The case of higher integers was computed by Cavalieri for n up to 9, using his method of indivisibles (Cavalieri's principle).[7] He interpreted these as higher integrals as computing higher-dimensional volumes, though only informally, as higher-dimensional objects were as yet unfamiliar.[8] This method of quadrature was then extended by Italian mathematician Evangelista Torricelli to other curves such as the cycloid, then the formula was generalized to fractional and negative powers by English mathematician John Wallis, in his Arithmetica Infinitorum (1656), which also standardized the notion and notation of rational powers – though Wallis incorrectly interpreted the exceptional case n = −1 (quadrature of the hyperbola) – before finally being put on rigorous ground with the development of integral calculus.