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Why the き and さ in the 送り仮名 of 大きい and 小さい?

I've always been puzzled over why 大きい isn't 大い and 小さい is not 小い. Is there some etymological reason? (I'm suspecting historical conjugations that changed the き and さ too, just like why 食べる has the べ ...
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Proper Terms For Representing GPS Coordinates

In another question, I mentioned using Kana to represent the GPS coordinates for: N 43° 09.725' W 077° 26.688' I used: キタ シジュウ サン ジスウ ク チョボ ナナヒャク ニジュウ ゴ フン kita shijuu san jisuu ku chobo ...