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Citing further from the decision:

http://caselaw.lp.findlaw.com/scripts/getcase.pl?court=us&vol=98&invol=145

“Polygamy has always been odious among the northern and western nations of Europe, and, until the establishment of the Mormon Church, was almost exclusively a feature of the life of Asiatic and of African people.

At common law, the second marriage was always void (2 Kent, Com. 79), and from the earliest history of England polygamy has been treated as an offence against society.

After the establishment of the ecclesiastical [98 U.S. 145, 165] courts, and until the time of James I., it was punished through the instrumentality of those tribunals, not merely because ecclesiastical rights had been violated, but because upon the separation of the ecclesiastical courts from the civil the ecclesiastical were supposed to be the most appropriate for the trial of matrimonial causes and offences against the rights of marriage, just as they were for testamentary causes and the settlement of the estates of deceased persons.”

Insofar as one resides within the domain of the United States- one is bound by the laws thereof - the definition of marriage as one man and one woman stemming from the English common law.