The elements of geometrie of the most auncient philosopher Euclide of Megara. Faithfully (now first) translated into the Englishe toung, by H. Billingsley, citizen of London. Whereunto are annexed certaine scholies, annotations, and inuentions, of the best mathematiciens, both of time past, and in this our age. With a very fruitfull præface made by M. I. Dee, specifying the chiefe mathematicall scie[n]ces, what they are, and wherunto commodious: where, also, are disclosed certaine new secrets mathematicall and mechanicall, vntill these our daies, greatly missed

* 1.14 Inclination of a plaine superficies to a plaine superficies, is an acute an∣gle contayned vnder the right lines, which being drawen in either of the plaine superficieces to one & the self same point of the cōmon section, make with the section right angles.

Suppose that there be two superficieces ABCD & EFGH,

[illustration]

and let the superficies ABCD be supposed to be erected not perpendicularly, but somewhat leaning and inclining vnto the plaine superficies EFGH, as much or as litle as ye will: the cōmon terme or section of which two superficieces let be the line CD. From some one point, a•• from the point M assigned in the common section of the two superficieces, namely, in the line CD, draw a perpendicular line in either superficies. In the ground superficies EFGH draw the line MK, and in the su∣perficies ABCD draw the line ML. Now if the angle LMK be an acute angle, then is that angle the inclination of the su∣perficies ABCD vnto the superficies EFGH, by this defini∣tion, because it is contained of perpendicular lines drawen in either of the superficieces to one and the self same point being the common section of them both.

Notes

• * 1.1

  Fourth diffi∣nition.