For the Situation of the Degree observed, whether Above or Below.

From the given Angles, as above, (the Angle P being counted in the Æquator, not from the Right Ascension of the Significator, but from that Degree which hath, oftentimes, been taken notice of, as that at the Medium or Imum Cæli) I seek for the Angle O or H.

And moreover, in the other Triangle, R P, the very Elevation of the Pole above the Horizon of the Promissor : At this Elevation of the Significator, if you observe that Degree

Occidental}you will gain the Obliquez Religion. } from which

take the given Ark of Direction, and the Remainder will be the Oblique

$ Afcenfion, } to which the Degree of the Ecliptick anşi

Defcenfion, S swers, but it must be counted from the Elevation of the Pole above the Horizon of the Promisor) and is the very Place, to which the Significator will come, by this Ark of Direction given.

Fig. L.
I. II.
III. IV.

ANCILLA MATHEMATICA

V E L,

Trigonometria Practica.

SECTION V.

OF

SCIOGRAPHIA,

OR

DI ALLING.

CH A P. I.

Of Dialling in general. F the Mathematical Sciences, I know none more Inge nious and Useful then This of the Description of Sun

Dials upon all sorts of - Plains howsoever situate : Neither is there any thing that draws more Admiration from all knowing Men; then to see streight Lines drawn upon a Plain at Unequal Distances to measure out exactly the Equal Divifions of the Time of an Artificial Day : For, although the Sun appears in different places of Heaven, according to the different Seasons of the Tear ; yet, the same Streight Lines, do ftill determine the same Hour, at all those different Seafons. And as this Science is of such

Aaa

Excellency Excellency and Use, I shall in this section, briefly Thew (and that by an A tifice not usually practiced) how such Hour-Lines may be described upon all Plains in any part of the World: And that by Trigononietrical Calculation, as well as by projecting the Circles. of the Globe upon a Plain.,

7 Now, All Plains have a particular respect to fome Point, in the Latitude of tirat Place in which they stand : Wherefore, some particular Tluce must be assigned for Exemplifying the same in all the Varieties. We will therefore take London, the Metropolis of England (which is situate in si deg. 30. in. of North Latitude) for our Examples following:

γ) Η Υ Ο .

CHA P. IT:

10 Of the Diversity of Plains, upon which Hour-lines may be described LL Plains upon which Sun-Dials may be made, in any La-

titude or Place of the World, are situate either Parallel Perpendicular > To the Horizon of that Oblique Place (or Country) in which they are made.. And, of these

feverally, I. A Plain' that lies Parallèl (or Level) to the Horizon, Is called an Horizontal Plain, for the Latitude of that Place in which it is to ftand.

II. Of Plains that are Perpendicular, or Erect, to the Horizon; . there are several Varieties. For, of such Plains, if the Face there of doth directly behold the

East Welt

Point of the Horizon of the Place North

South
wherein they stand, They are then called,

Éaft
West

Erect, Dire& Plains.'
North
South

Bat