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Fig. L.




Trigonometria Practica.







Of Dialling in general.

F the Mathematical Sciences, I know none more Inge nious and Useful then This of the Defcription of SunDials upon all forts of Plains howfoever fituate: Neither is there any thing that draws more Admiration from all knowing Men; then to fee ftreight Lines drawn upon a Plain at Unequal Diftances 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 fame Streight Lines, do ftill determine the fame Hour, at all thofe different Seafons. And as this Science is of fuch



Excellency and Ufe, I fhall in this Section, briefly fhew (and that by an Artifice not ufually practiced) how fuch Hour-Lines may be defcribed upon all Plains in any part of the World: And that by Trigonometrical Calculation, as well as by projecting the Circles. of the Globe upon a Plain..


Now, All Plains have a particular refpect to fome Point, in the Latitude of that Place in which they ftand: Wherefore, fome particular Place must be affigned for Exemplifying the fame, in all the Varieties. We will therefore take London, the Metropolis of England (which is fituate in 51 deg. 30 in. of North Latitude) for our Examples following.


Of the Diversity of Plains, upon which Hour-lines may be: defcribed.


Atitude of Place of the World, are fituate either

LL Plains upon which Sun-Dials may be made, in any La-

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Place (or Country) in which they are made.. And, of these feverally.

I. A Plain that lies Parallel (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 feveral Varieties. For, of fuch Plains, if the Face there-of doth directly behold the





Point of the Horizon of the Place

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But if fuch Erect Plains do not behold the Direct Eaft, Weft, North or South Points of the Horizon, they then will behold


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III. Of Plains that lie Obliquely to the Horizon: (fuch as the Roofs of Houfes, the Cooping of Walls, &c.) are called Reclining Plains. And if fuch Plains do behold the direct

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called Direct Eaft, Weft, North or South Plains: Reclining from the Zenith of the Place in which fuch Plain ftands.

But if fuch Reclining Plain doth not refpect the true Eaft, Weft, North, or South Points, then they will lie open either to the South-East 2

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And these are all the Varieties of Plains, upon which Haur-Lines, may be defcribed.

Only note,] That all Reclining Plains whatsoever; whether Direct or Declining, have Two Faces; the Upper-Face, which beholds the Zenith of the Place, is called the Reclining Plain And the Under-Face, which beholds the Horizon of the Place, is called the Incliner: And one and the fame Dial ferves for both Places.

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How to find the Situation of any Plain, in refpect of Declination and Reclination, in any Latitude.

I. To find the Reclination.

Fig. LI.. Definition. the Arch of that Vertical or Azimuth Circle which

is perpendicular to the Reclining Plain, comprehended between the Zenith of the Place and the Plain.

To find which, let A B C D reprefent fuch a Reclining Plain : Draw, first, thereon, by help of a Ruler and Quadrant, a Right Line G H, parallel to the Horizon of the place; which fhall be the Horizontal Line of the Plain.. Crofs this Line G H, with another Right Line K S at Right-Angles to it; which Line K S fhall be the Vertical Line of the Plain.

To this Line K S, apply a freight Ruler KL: And to that end of it which lyeth clear of the Plain, as at L; apply a Quadrant OE P, having a Thrid and Plummet hanging from the Centre. Then fee what number of Degrees of the Quadrant are contained between O and E; for fo much doth that Plain Re cline from the Zenith of the Place; and is the Reclination of the Plain.

II. To find the Declination.

Definition. THE Declination of a Plain, Is an Arch of the Ho

rizon comprehended between the Pole of the Plain, and the Meridian of the Place. Or,. It is the diftance of the Plain it felf, from the Prime Vertical Circle, or Azimuth of East or West.

To find out the Declination of any Plain, there are required two Obfervations, to be made by the Sun, both at the fame Time, as near as may be.The Firft, Of the Horizontal Distance of the Sim, from the Pole of the Plain.---And the Second, Of the Sim's. Altitude.

I. To find the Horizontal Distance..

Apply one Edge of the Quadrant to the Horizontal Line of the Plain, fo that the other may be Perpendicular to it; and let the Limb of the Quadrant be towards the Sun. The Quadrant thus


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