AXCIENT ANALYSIS. POEISMS. 61 



the Duke of Urbino (Francesco Maria) caused it to be pub- 

 lished in 1588, at Pisa, and a second edition was published at 

 Venice the next year : a fact most honourable to that learned 

 and accomplished age, when we recollect how many years 

 Newton's immortal work was published before it reached a 

 second edition, and that in the seventeenth and eighteenth 

 centuries. 



The two first books of Pappus appear to have been purely 

 arithmetical, so that their loss is little to be lamented. The 

 eighth is on mechanics, and the other five are geometrical. 

 The most interesting portion is the seventh ; the introduction 

 of which, addressed to his son as a guide of his geometrical 

 studies, contains a full enumeration of the works written by 

 the Greek geometers, and an account of the particular subjects 

 which each treated, in some instances giving a summary of 

 the propositions themselves with more or less obscurity, but 

 always with great brevity. Among them was a work which 

 excited great interest, and for a long time baffled the conjec- 

 tures of mathematicians, Euclid's three books of ' Porisms :' 

 of these we shall afterwards have occasion to speak more 

 fully. His ' Loci ad Superficiem,' apparently treating of 

 curves of double curvature, is another, the loss of which was 

 greatly lamented, the more because Pappus has given no 

 account of its contents. This he had done in the case of the 

 'Loci Plani' of :Apollonius. Euclid's four books on conic 

 sections are also lost ; but of Apollonius's eight books on the 

 same subject, the most important of the whole series, the 

 ' Elements ' excepted, four were preserved, and three more 

 were discovered in the seventeenth century. His Inclinations, 

 his Tactions or Tangencies, his Sections of Space and of 

 Eatio, and his Determinate Section, however curious, are of 

 less importance ; all of them are lost. 



For many years Commandini's publication of the ' Collec- 

 tions ' and his commentary did not lead to any attempt at 

 restoring the lost works from the general account given by 

 Pappus. Albert Girard, in 1634, informs us in a note to an 

 edition of Stevinus, that he had restored Euclid's 'Porisms,' a 



