GULDI'NUS, or GULDIN", HABAKKUK', afterwards Paul, was born at St. Gall in 1577, and was bred a Protestant, but became a Roman Catholic in or before 1597, in which year he took the vows of a Jesuit, as ' coadjutor temporalis.' Having shown a talent for mathe matics, he was allowed to study at Rome, and afterwards taught, first at Gratz, then at Vienna. lie wrote for the Gregorian Calendar against Calvisius, and against Scaliger, on the precession of the equi noxes; also on the geographical problem of the method of numbering the days of those who sail to the now world, on Ceutrobarycs, and other things. Ile died in 1643. This is the account given by Riccioli of a writer whose memory would not have required notice in this work if it had not been for some propositions mentioned by Mamma, which he appropriated without acknowledgement, and which for a long time passed uuder his name. These propositions, though they now merge in an elementary formula of the integral calculus, and are not used in the form iu which Pappua and Guldinus exhibited them, nevertheless give a very good conception of the properties of the centre of figure, and, under the title of the `Centroborye Method,' form an interesting step iu the chain of reasonings which preceded the differential calculus.
The work of Guldinus, 'De Centro Gravitatis' (of which the first book was published at Vienna in 1635, and the rest, owing to the disturbed state of the country, in 1640 and 144]), is a laboured geome trical treatise on the properties of the centre of gravity, including applications and verifications of the theorems of Pappus, but no demonstration. The attempt to prove these theorems was a failure iu
the hands of Guldinus. To put it beyond question that this writer really did borrow from his predecessor, we subjoin a paragraph from the preface of the seventh book of the collection of Pappus, taking the Latiu text of Comnaandiue, which was published before Guldinus, and which he cites. It must be remembered that the text of this preface is very imperfect :—" Perfectorum utrorumque ordiunin pro portio composita est ex proportions amphismatum, et rectaruin linearum similiter ad axes ductarum h puoctis, quas in ipais gravitatis contra aunt. Imperfectorum autem proportio composite eat ex pro portiouo amphismatum, et circumferentiaruni h punctis qua; in ipsis aunt centre gravitatis, factorial." But the work of Guldinus called the attention of a more powerful geometer to the subject. He had made some objections to the theory of indivisibles of Cavalieri, to which the latter replied io the third of his 'Exercitationess' and ended his reply by making the method of indivisibles furnish the demonstration which Guldinus was not able to find. It is therefore to Cavalieri, and not to Guldinus, that the credit is due of having made the first advance upon Pappus.