1 6

b

IS

The use of the Square in

be reduced to three wayes according as one.of these three, eitherthe Radius, Sine, or Tangent, doth lead in the Proportion, thethree way es are these :

1 As the radius, is to a tangent , So is a fine to a Tangent .

2 As a fine, is to a tangent, So the Radius is to another

tangent.

3 As a tangent, is to the radius', So another tangent, is to a

sine.

but this variety is not all, for each of these three wayes if

fubjcSl to variation, and that upon this occasion. _ Vpon

the square toe have no tangent greater then the radius,or tangent°f 45 degrees. Wherefore the proportion Musi be so contrived,as that no tangent greater then of 4^ gr. be ingredient into it •

To that purpose serves this general direStion, namely, -- If

the tangent which is copartner,in the proportion with the sine, begreater then of 45 gr. (alway provided that the two tangentsdoe neverft and immediately together, which if they doe, may bebrought into frame by transposition or alteration of the middleterm.) Then, In the two sirii wayes the radius and sine mnsichange places ; and for the two tangents musi be taken the tan-gents of their complements ; In the third way,the co-tangents ofthe third and first terms must remove into the first and thirdplaces. J

Tofiew this more particularly in the 3 former wayes,

In the first,

If the tangent required in the fourth place prove greater then°f 45 g r ' (™bicb how to discover is stewed hereafter) then bythe former direction this alteration must be made.

As the fine in the third place, is to the cotangent in the st'second,

So is the radius in the first place, to the cotangent of^ efourth.

In the Second, >

If the tangent in the second place , be greater then of 4§then by the former direttion this proportion must be th#changed.

As the radius in the third place, is to the cotangent oft^ esecond.

So is the fine in the first placebo the co-ungent oftbefM^