The Knew

It is fcarce poffible to improve the Practice without Theory, and reciprocally to be Mafter of the Theory without Practice, as there is in every Art a great Number of Circumftances relative to the Materials, to the Inftruments, and to the Operation which can be learned only by ledge of the Ufe. It is the Business of Practice to point out the Difficulties, and to Theory abfurnish the Phenomena. It is the Bufinefs of the Theory to explain the folutely neceflary to Phenomena, to remove Difficulties and to open the Road to further Im- every Artift. provement; from whence it follows, that only fuch Artists who have a competent Knowledge of the Theory, can become eminent in their Profeffion.

But unfortunately fuch is the Influence of Prejudice in this Country, that Artifts, Mechanicks, &c. are confidered as incapable of acquiring any Knowledge in the Principles of their refpective Profeffions, and our Youth destined to receive a liberal Education, are taught to think it beneath them to give a conftant Application to Experiments and particular fenfible Objects, for to practice or even to study the mechanic Arts, is to stoop to Things whose Research is laborious, the Meditation ignoble, the Expofition difficult, the Exercise dishonourable, the Number endlefs, and the Value inconfiderable. Prejudice which has debased an useful and estimable Class of Men, and peopled our Towns with arrogant Reasoners, ufelefs Comtemplators, and the Country with idle and haughty Landlords.

The Judicious, fenfible of the Injustice and of the fatal Confequences attending this Contempt for the mechanic Arts, the Industry of the People and Establishment of Manufactures being the most affured Riches of this Country, have come to the Refolution that the Juftice which is due to the Arts and Manufactures, fhall be rendered them; that the mechanick Arts shall be raised from that State of Meanefs, which Prejudice has hitherto kept them; that the Protection of the Noblemen and Gentlemen of Fortune shall secure the Artists and Mechanicks from that Indigence in which they languish, who have thought themselves contemptible because they have been despised; that they shall be taught to have a better Opinion of themselves, as being the only Means of obtaining from them more perfect Productions.

A School of mechanic Arts is established, where all the Phenomena of The Estathe Arts are collected, to determine the Artists to study, teach the Men blithment of a School of of Genius to think usefully, and the Opulent to make a proper Use of mechanic their Authority and their Rewards. There the Artiffs receive the In- Arts, ftructions they stand in need of, they are delivered from a Number of Prejudices, particularly that from which scarce any are free, of imagining that their Art has acquired the last Degrees of Perfection; their narrow Views expofing them often to attribute, to the Nature of Things, Defects which arife wholly from themselves; Difficulties appearing to

them unfurmountable, when they are ignorant of the Means of removing them. They are rendered capable of reflecting and combining, and of discovering, in short, the only Means of excelling; the Means of faving the Matter, and the Time, of aiding Industry, either by a new Machine, or by a more commodious Method of Working. There Experiments are made, to advance whofe Succefs, every one contributes, the Ingenious direct, the Artist executes, and the Man of Fortune defrays the Expence of the Materials, Labour and Time. There Inspectors are appointed who take Care that good Stuff is employed in our Manufactures, and that they are properly fupplied with Hands; that each Operation employs a different Man, and that each Workman fhall do, during his Life, but one Thing only; from whence it will refult, that each will be well and expeditiously executed, and the best Work will be also the cheapest. Thus, in a fhort Time, our Arts and Manufactures will be brought to as great a Degree of Perfection, as in any other Part of Europe.

GENERAL CONCLUSION.

Such is the Plan of the new Scene of useful and agreeable Knowledge calculated for all Stations in Life, which the Nobility and Gentry of the Kingdom of Ireland, pursuant to their Refolution of the 4th of February 1768, have opened to Youth, in the Drawing-School established under their immediate Inspection. Encouraging Men of Genius and Education, from all Parts, to appear as Teachers, inviting the Artists and Connoifieurs to devote their Attention to excite the Emulation of the Pupils by adjudging and diftributing the Premiums granted to engage them to advance more and more their Studies to the Point of Perfection, and taking under their Patronage fuch young Citizens favoured by Nature more than by Fortune, who difcover happy Difpofitions and fuperior Talents for the Service of their Country.

ERRATA.

Page LXIII Line 15, for the Centrifugal Force diminishes the Cen trifugal Force, read the Centrifugal Force diminishes the Centripetal Force.

400

94/

Page LXXXV Line 41, for this Expreffion 69 for (a), 70 for (b), read, this Expreffion, for (a) 70, for (b) 69.

The ELEMENTS of EUCLID. BOOK I.

I

Fig.2

Fig.1

DEFINITIONS.
.I.

A Point, is that which has no parts, or which hath no magnitude. Fig. 1.

IN this definition, as well as in the second and fifth, Euclid fimply explains the manner of conceiving the first objects of Geometry, a Point, a Line, and a Superficies; be does not demonftrate that there are fuch objects in the class of real beings. Thefe notions, though very useful in geometry, are only abstractions which are not to be realifed, by being reprefented as exifting independent of the mind, where they took their rife. There are no mathematical points in nature, (at least what Euclid says does not prove it); but there exift things which have extenfion, which may be treated as fimple marks without magnitude, as often as they are confidered not as compofed of parts, but merely as the limits of fome other magnitude. Thus, when it is required to measure the distance of two ftars, the Aftronomer proceeds, as if thofe ftars were indivifible points: and he is in the right; fince be does not propofe to determine their magnitude, but the diftance that feparates them, of which they are looked upon as the terms. The fame is to be underflood with respect of the other notions of this kind. We reprefent under the form of a line, or of a length without breadth, every magnitude whofe length alone is the object of our confideration, whatever may be its breadth, its depth, or its other qualities. The imagination, always difpfed to transform into realities what has none, forms of thofe abftractions a class of beings which feem to exift independent of the mind. The Geometer has a right to adopt those beings, as they may ferve to render his fpeculations on magnitude, confidered in different points of view, more intelligible; but it is by no means allowed to him, to form wrong notions as to their origin and their real use.

II.

A Line is Length without breadth. Fig. 2.

A

THE Extremities of a Line, are points (A, B,). Fig. 3.

IV.

A ftraight Line, is that which lies evenly between its extreme points (A, P,). Fig. 3.

This definition is imperfect, fince it prefents no effential character of a ftraight line; for which reafon, Euclid could make no use of it: it is no more quoted in the body of the work. He is obliged to have recourse to other principles (for example, to the 12th axiom) as often as he has occafion of employing truths, which depend on a perfect definition of a straight line.

ས.

A Superficies, is that which hath only length and breadth. Fig. 4.

VI:

The Extremities of a Superficies, are lines (AB, CD, A C, BD,). Fig. 4.

VII.

A Plare Superfices, or fimply a Plone, (AD) is that which lies evenly between its extremities (AB, CD, AC, BD,). Fig. 5.

This definition is liable to the fame exceptions as the fourth.

A

DEFINITION S.

VIII.

Plane Angle, is the inclination of two lines (AB, BC,) to one another, which meet together, and which are fituated in the fame plane. Fig. 6.

IX.

A Plane Rectilineal Angle, is the inclination of two straight lines to one another. Fig. 6.

N. B. When feveral angles are at one point B, any one of them is expressed by three letters, of which the letter that is at the vertex of the angle, that is at the point in which the ftraight lines that contain the angle meet one another, is put between the other two letters, and one of these two is fomewhere upon one of thofe ftraight lines, and the other upon the other line.

X.

When a ftraight line (AB) standing on another ftright line (CD) makes the adjacent angles (ABD, ABC,) equal to one another, each of the angles is called a right angle; and the ftraight line (AB) which stands on the other (CD) is called a perpendicular. Fig. 7.

XI.

An Obtufe Angle, (ABC) is that which is greater than a right angle (EBC). Fig. 8.

XII.

An Acute Angle, (ABC) is that which is less than a right angle (EBC). Fig. 9.

XIII.

A Term or Boundary, is the extremity of any magnitude.