koi8-u
+Times new roman bold italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-koi8-uni
+Times new roman bold italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-microsoft-cp1252
+Times new roman bold italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-suneu-greek
+Times new roman bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-adobe-standard
+Times new roman bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-ascii-0
+Times new roman bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-ibm-cp437
+Times new roman bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-ibm-cp850
+Times new roman bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-ibm-cp852
+Times new roman bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-ibm-cp866
+Times new roman bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-iso10646-1
+Times new roman bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-iso8859-1
+Times new roman bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-iso8859-10
+Times new roman bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-iso8859-13
+Times new roman bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-iso8859-15
+Times new roman bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-iso8859-16
+Times new roman bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-iso8859-2
+Times new roman bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-iso8859-3
+Times new roman bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-iso8859-4
+Times new roman bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-iso8859-5
+Times new roman bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-iso8859-8
+Times new roman bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-iso8859-9
+Times new roman bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-koi8-e
+Times new roman bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-koi8-r
+Times new roman bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-koi8-ru
+Times new roman bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-koi8-u
+Times new roman bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-koi8-uni
+Times new roman bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-microsoft-cp1252
+Times new roman bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-suneu-greek
+Times new roman italic.ttf -monotype-times new roman-medium-i-normal--0-0-0-0-p-0-adobe-standard
+Times new roman italic.ttf -monotype-times new roman-medium-i-normal--0-0-0-0-p-0-ascii-0
+Times new roman italic.ttf -monotype-times new roman-medium-i-normal--0-0-0-0-p-0-ibm-cp437
+Times new roman italic.ttf -monotype-times new roman-medium-i-normal--0-0-0-0-p-0-ibm-cp850
+Times new roman italic.ttf -monotype-times new roman-medium-i-normal--0-0-0-0-p-0-ibm-cp852
+Times new roman italic.ttf -monotype-times new roman-medium-i-normal--0-0-0-0-p-0-ibm-cp866
+Times new roman italic.ttf -monotype-times new roman-medium-i-normal--0-0-0-0-p-0-iso10646-1
+Times new roman italic.ttf -monotype-times new roman-medium-i-normal--0-0-0-0-p-0-iso8859-1
+Times new roman italic.ttf -monotype-times new roman-medium-i-normal--0-0-0-0-p-0-iso8859-10
+Times new roman italic.ttf -monotype-times new roman-medium-i-normal--0-0-0-0-p-0-iso8859-13
+Times new roman italic.ttf -monotype-times new roman-medium-i-normal--0-0-0-0-p-0-iso8859-15
+Times new roman italic.ttf -monotype-times new roman-medium-i-normal--0-0-0-0-p-0-iso8859-16
+Times new roman italic.ttf -monotype-times new roman-medium-i-normal--0-0-0-0-p-0-iso8859-2
+Times new roman italic.ttf -monotype-times new roman-medium-i-normal--0-0-0-0-p-0-iso8859-3
+Times new roman italic.ttf -monotype-times new roman-medium-i-normal--0-0-0-0-p-0-iso8859-4
+Times new roman italic.ttf -monotype-times new roman-medium-i-normal--0-0-0-0-p-0-iso8859-5
+Times new roman italic.ttf -monotype-times new roman-medium-i-normal--0-0-0-0-p-0-iso8859-8
+Times new roman italic.ttf -monotype-times new roman-medium-i-normal--0-0-0-0-p-0-iso8859-9
+Times new roman italic.ttf -monotype-times new roman-medium-i-normal--0-0-0-0-p-0-koi8-e
+Times new roman italic.ttf -monotype-times new roman-medium-i-normal--0-0-0-0-p-0-koi8-r
+Times new roman italic.ttf -monotype-times new roman-medium-i-normal--0-0-0-0-p-0-koi8-ru
+Times new roman italic.ttf -monotype-times new roman-medium-i-normal--0-0-0-0-p-0-koi8-u
+Times new roman italic.ttf -monotype-times new roman-medium-i-normal--0-0-0-0-p-0-koi8-uni
+Times new roman italic.ttf -monotype-times new roman-medium-i-normal--0-0-0-0-p-0-microsoft-cp1252
+Times new roman italic.ttf -monotype-times new roman-medium-i-normal--0-0-0-0-p-0-suneu-greek
+Times new roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-adobe-standard
+Times new roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-ascii-0
+Times new roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-ibm-cp437
+Times new roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-ibm-cp850
+Times new roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-ibm-cp852
+Times new roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-ibm-cp866
+Times new roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-iso10646-1
+Times new roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-iso8859-1
+Times new roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-iso8859-10
+Times new roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-iso8859-13
+Times new roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-iso8859-15
+Times new roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-iso8859-16
+Times new roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-iso8859-2
+Times new roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-iso8859-3
+Times new roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-iso8859-4
+Times new roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-iso8859-5
+Times new roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-iso8859-8
+Times new roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-iso8859-9
+Times new roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-koi8-e
+Times new roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-koi8-r
+Times new roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-koi8-ru
+Times new roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-koi8-u
+Times new roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-koi8-uni
+Times new roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-microsoft-cp1252
+Times new roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-suneu-greek

fonts/Times New Roman/fonts.scale

@@ -0,0 +1,101 @@
+100
+Times New Roman Bold Italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-adobe-standard
+Times New Roman Bold Italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-ascii-0
+Times New Roman Bold Italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-ibm-cp437
+Times New Roman Bold Italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-ibm-cp850
+Times New Roman Bold Italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-ibm-cp852
+Times New Roman Bold Italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-ibm-cp866
+Times New Roman Bold Italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-iso10646-1
+Times New Roman Bold Italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-iso8859-1
+Times New Roman Bold Italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-iso8859-10
+Times New Roman Bold Italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-iso8859-13
+Times New Roman Bold Italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-iso8859-15
+Times New Roman Bold Italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-iso8859-16
+Times New Roman Bold Italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-iso8859-2
+Times New Roman Bold Italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-iso8859-3
+Times New Roman Bold Italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-iso8859-4
+Times New Roman Bold Italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-iso8859-5
+Times New Roman Bold Italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-iso8859-8
+Times New Roman Bold Italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-iso8859-9
+Times New Roman Bold Italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-koi8-e
+Times New Roman Bold Italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-koi8-r
+Times New Roman Bold Italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-koi8-ru
+Times New Roman Bold Italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-koi8-u
+Times New Roman Bold Italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-koi8-uni
+Times New Roman Bold Italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-microsoft-cp1252
+Times New Roman Bold Italic.ttf -monotype-times new roman-bold-i-normal--0-0-0-0-p-0-suneu-greek
+Times New Roman Bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-adobe-standard
+Times New Roman Bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-ascii-0
+Times New Roman Bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-ibm-cp437
+Times New Roman Bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-ibm-cp850
+Times New Roman Bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-ibm-cp852
+Times New Roman Bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-ibm-cp866
+Times New Roman Bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-iso10646-1
+Times New Roman Bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-iso8859-1
+Times New Roman Bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-iso8859-10
+Times New Roman Bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-iso8859-13
+Times New Roman Bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-iso8859-15
+Times New Roman Bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-iso8859-16
+Times New Roman Bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-iso8859-2
+Times New Roman Bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-iso8859-3
+Times New Roman Bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-iso8859-4
+Times New Roman Bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-iso8859-5
+Times New Roman Bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-iso8859-8
+Times New Roman Bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-iso8859-9
+Times New Roman Bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-koi8-e
+Times New Roman Bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-koi8-r
+Times New Roman Bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-koi8-ru
+Times New Roman Bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-koi8-u
+Times New Roman Bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-koi8-uni
+Times New Roman Bold.ttf -monotype-times new roman-bold-r-normal--0-0-0-0-p-0-microsoft-cp1252
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washington_letterhead_letter-matrix-deptartment.tex

@@ -32,6 +32,18 @@ ItalicFont      =   *-It,
 BoldItalicFont  =   *-BdIt
 ]
 
+% \setmainfont{Times New Roman}[
+% Path = ./fonts/Times New Roman/,
+% Extension       = .ttf,
+% BoldFont        =   * Bold,
+% ItalicFont      =   * Italic,
+% BoldItalicFont  =   * Bold Italic
+% ]
+
+\usepackage{amsmath}
+\usepackage{amsthm}
+%\usepackage{mathrsfs}
+
 \usepackage{polyglossia}
 \setdefaultlanguage{english}
 
@@ -89,6 +101,34 @@ BoldItalicFont  =   *-BdIt
 % \raggedright
 \linespread{1.05}
 
+\newtheorem{theorem}{Theorem}[section]
+\newtheorem{definition}{Definition}[section]
+\newenvironment{demo}{\noindent {\bf Dem.}}{\qed}
+\newenvironment{remarque}{\noindent {\bf Rem.} \small \itshape}{}
+\newenvironment{exemple}{\noindent {\bf Example}}{}
+
+\newcommand{\Lu}{L^1(\Rset)}
+\newcommand{\tf}[1]{{\cal F}\left(#1\right)}
+\newcommand{\ii}{{\mathrm{i}}}
+\newcommand{\Cn}{{\cal C}^{n}}
+\newcommand{\dd}{\mathrm{d}}
+% ;; \newcommand{\Rset}{{\mathbb R}}
+\newcommand{\Rset}{R}
+\newcommand{\R}{\mathbb R}
+\newcommand{\Cx}{\mathbb R}
+\newcommand{\ex}{\mathrm{e}}
+\newcommand{\Cinf}{{\cal C}^{\infty}}
+\newcommand{\abs}[1]{\left| #1 \right|}
+\newcommand{\dx}{\dd x}
+\newcommand{\ds}{\displaystyle}
+\newcommand{\vect}[1]{\overrightarrow{#1}}
+\newcommand{\Boule}[2]{\mathscr B(#1,#2)}
+\newcommand{\Cercle}[2]{\mathscr C(#1,#2)}
+\DeclareMathOperator{\Arg}{Arg}
+
+\newcommand{\dep}[2]{\ds \frac{\partial #1}{\partial #2}}
+
+% \usepackage[cal=scr,mdpgd,greekfamily = didot]{mathdesign}
 
 \begin{document}
 
@@ -131,6 +171,206 @@ Enim facilisis gravida neque convallis a cras semper auctor. Lorem ipsum dolor s
 
 Nunc consequat interdum varius sit. Nibh tortor id aliquet lectus. Lacus laoreet non curabitur gravida arcu ac tortor dignissim. Tortor condimentum lacinia quis vel eros donec ac odio tempor. Varius sit amet mattis vulputate. Ut tristique et egestas quis. Enim blandit volutpat maecenas volutpat blandit aliquam. Ullamcorper morbi tincidunt ornare massa eget egestas purus. Maecenas ultricies mi eget mauris pharetra et ultrices neque ornare. Libero nunc consequat interdum varius sit. Turpis tincidunt id aliquet risus feugiat in ante metus. Ut enim blandit volutpat maecenas volutpat blandit aliquam. Nisl vel pretium lectus quam id leo in vitae turpis. Porttitor eget dolor morbi non arcu risus quis varius. Mi in nulla posuere sollicitudin. Eleifend donec pretium vulputate sapien nec. Aliquet nibh praesent tristique magna sit amet. Sagittis purus sit amet volutpat consequat mauris nunc congue nisi.
 
+
+Consider a change of variable  $(x,y)\mapsto
+(u,v)=\big(u(x,y),v(x,y)\big)$ in the plane $\R^2$, identified
+with~$\Cx$. This change of variable really only deserves the name if
+$f$ is locally bijective (i.e., one-to-one); this is the case if the
+jacobian of the map is nonzero (then so is the jacobian of the
+inverse map):
+\begin{equation*}
+  \left| \frac{{D}(u,v)}{{D}(x,y)}\right| =
+  \begin{vmatrix}
+    \ds\frac{\displaystyle\partial u}{\displaystyle\partial x} &
+    \ds\frac{\displaystyle\partial u}{\displaystyle\partial y} \\[4mm]
+    \ds\frac{\displaystyle\partial v}{\displaystyle\partial x} &
+    \ds\frac{\displaystyle\partial v}{\displaystyle\partial y}
+  \end{vmatrix}\neq 0
+  \qquad\text{and}\qquad
+  \left| \frac{{D}(x,y)}{{D}(u,v)}\right|
+  =\begin{vmatrix}\ds\dep{x}{u} &\ds \dep{x}{v}\\[4mm]
+    \ds\dep{y}{u} &\ds \dep{y}{v}
+  \end{vmatrix}\neq 0.
+\end{equation*}
+\begin{theorem}
+In a complex change of variable
+\begin{equation*}
+        z= x+\ii y\longmapsto w=f(z)=u+\ii v,
+\end{equation*}
+and \emph{if $f$ is holomorphic}, then the jacobian of the map is equal to
+\begin{equation*}
+  J_f(z)=\left| \frac{{D}(u,v)}{{D}(x,y)}\right|=
+  \abs{f'(z)}^2.
+\end{equation*}
+\end{theorem}
+\begin{demo}
+  Indeed, we have $f'(z)=\dep{u}{x}+\ii\dep{v}{x}$ and hence, by the
+  Cauchy-Riemann relations,
+  \begin{align*}
+    \abs{f'(z)}^2 & =
+    \left(\dep{u}{x}\right)^2+\left(\dep{v}{x}\right)^2
+    =
+    \dep{u}{x}\dep{v}{y}-\dep{v}{x}\dep{u}{y}=J_f(z).
+  \end{align*}
+\end{demo}
+
+
+\begin{definition}
+  \index{Conformal map}%
+  \index{Transformation!conformal ---}%
+  A \emph{conformal map} or \emph{conformal transformation} of an
+  open subset $\Omega\subset\R^2$ into another open subset
+  $\Omega'\subset\R^2$ is any map $f:\Omega\mapsto \Omega'$, locally
+  bijective, that preserves angles and orientation.
+\end{definition}
+
+\begin{theorem}
+  Any conformal map is given by a holomorphic function $f$ such
+  that the derivative of $f$ does not vanish.
+\end{theorem}
+
+This justifies the next definition:
+%% ----------------------------------------------------------------------
+\begin{definition}
+  \index{Conformal map}%
+  \index{Transformation!conformal ---}%
+  A \emph{conformal transformation} or \emph{conformal map} of
+  an open subset
+  $\Omega\subset\Cx$ into another open subset
+  $\Omega'\subset\Cx$ is any holomorphic function
+  $f:\Omega\mapsto \Omega'$ such that
+  $f'(z)\neq 0$ for all $z\in\Omega$.
+\end{definition}
+%% ----------------------------------------------------------------------
+
+%% ----------------------------------------------------------------------
+\begin{demo}[that the definitions are equivalent]
+  We will denote in general $w=f(z)$.  Consider, in the complex plane, two
+  line segments $\gamma_1$ and $\gamma_2$ contained inside the set $\Omega$
+  where $f$ is defined, and intersecting at a point $z_0$ in $\Omega$.
+  Denote by $\gamma'_1$ and $\gamma_2'$ their images by~$f$.
+
+  We want to show that if the angle between $\gamma_1$ and $\gamma_2$ is
+  equal to $\theta$, then the same holds for their images, which means that
+  the angle between the tangent lines to $\gamma'_1$ and $\gamma'_2$ at
+  $w_0=f(z_0)$ is also equal to $\theta$.
+
+  Consider a point $z\in\gamma_1$ close to~$z_0$. Its image $w=f(z)$
+  satisfies
+  \begin{equation*}
+    \lim_{z\to z_0} \frac{w-w_0}{z-z_0}=f'(z_0),
+  \end{equation*}
+  and hence
+  $$\displaystyle \lim_{z\to z_0} \Arg
+   (w-w_0)-\Arg(z-z_0) = \Arg f'(z_0), $$%
+  which shows that the angle between the curve $\gamma'_1$ and the real
+  axis is equal to the angle between the original segment $\gamma_1$ and
+  the real axis, plus the angle $\alpha=\Arg f'(z_0)$ (which is well
+  defined because $f'(z)\neq 0$).
+
+  Similarly, the angle between the image curve $\gamma'_2$ and the real
+  axis is equal to that between the segment $\gamma_2$ and the real axis,
+  plus the same~$\alpha$.
+
+  Therefore, the angle between the two image curves is the same as that
+  between the two line segments, namely, $\theta$.
+
+  Another way to see this is as follows: the tangent vectors of the curves
+  are transformed according to the rule $\vect{V}'=\dd f_{z_0}\vect{V}$. But the
+  differential of $f$ (when $f$ is seen as a map from $\R^2$ to~$\R^2$) is
+  of the form
+  \begin{equation}
+    \displaystyle \dd f_{z_0}=\begin{pmatrix}
+      \displaystyle \dep{P}{x} & \displaystyle \dep{P}{y} \\[4mm]
+      \displaystyle \dep{Q}{x} & \displaystyle \dep{Q}{y}\end{pmatrix}
+    =
+    \abs{f'(z_0)}\begin{pmatrix}\cos\alpha& -\sin\alpha
+      \\ \sin\alpha &\cos\alpha \end{pmatrix},
+    \label{eq:FSimil}
+  \end{equation}
+  where $\alpha$ is the argument of $f'(z_0)$. This is the matrix of a
+  rotation composed with a homothety, that is, a similitude.
+
+  \medskip
+%% ······································································
+  % {\begin{picture}(300,100)
+      % \put(0,0){\epsfig{file=\Figures/TC.\Ext,height=3.2cm}}
+      % \put(20,65){$\gamma_2$} \put(80,55){$\theta$}
+      % \put(100,80){$\gamma_1$} \put(195,85){$\gamma'_1$}
+      % \put(245,35){$\theta$} \put(270,60){$\gamma'_2$}
+    % \end{picture}}
+%% ······································································
+
+  Conversely, if $f$ is a map which is $\R^2$-differentiable and preserves
+  angles, then at any point $\dd f$ is an endomorphism of~$\R^2$ which
+  preserves angles. Since $f$ also preserves orientation, its determinant
+  is positive, so $\dd f$ is a similitude, and its matrix is exactly
+  as in equation~\eqref{eq:FSimil}. The Cauchy-Riemann equations are
+  immediate consequences.
+\end{demo}
+%% ----------------------------------------------------------------------
+
+%% ----------------------------------------------------------------------
+\begin{remarque}
+  \index{Antiholomorphic function}%
+  \index{Function!antiholomorphic ---}%
+  An \emph{antiholomorphic} map also preserves angles, but it
+  reverses the orientation.
+\end{remarque}
+%% ----------------------------------------------------------------------
+\newpage
+\subsection*{Calcul différentiel}
+
+
+
+Pour obtenir la différentielle totale de cette expression, considérée comme fonction de $x$, $y$, ..., donnons à $x$, $y$, ... des accroissements $d\!x$, $d\!y$, .... Soient $\Delta u$, $\Delta v$, ..., $\Delta f$ les accroissements correspondants de $u$, $v$, ...,$f$. On aura
+\begin{equation*}
+  \Delta f= \dfrac{\partial\! f}{\partial u} \Delta u +  \dfrac{\partial\! f}{\partial v} \Delta v + \hdots + R\Delta u + R_1 \Delta v + \hdots,
+\end{equation*}
+$R$, $R_1$, ... tendant vers zéro avec $\Delta u$, $\Delta v$, ....
+
+Mais on a, d'autre part,
+\begin{align*}
+  \Delta u & =  \dfrac{\partial u}{\partial x} d\! x +   +  \dfrac{\partial u}{\partial y} \Delta y + \hdots + S\Delta x + S_1 \Delta y + \hdots \\
+& = du + Sd\! x + S_1 d\! y + \hdots \\
+ \Delta v & =  \dfrac{\partial v}{\partial x} d\! x +   +  \dfrac{\partial v}{\partial y} \Delta y + \hdots + T\Delta x + T_1 \Delta y + \hdots \\
+& = dv + Td\! x + T_1 d\! y + \hdots \\
+\hdots
+\end{align*}
+$S$, $S_1$, ..., $T$, $T_1$,... tendant vers zéro avec $d\! x$, $d\! y$, ....
+
+Substituant ces valeurs dans l'expression de $\Delta f$, il vient
+\begin{equation*}
+\begin{array}{rcl}
+ \vbox to 25pt {} \Delta f & = &\dfrac{\partial\! f}{\partial u} d u +  \dfrac{\partial\! f}{\partial v} d v + \hdots + \rho d\! x  + \rho_1 d\! y  + \hdots \\
+\vbox to 25pt {}& = & \phantom{+} \left( \dfrac{\partial\! f}{\partial u} \dfrac{\partial u}{\partial x} + \dfrac{\partial\! f}{\partial v} \dfrac{\partial v}{\partial x} + \hdots \right) d\! x \\
+\vbox to 25pt {}& & + \left( \dfrac{\partial\! f}{\partial u} \dfrac{\partial u}{\partial y} + \dfrac{\partial\! f}{\partial v} \dfrac{\partial v}{\partial y} + \hdots \right) d\! y \\
+\vbox to 25pt {}&& + \hdots + \rho d\! x  + \rho_1 d\! y  + \hdots
+\end{array}
+\end{equation*}
+$\rho$, $\rho_1$, ... tendant vers zéro avec $d\! x$, $d\! y$, ....
+
+On aura donc
+\begin{align*}
+  \dfrac{\partial\! f}{\partial x}& = \dfrac{\partial\! f}{\partial u} \dfrac{\partial u}{\partial x} + \dfrac{\partial\! f}{\partial v} \dfrac{\partial v}{\partial x} + \hdots, \\
+  \dfrac{\partial\! f}{\partial y}& = \dfrac{\partial\! f}{\partial u} \dfrac{\partial u}{\partial y} + \dfrac{\partial\! f}{\partial v} \dfrac{\partial v}{\partial y} + \hdots, \\
+\hdots
+\end{align*}
+et, d'autre part,
+\begin{equation*}
+    df  = \dfrac{\partial\! f}{\partial u} {\mathrm d} u +  \dfrac{\partial\! f}{\partial v}  {\mathrm d} v + \hdots ;
+\end{equation*}
+d'où les deux propositions suivantes :
+
+{\em La dérivée, par rapport à une variable indépendante $x$, d'une fonction composée $f(u,v,\hdots)$ s'obtient en ajoutant ensemble les dérivées partielles $\dfrac{\partial\! f}{\partial u}$, $\dfrac{\partial\! f}{\partial v}$, ..., respectivement multipliées par les dérivées de $u$, $v$, ... par rapport à $x$.
+
+La différentielle totale $df$ s'exprimer au moyen de $u$, $v$, ..., $du$, $dv$, ..., de la même manière que si $u$, $v$, ... étaient des variables indépendantes.
+}
+
+\hbox to \textwidth { \hfill
+    {\sc Camille Jordan}, {\em Cours d'analyse de l'\'Ecole polytechnique}
+}
+
 Varius sit amet mattis vulputate enim nulla aliquet. Augue ut lectus arcu bibendum at. Auctor eu augue ut lectus arcu bibendum at varius vel. Cras ornare arcu dui vivamus arcu felis. Diam maecenas sed enim ut sem viverra aliquet eget sit. Purus in mollis nunc sed id semper risus in. Arcu risus quis varius quam quisque id diam vel quam. Justo nec ultrices dui sapien eget. Tortor consequat id porta nibh venenatis. Porttitor massa id neque aliquam. Tortor id aliquet lectus proin nibh nisl. Volutpat blandit aliquam etiam erat velit scelerisque in dictum non.
 
 Pharetra magna ac placerat vestibulum. Turpis massa sed elementum tempus egestas sed. Mollis aliquam ut porttitor leo a diam sollicitudin tempor. Mattis vulputate enim nulla aliquet porttitor. Tempus egestas sed sed risus pretium. Non pulvinar neque laoreet suspendisse interdum consectetur libero id faucibus. Pellentesque elit ullamcorper dignissim cras. Cras ornare arcu dui vivamus. Viverra maecenas accumsan lacus vel facilisis volutpat est. Tristique senectus et netus et. Adipiscing vitae proin sagittis nisl rhoncus. Vulputate mi sit amet mauris.