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INVESTIGATION of PORISMS. — 191 
the conditions by which that is brought about, they are of the 
nature of problems. 
17. In the preceding definition alfo, and the inftances 
from which it is deduced, we may trace that imperfeé de- 
{cription of Porifms which Pappus afcribes to the later geo- 
meters, viz. “* Porifma eft quod deficit hypothefi a theore- 
“mate locali.””. Now, to underftand this, it muft be ob- 
ferved, that if we take the converfe of one of the propofitions 
called Loct, and make the conftruction of the figure a part of 
the hypothefis, we have what was called by the ancients a Lo- 
cal Theorem. And again, if, in enunciating this theorem, 
that part of the hypothefis which contains the conftruction’ be 
fuppreffed, the propofition arifing from thence will be a Porifm ; 
for it will enunciate a truth, and will alfo require, to the full 
underftanding and inveftigation of that truth, that fomething 
fhould be found, viz. the circumftances in the conftruction, fup- 
pofed to be omitted. 
' Tuus, when we fay; If from two given points E and 
D, (fig. 4.) two lines E F and FD are infle@ted toa third point 
F, fo as to be to one another in a given ratio, the point F is in 
the circumference of a circle given in pofition: we have a Lo- 
Cus. 
Bur when converfely it is faid; If a circle ABC, of 
which the centre is O, be given in potent as alfo a point E, 
and if D be taken in the line E O, fo that the rectangle EO.OD 
be equal to the fquare of AO, the femidiameter of the circles 
and if from E and D, the lines EF and DF be infle@ed to 
any point whatever in the circumference ABC; the ratio of 
EF to D F will be a given ratio, and the fame with that of EA 
to AD: we have a local theorem. 
_ Awp, laftly, when it is faid; If a circle ABC be given 
in pofition, and alfo a point E, a point D may be found, fuch, 
that if the two lines E F and FD be infleéted from E and D to 
-any point whatever F, in the circumference, thefe lines ‘hall 
Y 2 + have 
