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The Analogie or Proportion is,
As the Sine of the Hypotenuse A B 30 degr. is to the Radius, So is the Sine of the Base A C 27 degr. 54 min. to the Sine of the Angle at the Perpendicular B.
HAving drawn your Quadrant, take from your Line of Chords 30 degr. the quantity of the Hypotenuse, and set them upon your Quadrant from B to 2; also take 27 degr. 54 min. the quantity of the Base, from your Chords, and set them from B to K, and draw the Lines 2 6 and K H, both parallel to the Line B A. Then taking in your Compasses the distance A 6, set one foot of them in C, and with the other de∣scribe the Arch Z, and draw the Line A X, so that it onely touch the Arch Z. Then taking in your Compasses the di∣stance A H, set one foot upon the Line A C, moving it along till the other foot, being turned about, will onely touch the Line A Z; and where the point of the Compasses resteth up∣on the Line A C, which it will doe at e, through that Point draw the Line o e parallel to B A. So shall B o, being mea∣sured upon your Line of Chords, give you 69 degr. 22 min. the quantity of the enquired Angle at B.