we think it not itn proper to relate 'em as he has laid 'cm 
down himfelf. 
10. An unknown Line is^ always t-erminated in an 
unknown Point 5 hence to avoid conf ifion, the unknown 
Points ought to be Denoted with the Lft Letters of the 
Alphabet &c. to diftinguifh cm from the 
known Points &c. and if there is occafion, 
one and the fame Point may be denoted with twoLetters» 
when a known and unknown Line concur in it.. 
Firjl Deftnitton. 
Additive Ratio is that whofe Terms are difpos'd to 
Addition, that is, to Compofition. Subtraffive Ratio is 
that whole Terms arcdifpos'd to SubtcadioUj that is, t© 
Divifion.. 
I i } 1 
^ h dc c 
Let the Line a r, be divided in the Points and 
the Ratio between ab^ and ^at, is Additive 5 becaufe the 
Terms aby and bx^ compofethe whole ax-^ but the. 
Ratio between ax and i'X' is Subtraffive^ becaufe the 
Terms and^^, differ by the Line ab. 
20. The fame order of the Letters which is in the 
Figure,ought to be kept in your Analyfis, that fo by meer 
Inipedionyou may know whether the Ratio is Additivr 
or Sfsbtra^iive ; and confequently whether you ought 
to Compofe or Divide, 
3 p. When you are to argue by Proportions , and the. 
Proportion lies in a Right Line , you have no other 
way to proceed on but by Compofition or Divifion : 
Therefore if both Ratios are Additive, yoia muft argue 
by Compofition 5 if both Subtradive^ by Divifion; fo 
as always to ufe that way of arguing which is the fitteft 
for the prefervation of thofe Terms that are known 5 but 
when» one Ratio is Additive and th'other Subtradive 
the Additive muft either be made Subtraaive/>r the Sub^ 
tradfeive Additive 5 Now this change it wrought by 
cepeating either Tcrxn.^ Pog 
