Page:Philosophical Transactions - Volume 003.djvu/254

 Publici Juris fecimus elapso anno 1658. libellum quendam, cui titulus, Sexaginta Problemata Geometrica: In hujus calco Appendiculam adjunximus, in qua occurritur Mario Bettino, ''Calveriana Indivisibilia veluti Dæmonas paventi. Paucis vero transactis diebus a modo dicti Libelli impressione, incidimus forte Venetiis in opus Aureum'' And. Tacquet,  nuncupatum; in quo cum incideremus in Schol. prop. 12. l. 1. Authorem carpere Indivisibilia invenimus.

Doluimus vehementer (saith Angeli) Opus tanta eruditione refertum non prius admanus nostras pervenisse; censura autem in ipso conta Indivisibilia pronunciata, parum aut nihil nos turbat: Vetera enim continet & non nis corum modica, & imbecilliora, quæ prius ab ipsp Cavalerio in Præfat. Geometriæ Indivisibilium, & a Guldino in Centro-baryca objiciuntur; quibus satis superque occurrit ipse Cavalerius.

And Angeli in the Preface of his Treatise De Infinitorum Spiralium Spatiorum Mensura (Venetiis 1660.) having occasion so mention the fruitless endeavour of Guldin in finding the Center of Gravity of a Spiral Line, and a Right line equal thereto, saith thus;

P. Guldinus, Centrobarycæ (Anno 1635. & 1640. editæ) Author famosus (at Cavalerianorum Indivisibilium contemptor & irrisor, qui dum Indivisibilius irrist, seipsum ridiculum præbuit) altius omnibus volatum sumpsit, at conatu irrito, & Icari fine, ut ipsemet fatetur.

But Guldinus doth not confess himself in an error in opposing Cavalier's Geometria Indivisibilium, publisht 1632; but saith, he was very aged, of an infirme memory, and that he had not (as we may gather) leisure to peruse it thoroughly, when he had health, nor health when he had leisure. The Controversie, and the Reply about it, is exceeding pleasant, and to be found with other considerable Miscellanies in the ''Geometr. Exercitat. of Cavalerius printed at Bononia'' 1647. Which Book if Tacquet had seen (for he quotes it not) he would probably not have made any such opposition.

Angeli doth not only answer what is objected by Tacquet, but shews, what famous Authors he hath on his side, who have derived many excellent Inventions from this Method of Indivisibles, ''viz. Beaugrand, Rocca, Magiottus, Van Schoten, Rich. White, Bullialdus, Torricellius, who calls Cavalieriuss First Book the Ocean of Indivisibles, and the Fountain of Inventions.'' Of which Doctrine he renders many excellent Examples.

Moreover the same Angeli in the Preface to his said Tract, ''De Infinit. Spiral. Spatiorum Mensura,'' hath these words:

Pro Indivisibilibus est veritas ipsa, stantque illiomnes præclarissumu Geometræ, quos in Epist. ad Lectorem Operis nostri De Infinitis Parabolis recensuimus; quibus nuper ultro se associavit Vinc. Viviani l. 1. De Maximis & Minimis, monito posf Prop. 17. ubi ait, Ut hoc loco, ex adverso indirectæ Antiquorum viæ per duplicem positionem, luce clarius pateat, quantum facilitatis, brevitatis, atgue evidentiae nanciscatur e nova directaque methodo (recite Rh