If I visit every Schengen state for equal duration, then am I eligible to apply for a Schengen visa with the embassy or consulate of any country?
The Schengen Visa Code is explicit about this. You must first consider whether your trip has a main destination. If, for example, you're attending a conference in one of those countries, and that is the principal reason for your trip, then you must apply in the country where the conference is being held.
If there is no other means for determining the main destination, then you use the duration of stay to determine the main destination. You have already ruled that out, because you are staying an equal amount of time in each country you will visit.
In such a case, you should apply to the country where you will enter the Schengen area.
This is governed by Article 5:
Member State competent for examining and deciding on an application
1. The Member State competent for examining and deciding on an application for a uniform visa shall be:
(a) the Member State whose territory constitutes the sole destination of the visit(s);
(b) if the visit includes more than one destination, the Member State whose territory constitutes the main destination of the visit(s) in terms of the length or purpose of stay; or
(c) if no main destination can be determined, the Member State whose external border the applicant intends to cross in order to enter the territory of the Member States.