168 Mr. Samuel Foſter sthis diſtance meaſured upon the Scale of equal parts, ſhall give 30 thenumber required: Therefore as 60 gr. to 3 5, ſo 48 gr. to 30.

But if it had been as the Sine 60 is to the number o; ſo the Sine ot48 to what? Here if you meaſure the number 90 with the Sine of 60,you ſhall find the number 90 to be the longeſt extent. So that now thelateral work muſt be upon the Line of Lines; I take therefore the Sineof 60 out of the Sines, and ſetting one foot of that extent upon thethe number 90 in the e qual parts, with the other foot turned about,open the other Leg, till I ſee the ſame foot only to touch ſome oneLine on the other Leg of the Sector, which ifſueth from the Center.

Note that vhat Line ſeever I begin to work with, I muſt E ſure always tocontinue and end with the ſame, but that Line on the ot her Leg, whichlieth net the inner edge of the Sektor, is almays moſi convenient.

Then again I take the Sine of 48, and keeping one foot of that extentcontinually upon the Line of Lines, I remove the ſame till J find theother foot juſtly to touch the former Line on the other Leg; and thenI ſee the other foot to ſtay upon the Line of Lines on the number 77 5,which is the number ſought..

4. A, tb Sine of 60, 4 to the Tangent of J gr. So the Sine of 50 te tbe

Tangent f what Ark?

Fu to know upon what Line to work, I take the Tangent ofIL 5Yęr. and ſet ii to the Sine of 60 gr. and becauſe I ſee the Sine of60 to be the greater, I know that the work muſt be done upon the Lineof Sines. And by the firſt Rule accordingly therefore I take the Tan-gent of 55 gr. and from the Sine of 60 J open the Sector to ſome oneLine on the other Leg of the Sector, which iſſueth from the Centeraccording to that extent; then I take the leaſt diſtance from the Sineof 5o to the former Line on the other Leg, and meaſuring it upon theTangent, J find it to reach to the Tangent of 51 4, which is the Tan-gent required. 3 5But if the terms were as the Sine of 40 is to the Tangent of 55 r.ſo is the Sine of 50 to what? Then meaſuring the Tangene of 55 fr.upon the Line of Sines, and finding the firſt term 40 to be leſler, Iſee that the work muſt be done upon the Line of Tangents: Where-fore take the firſt term the Sine of 40, and ſetting one foot of chat

extent