fore it is evident the work muſt be done upon the Line of Superficies,

Line of Lines, and enter it Parallelly between the Superficies and the

alieratiom o the Sector. 169extent upon the Tangent of 55. by turning the other foot of the Com-paſſes, I open the other Leg of the Sector, till the other foot do juſt-y touch ſome one Line on the other Leg of the Sector, ahich iflüuerhfrom the Center; then] take the ſecond term, the Sine of 30 gr. andſetting one foot of that extent upon the Scale of Tangents, untill theother foot being turned about, will juſtly touch the former Line onthe other Leg: I find the Compaſſes to ſtay upon the Tangent of59 2 gr. uhich is the Tangent required.*

Tüte like may be done upon the Sines and Secants, or Tangents orSecants, when any ſuch queſtion ſhall be required. And the like mayde done in Tangents and Numbers, or equal parts, by the joynt uſeof theſe two Scales, which is frequent in Menſurations of uprighebuildipgs. i a i 5

5. Having three numbers, to find a Furth in duplicated proportion.

1 work is performed by the two Scales of Superficies and Linesjoyntly uſed. Let the example be as 22 to 24. ſo 64 to hae num-ber in a duplicated proportion? Here the two firſt terms are of onekind, and the two latter will therefore be of one kind. Whereforeto know upon what Scale to work, it will be beſt to change the placesof the ſecond and third terms, that ſo the firſt and third may be of onekind, as allo the ſecond and fourth. Thus as 32 to 64, ſo 24 to what?Now in this diſpoſition of terms you muſt firſt meaſure 32(taken outof the equal parts) upon the Line of Superficies, and ſo doing youhall find it fall far ſhort of the number 64, the ſecond term; there-

lo chat Itake 3 2 from the Line of equal parts, and putting one footof that extent upon 64 in the Line of Superficies; I thereby open theSector to ſome one Line on the other leg of the Sector, uhich iſſuethfrom the Center. Then again, Itake the third number 24 out of the

former Line on the other Leg(in che manner that hath been ſhewedbefore) and J find it to ſtay at 36 in the Line of Superficies: So thatIconclude, 28 3 2 to 64, ſo 64 to 36 in duplicated proportion. Thatis, ſo is the quare of 64(namely 8) to the ſquare root of 36(namely6) in a ſimple proportion. N