In all municipalities, counties and school districts the rates of taxation as herein limited may be increased for their respective purposes when the rate and purpose of the increase are submitted to a vote and two-thirds of the qualified electors voting thereon shall vote therefor; provided in school districts the rate of taxation as herein limited may be increased for school purposes so that the total levy shall not exceed six dollars on the hundred dollars assessed valuation, except as herein provided, when the rate and the purpose of the increase are submitted to a vote and a majority of the qualified electors voting thereon shall vote therefor; provided, that in any school district where the board of education is not proposing a higher tax rate for school purposes, the last tax rate approved shall continue and the tax rate need not be submitted to the voters; provided, that in school districts where the qualified voters have voted against a proposed higher tax rate for school purposes, then the rate shall remain at the rate approved in the last previous school election except that the board of education shall be free to resubmit any higher tax rate at any time; provided that any board of education may levy a lower tax rate than approved by the voters as authorized by any provision of this section; and provided, that the rates herein fixed, and the amounts by which they may be increased may be further limited by law; and provided further, that any county or other political subdivision, when authorized by law and within the limits fixed by law, may levy a rate of taxation on all property subject to its taxing powers in excess of the rates herein limited, for library, hospital, public health, recreation grounds and museum purposes.