352 Mr. Bassace on the Influence of Signs 
without repeating any part of the process by which that was 
produced, we can examine with ease all those modifications 
which any differences in the actual magnitude of the data can 
introduce into the question under consideration: and moreover 
the equation itself will suggest to us such relations amongst 
those quantities as will have the effect of lowering the number 
of its dimensions, or of rendering it the product of two or more 
factors. 
It sometimes happens that by a peculiar relation amongst 
the data of a question, the number of solutions instead of being 
limited becomes infinite: thus, if the position of a line is deter- 
mined by two points, when those points coincide, any line passing 
through the poit in which they coalesce, will satisfy the con- 
ditions of the question which becomes to a certain extent inde- 
terminate: this gives rise to a class of propositions in Geometry 
which are called porisms. When the data on which questions 
depend are numerous, it is by no means so easy to discover by 
Geometrical considerations that relation amongst them in which 
the question becomes indeterminate, as it is by an Algebraical 
inquiry where the solution is presented in its most condensed 
form: one consequence of this is, that such cases have 
frequently escaped the notice of those who have treated the 
problems to which they belong in a Geometrical manner. One 
celebrated and important oversight of this kind occurred in a 
problem which Newton solved in order to determine the orbit 
of a Comet. 
Having four lines given in position, it was required to draw 
a fifth line which should be cut by the other four into segments, 
having a given ratio to each other. Of this question Wren, 
Wallis, and Newton had given solutions, but when Zanotti, 
Boscovich and other Astronomers made use of them, employing 
the observed places of a Comet, the results were found greatly 
