Struck by the elegance of Kepler's ‘Platonic Solids' and Galileo's ‘Platonic Cosmogony,' Boulliau sought a single solution to two long-standing problems: planetary motion (Kepler's Problem) and accelerated circular free fall (Galileo's Problem).  The solution, Boulliau suggested, would be found in the ‘secret that lay hidden in uniform acceleration' and in the rule that governed the attenuation of light.  Alas, a solution proved no mean feat, and Boulliau was not equal to the task.  But his Philolaus received wide notice.  It underscored Boulliau's belief that a deeper unity - simple and elegant - would unite heaven and earth.

The clearest expression of these commitments came in Boulliau's Astronomia philolaïca (1645), arguably the most influential book in astronomy between Kepler and Newton.  The principles of Boulliau's 'Philolaic Astronomy' are outlined below, translated from the original Latin.  Without doubt, the Astronomia philolaïca was a critical work drawing together the efforts of Copernicus, Kepler, and Galileo, and without doubt, the work helped to extend awareness of Kepler's planetary ellipses.  But where Kepler had sought a physical cause for planetary motion - and called on astronomers and mathematicians for assistance - Boulliau provided an alternative planetary hypothesis, the foundations for a new cosmology, the ‘Conical Hypothesis.'  It is appropriate to describe in broad outline the features of this hypothesis. 

Following this brief description the reader will find several primary printed texts (parts of which are translated here for the first time) and an important manuscript letter by Boulliau to Prince Leopold (previously unpublished) that provides a critique of Borelli's hypothesis and explanation of his own view about the nature of such hypotheses.

Arguing that planets orbit the sun in an elliptical path, Boulliau again sought a single solution to two problems.  For astronomers, the problem was to locate the planet at a given time; for cosmologists, the problem was to explain orbital motion.  Because circles and ellipses are conic sections, Boulliau imagined each planet moving on the surface of an oblique cone in an elliptical orbit with the sun at the lower focus.  By construction, the axis of the cone bisected the base, which simultaneously defined the empty focus of the ellipse and the centers of circular motion.  The position of a planet on the ellipse at a given time (Kepler's Problem) was thus defined by the intersecting circles (parallel to the base of the cone) where the planet's motion, at any instant, was uniform and circular around its center (Plato's Dictum).  But where Kepler invoked analogies of the lever and magnetic attractions and repulsions, Boulliau explained acceleration and deceleration along the ellipse as the natural motion of the planet from smaller or larger circles. The result was elegant and practical.  If Kepler's ‘area rule' was suspect on physical and geometrical grounds, it was also difficult to apply.  By contrast, Boulliau provided a model of simplicity:  Planetary motion was not caused by external forces but by reason of geometry.  Tedious trial-and-error calculation was now simple and direct.  Arguably Kepler's construction was ingenious but useless.

The foundations of Boulliau's cosmology, however, were soon called into question.  In 1653 Seth Ward attacked his hypothesis claiming to provide a more simple and accurate model.  In his published response (1657), Boulliau acknowledged the difficulty (noted in his Philolaïca) but showed that Ward's alternative (the ‘simple elliptical' model) was not equivalent in fact.  If they were observationally equivalent, the Conical Hypothesis would show an error of 8' of maximum heliocentric longitude, not 2.5'.  Ward failed to note the difference.  Boulliau nevertheless supplied a new ‘modified elliptical' model.  Compared to Kepler calculations (using the same Tychonic data) the new model was slightly more accurate for several of the planets.  Although the Boulliau-Ward debate ended abruptly-- and Boulliau's tables were widely copied in England and Italy-- the ‘problem of the planets' was far from resolved.