6
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I would guess it was well known by the time of Cauchy. But are there earlier references to it?

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    $\begingroup$ Joshua 6:3-4? "You shall march around the city, all the men of war going around the city once... and on the seventh day you shall march around the city seven times..." $\endgroup$ – Robert Israel Jan 6 '13 at 20:18
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    $\begingroup$ @Robert: Does the next line say "And if you reverse orientation on every other day then in fact you shall only march around the city once..."? $\endgroup$ – Vidit Nanda Jan 6 '13 at 20:25
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    $\begingroup$ No. If you reverse orientation on every successive day, you will have marched around the city seven times. The instructions were to march around the city once on each of days 1-6 and then seven times on the seventh day. $\endgroup$ – Michael Renardy Jan 6 '13 at 21:21
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Grünbaum and Shephard suggest that the winding numbers (for closed polygons) have been discussed in the literature at least since 1769.

See A.L.F. Meister, Generalia de genesi figurarum planarum et inde pendentibus earum ajfectionibus, Novi Comm. Soc. Reg. Scient. Gotting. 1 (1769/70), pp. 144-180.

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