Goshen
Overview
The name גֹשֶׁן appears fifteen times in all of Tanakh. Most of these occur at the end of Bereshis and the beginning of Shmos and refer to the area in Egypt where Yaakov's sons and their descendants lived. The other three occurrences are in Sefer Yehoshua and refer to an area and city which the Israelites conquered.
Goshen in Egypt
The first mention of Goshen is in Bereshis 45:10:
וְיָשַׁבְתָ בְאֶרֶץ גֹּשֶן וְהָיִיתָ קָרוֹב אֵלַׁי אַׁתָה וּבָנֶיךָ וּבְנֵי בָנֶיךָ וְצֹּאנְךָ וּבְקָרְ ךָ וְכָל אֲשֶר לָךְ.
From this verse it appears that the Land of Goshen is near the capital of Egypt, since Yaakov will settle near Yosef, who presumably lived in the capital.
An additional clue to the location of Goshen is found in Bereshis 46:34:
וַׁאֲמַׁרְ תֶם אַׁנְשֵי מִקְנֶה הָיוּ עֲבָדֶיךָ מִנְעוּרֵינוּ וְעַׁד עַׁתָה גַׁם אֲנַׁחְנוּ גַׁם אֲבֹּתֵינוּ בַׁעֲבוּר תֵשְבוּ בְאֶרֶץ גֹּשֶן כִי תוֹעֲבַׁת מִצְרַׁ יִם כָל רֹּעֵה צֹּאן.
From this verse and others, it sounds like the Land of Goshen is especially suitable for grazing. However, in Bereshis 47:6 we are told:
אֶרֶץ מִצְרַׁיִם לְפָנֶיךָ הִוא בְמֵיטַׁב הָאָרֶץ הוֹשֵב אֶת אָבִיךָ וְאֶת אַׁחֶיךָ יֵשְבוּ בְאֶרֶץ גֹּשֶן וְאִם יָדַׁעְתָ וְיֶש בָם אַׁנְשֵי חַׁיִל וְשַׁמְתָם שָרֵי מִקְנֶה עַׁל אֲשֶר לִי.
Paroh refers to the Land of Goshen as the best of land, implying that it is well suited for farming. In addition, the term "מֵיטַב הָאָרֶׁץ" appears only once more, in Bereshis 47:11:
וַׁיּוֹשֵב יוֹסֵף אֶת אָבִיו וְאֶת אֶחָיו וַׁיִּתֵן לָהֶם אֲחֻזָה בְאֶרֶץ מִצְרַׁיִם בְמֵיטַׁב הָאָרֶץ בְאֶרֶץ רַׁעְמְסֵס כַׁאֲשֶר צִוָּה פַׁרְ עֹּה.
The combination of these verses implies that the Land of Goshen is identical to "אֶׁרֶׁץ רַעְמְסֵס " ("the Land of Ramesses").
Goshen in Israel
While the verses in Bereshis and Shmos appear to be describing an area in Egypt, the three verses in Yehoshua seem to be referring to a totally different place. Yehoshua 10:41 and 11:16 both mention the "Land of Goshen" ("אֶׁרֶׁץ גֹשֶׁן" or "אֶׁרֶׁץ הַגֹשֶׁן") and seem to place it in the Southern Israel:
וַׁיַּׁכֵם יְהוֹשֻעַׁ מִקָדֵש בַׁרְ נֵעַׁ וְעַׁד עַׁזָה וְאֵת כָל אֶרֶץ גֹּשֶן וְעַׁד גִבְעוֹן. (יהושע י':מ"א)
וַׁיִּקַׁח יְהוֹשֻעַׁ אֶת כָל הָאָרֶץ הַׁזֹּאת הָהָר וְאֶת כָל הַׁנֶגֶב וְאֵת כָל אֶרֶץ הַׁגֹּשֶ ן וְאֶת הַׁשְפֵלָה וְאֶת הָעֲרָבָה וְאֶת הַׁר יִשְרָאֵל וּשְפֵלָתֹּה. (יהושע י"א:ט"ז)
The third verse, Yehoshua 15:51, refers to a city in the inheritance of Yehuda:
וְגֹּשֶן וְחֹּלֹן וְגִלֹה עָרִ ים אַׁחַׁת עֶשְרֵה וְחַׁצְרֵיהֶן.
Map of Possible Locations of Goshen
