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COMPRISING

AN ACCURATE AND POPULAR VIEW

OF THE PRISBKT

IMPROVED STATE OF HUMAN KNOWLEDGE.

BY WILLIAM NICHOLSON,

Author and Proprietor of the Philosophical Journal, and various other Chemical, Philosophical, and
Mathematical Works.

ILLUSTRATED WITH

UPWARDS OF 150 ELEGANT ENGRAVINGS,

BY

MESSRS. LOWRYAND SCOTT.

VOL. III. E....I.

LONDON:

PRINTED BY C. WHITTINCHAM,
Goswell Strut;

FOR LONGMAN, HURST, REES, AND ORME, PATERNOSTER-ROW;

J. JOHNSON; R. BALDWIN i T. AND C. RIVINCTON l A.STRAHAN; T. PAYNE; J. STOCKDALE; SCATCHERD
AND LETTERMAN; CUTHEIX AND MARTIN; R. LEA; LACKING TON AND CO., VERNOR, HOOD, M
EGAN ; J. BUTTERWOKTH , J. AND A. ARCH; CADELL AND DAVIES; S. BAGSTER; BUCK, LARRY,
AND KINGSBURY; J. HARDING; J. MAWMAN; P. AND W. WYNNE ; SHERWOOD, NEELY, AND JONES;
B. C. COLLINS ; AND T. WILSON AND SON.

1809.

LIST OF PLATES

IN

VOL. III.

The Binder is requested to place the Plates in the following order, taking care to make all the Plates face an even Page, unless otherwise directed.

Aves VI. middle of Sheet Q. VII. middle of Sheet E e.

Fortification, at the end of Sheet O.

Galvanism, opposite the article Gamboge.

Geometry, opposite the article Georgic.

Glass Blowing, at the end of Sheet Y.

Gothic Architecture, opposite the article Gouania.

Heraldry I. and II. middle of Sheet G g.
Horology, middle of Sheet I i.
Hydraulics, at the end of Sheet K k.

Iron Foundry, at the end of Vol. HI.

Mammalia X. to face the first article, Ellipsis.

XI. at the end of Sheet D.

XII. at the end of Sheet G.

— XIII. at the end of Sheet I.

XIV. at the end of Sheet L.

Miscellanies V. at the end of Sheet M. VI. at the middle of Sheet D d.

VII. at the middle of Sheet M ra.

Pisces IV. opposite the article Gymnotus.

Rowntree's Fire Engine

double barrelled Pump Engine 1 °PP°5rte Ae artide

Trevithick's Pressure Engine J Engineer.

THE

BRITISH ENCYCLOPEDIA.

ELLIPSIS.

"C'LLIPSIS, in geometry, a curve line re-*-i turning into itself, and produced from the section of a cone by a plane cutting both its sides, but not parallel to the base. See Conic Sections.

The easiest way of describing this curve, in piano, when the transverse and conjuaxesAB, ED, (Plate V. Miscell. fig. 1.) are given, is this: first take the points F, t , in the transverse axis A B, so that the distances C F, C/, from the centre C, be each equal to y'AC — CD; or, that the lines EDD, be each equal to AC; then, having fixed two pins in the points 1',/, which are called the foci of the ellipsis, take a thread equal in length to the transverse axis A B; and fastening its two ends, one to the pin F, and the other to /, with another pin M stretch the thread tight; then if this pin M be moved round till it returns to the place from whence it first set out, keeping the thread always extended so as to form the triangle F M/, it will describe an ellipsis, whose axes are A B, D E.

The greater axis, A B, passing through the two foci Vi. is called the transverse axis; and the lesser one D E, is called the conjugate, or second axis : these two always bisect each other at right angles, and the centre of the ellipsis is the point C, where they intersect. Any right line passing through the centre, and terminated by the curve of the ellipsis on each side, is called a diameter; and two diameters, which naturally bisect all the parallels to each other, bounded by the ellipsis, are called conjugate diameters. Any right line, not passing through the centre, but terminated by the ellipsis, and bisected by a diameter, is VOL. III.

called the ordinate, or ordinatc-applicatc' to that diameter; and a third proportional to two conjugate diameters, is called the lo tus rectum, or parameter of that diameter which is the first of the three propertionals.

The reason of the name is this: let B A, E D, be any two conjugate diameters of an ellipsis (fig. 2, where they are the two axes) at the end A, of the diameter A B, raise the perpendicular A F, equal to the latiis rectum, or parameter, being a third proportional to AB, ED, and draw the right line B F; then if any point P be taken in BA, and an ordinate PM be drawn, cutting B F in N, the rectangle under the absciss A P, and the line P N will be equal to the square of the ordinate P M. Hence drawing N O parallel to A B, it appears that this rectangle, or the square of the ordinate, is less than that under the absciss A P, and the parameter A F, by the rectangle under AP and o F, or N O and O F; on account of which deficiency, Apollonius first gave this curve the name of an ellipsis, from Ixxhiw, to be deficient.

In every ellipsis, as A E B D, (fig. 2), the squares of the semi-ordinates MP, mp, are as the rectangles under the segments of the transverse axis APxPB, ApxpB, made by these ordinates respectively ; which holds equally true of the circle, where the squares of the ordinates are equal to such rectangles, as being mean proportionals between the segments of the diameter. In the same manner, the ordinates to any diameter whatever, are as the rectangles under the segments of that diameter.

As to the other principal properties of B

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