PRO
Call. Or to the right Sine of double the Angle of Eleva- tion, the whole Sine and the fourth part of the Amplitude, find a fourth Proportional. This will be the Radius IQ_or j the double whereof A D is the Altitude required. 'PROJECTION, in Mechanics, the Adion of giving a Projectile its Motion. See Projectile.
If the Direction of the Force whereby the Projectile is put in motion, be perpendicular to the Horizon; the Pro- jection is faid to bcFerpcndicular : If parallel to the apparent Horizon, it is faid to be a horizontal Projection : If it make an oblique Angle with the Horizon, the Projection is ob- lique. See Oblique.
The Angle A RB, (Tab. Mechanics, jfg.47.) which the Line of Direction A R makes with the horizontal Line A B, is call'd the Jingle of Elevation of the Projectile.
Projection, in Peripeclive, the Appearance or Re- prefentation of an Objecl on the perfpective Plane. See Plane.
The Projection, e.gr. of a Point, as A, (Tab. Perspec- tive, jig 1.) is a Point a thro which the Optic Kay O A paffesfrom the objective Point, thro' the Plane, to theEyej or the Point a wherein the Plane cuts the optic Ray.
And hence is ealily conceiv'd what is meant by the Pro- jection of a Line, a Plane, or a Solid. See Perspective.
Projection of the Sphere in 'Piano, isa Reprefentation of the Icveral Points or Places of the Surface of the Sphere, . and of the Circles dcfcribed thereon, or of any affign'd parts thereot, fuch as they appear to the Eye fituate at a given diilance, upon atranfparent Plane placed between the Eye and the Sphere. See Sphere.
For the Laws of this 'Projection, fee Perspective; the Projection of the Sphere being only a particular Cafe of Peripeclive.
The principal Ufe of the Projetlion of the Sphere is in the Conllruction of Plamfpheres, and particularly Maps and Cherts 5 which are faid to be of this or that Projection, according to the feveral Situations of the Eye, and the per- fpective Plane with regard to the Meridians, Parallels, and other Points and Places to be reprefented. See Plani- sphere, ci/C.
The moil ufual ProjeBion of Maps of the World is that on the Plane of the Meridian, which exhibitsa right Sphere; the firtt Meridian being the Horizon. The next is that on the Plane of the Equator, wherein the Pole is in the Cen- tre, and the Meridians the Radii of a Circle, %$c. This re- prefents a parallel Sphere.
See the Application of the liottrine of the Projection of the Sphere, in the Conflruclion of the various kinds of Maps, under the Article Map.
'the 'Projetlion of the Sphere is ufually divided into Or- thographic and Stenographic 3 to which may be added Gnombnic.
OrthographicVRoj-ECTiou, is that wherein the Superfi- cies of the Sphere is drawn on a Plane, cutting it in the Middle 5 the Eye being placed at an infinite dillance verti- cally to one of the Hemifpheres. See Orthographic.
Zaies and Properties of the Orthographic Projection.
1. The Rays by which the Eye at an infinite diflance perceives any Object, are parallel.
2. A right Line perpendicular to the Plane of the Pro- jetlion is projecied into a Point, where that right Line cuts the Plane of the 'Projetlion.
3. A rightLine, as A B, or CD, (fig. 17.) not perpendi- cular, but either parallel or oblique to the Plane of the 'Projetlion, is projected into a right Line, as E F, or G H, and is always comprehended between the extreme Perpen- diculars AF, and BE.
4. The 'Projetlion of the right Line A B, is the greater! when A B is parallel to the Plane of the Projetlion.
5. Hence it is evident, that a Line parallel to the Plane of the Projetlion, is projecied into a right Line equal to itfelf; hut if it be oblique to the Plane of the Projetlion, 'tis pto- jecled into one which is lefs.
6. A plane Sutface as A BCD, (fig. 18.) atright Angles to the Plane of the Projetlion, is projecied into that right Line;e.£?\ AB.inwhich it cuts the Plane of the Projetlion.
Henceit is evident, that the Circle B C A D, ftanding at right Angles to the Plane of the Projetlion, which paflVs thro' its Centre, is projecied into that Diameter A B, in which it cuts the Plane of the Projetlion.
It is likewife evident, that any Arch, ascc, is projecied into equal to C a, C b, which is the right Sine of that Arch; and the complimental Arch c A is projecied into oA, the verfedSine of the fame Arch C C.
7- A Circle parallel to the Plane of the Projetlion, is projecied into a Circle equal to itfelf; and a Circle oblique «o the Plane of the Projetlion, is projecied into an El-
lipfis.
Siereographic Projection, is that wherein the Surface and Circles of the Sphere are drawn upon the Plane of a
(88p)
great Circle, the Eye being Stereographic.
PR O
the Pole of that Circle. See
Properties of the Stereographic Proj ectioh.
1. In this Projetlion, a right Circle is proiefled into a Line of half Tangents.
2. The Reprefentation of a right Circle, perpendicularly oppofed to the Eye, will be a Circle in the Plane of the Projetlion.
3. The Reprefentation of a Circle placed oblique to the Eye, will be a Circle in the Plane of the 'Projetlion.
4. If a great Circle be to be projefled upon the Plane of another great Circle, its Centre will lie in the Line of Mea- fures, dillant from the Centre of the primitive by the Tan- gent of its Elevation above the Plane of the primitive.
5. If a leffer Circle, whole Poles lie in the Plane of the Projetlion, were to be projeQed; the Centre of its Re- prefentation would be in the Line of Meafures, diflant from the Centre of the primitive, by the Secant of the leffer Circles diflance from its Pole, and its Semi-diameter or Ra- dius, be equal to the Tangent of that diflance.
6. If a leffer Circle were to be projecied, whofe Poles lie not in the Plane of the Projetlion, its Diameter in the Projetlion, if it falls on each fide of the Pole of the Pri- mitive, will be equal to the Sum of the half Tangents of - its greateft and neareft Diflance from rhe Pole of the Pri- mitive, fet each way from the Centre of the Primitive in the Line of Meafures.
7. If a leffer Circle to be projecied, fall entirely on one fide of the Pole of the Projetlion, and do not encompafs it' 3 then will its Diameter be equal to the difference of the half Tangents of its greateft and neareft diflance from the Pole of the Primitive, fet off from the Centre of the Pri- mitive one and the fame way in the Line of Meafures.
8. In the Stereographic Projetlion, the Angles made by the Circles of the Surface of the Sphere, are equal to the Angles made by their Representatives in the Plane of their Projection.
Gnomonic Projection of th: Sphere, fee GnomoniC Projection.
Project ion of Globes, i$c. fee Glop,e,£-?c. Projection, in Alchytny, the calling of a certain, imaginary Powder, call'd Powder of Projetlion, into a Cru- cible, or other Veffel full of prepared Metal, or other Mat- ter, which is to be hereby tranfmuted into Gold. Se« Pokvder (/Projection.
Powder of Projection, or of the Philofopher's Stone, is a Powder iuppofed to have the Virtue of changing any quantity of an imperfeel Metal, as Copper, or Lead, into a more perfeel one, as Silver or Gold; by the admix- ture of a little quantity thereof. See Transmutation.
The Mark to which the Alchymitls direel all their En- deavours, is to find the Powder of Projetlion; which every one of 'em has been within an Ace of, an hundred times. See Alchymy.
For the Characters, Properties, Virtues, &c. of this Powder, fee Philosopher's Stone.
Projection in'Building, fee Projecture. PROJECTIVE dialling, a Method of Drawing, by a Method of Projection, the true Hour-Lines, Furniture of Dials, cifc. on any kind of Surface whatfoever, without any regard had to the Situation of thofe Surfaces, either as to Declination, Reclination, or Inclination. See Dialling.
PROJECTURE, in Architecture, the Out-jetting, or Prominency, which the Mouldings and Members have, be- yond the Naked of the Wall, Column, &c. See Naked, Column, &c.
Thefe the Greeks call Ecphoree, the Italians Spcrti, the French Sallies, our Workmen frequently Sailings over, and the LatinsProjetla, from projicio, I cafl forward; whence the Englijb, Projeclure.
Vitruvius gives it as a general Rule, that all the projec- ting Members in Buildings have their Projeflltres equal to their Heights : But this is not to be underflood of the par- ticular Members, or Mouldings, as Dentils, Corona's, the Fafciae of Architraves, the Abacus of the Tit/can and 3)o- ric Capital, t£c. but only of the Projeclures of entire Cor- nices, $$c. See Cornice, cevc.
The great Point of Building, according to fome modern Architects, confifls in knowing how to vary the Proportions of Projetlures, &c. agreeably to the Circumflances of the Building: Thus, fay they, the nearnefs and remotenefs making a difference in the View, requires different Pro- jetlures; but 'tis evident the Antients had no fuch Intention. See Proportion.
The Projeclure of the Bafe and Cornice of Pedeftals, M. Perrault obferves, is greater in the antique than the modern Buildings by one third; which feems to follow, in good meafure, from the Antients proportioning this Projeclure to the height of the Pedeftals; whereas the Moderns make the projeclure the fame in all the Orders, tho' the height of the Pedeflal be very different. 10 R Th?
