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To specify a geographic coordinate we use the terms “longitude” and “latitude”. Far as I know, these terms derive from the Latin latitudo (= breadth) and longitudo (= length). In German we use the terms “Breite” (=english “breadth”) and “Länge“ (= english “length”).

The earth is a sphere. Why do we use “breadth” and “length” here? The earth has the same breadth and length in all directions. We may also use the terms “longitude” and “latitude” just the opposite. enter image description here

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The earth is not a sphere. It's more accurately approximated as an ellipsoid. See Figure of the Earth on Wikipedia. –  blah238 May 16 '13 at 1:51
geoid vs spheroids vs ellipsoids here -> support.esri.com/en/knowledgebase/techarticles/detail/25398 –  SoilSciGuy May 22 '13 at 14:16

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The terms are medieval:

latitude (n.) late 14c., "breadth," from Old French latitude (13c.) and directly from Latin latitudo "breadth, width, extent, size," from latus "wide," ... . Geographical sense also is from late 14c., literally "breadth" of a map of the known world...

In the fourteenth century, most known-world maps made in the Christian and Muslim West were T & O maps conventionally oriented to place Eden (believed to lie in the extreme East) at the top:

enter image description here

(From Wikimedia.) The black body in the lower middle represents the Mediterranean Sea, with Europe (North) to the left, Africa (South) to the right, and Asia (East) at the top. Breadth (latitude) on this map is north-south and length (longitude) is east-west.

For at least 2300 years it has been well known in the West that the Earth has a globular shape, so in the minds of medieval cartographers and their readers there would have been no confusion between the (flat) shape of the map and the actual shape of the Earth. We deduce these terms are derived from the cartographic point of view of a map reader rather than from descriptive geometry, even though today their definitions are geometric.

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+1 for being very interesting. Not that you need any more rep... –  Rob Quincey May 15 '13 at 13:51
+1. May be interesting to add that the location of east at the "top" of a conception of the earth dates back much further than the 14th century AD. The ancient Hebrew words for "south" (yamin) and "east" (qedem) also meant "right hand" and "front" respectively. –  LarsH May 15 '13 at 14:06
@LarsH I knew this convention was older--the references in the answer attest to that--but had no idea that it went so far back. Thank you for sharing that! –  whuber May 15 '13 at 15:26

The Earth isn't a actually sphere; it does not have the same length and breadth in all directions. It is in fact fatter around the equator.

But never mind that, the planet isn't a logical sphere from the perspective of human exploration. Humans trot the globe mostly in the east-west dimension. Large areas around the north and sound poles are uninhabited and hostile to even temporary visitation.

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Doesn't answer the question as no explanation is offered of why those words (longitude and latitude) were chosen. –  David Navarre May 15 '13 at 16:22
European exploration of the earth around the time these terms were first used was primarily north and south, rather than east and west, as the Portuguese (such as Henry the Navigator) were undertaking ocean voyages down the western coast of Africa. –  whuber May 15 '13 at 16:38
The Century Dictionary defines longitude as: Length; measure along the longest line. –  nhopton May 19 '13 at 18:39

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