Page:Encyclopædia Britannica, Ninth Edition, v. 6.djvu/752

716 ginger, lime-juice, vinegar, the leaves of Bergera Kcenig d (the curry-leaf tree), mace, mangoes, nutmeg, pepper, saffron, salt, tamarinds, and turmeric. The annexed table shows the composition of four kinds of Indian curry powder:—

Lbs 02. Black pepper 2 1 1 g Cardamoms 2 A Chillies 1 2 1 Q Cinnamon 2 A Coriander seeds 20 12 3

Cumin seeds 1 2 i Fenugreek. . 1 i Garlic 2 1 $

Ginger 2 2 i Q Mustard seed 1 1 I Turmeric 4 2 q Poppy seed 2 2

The cumin and coriander sesds are generally used roasted The various materials are cleaned, dried, ground, sifted, thoroughly mixed, and bottled. Upwards of forty different methods of preparing curry are given in the Indian Domestic Economy and Receipt Book, 2d ed. Madras, 1850.  CURRYING. See.  CURTIUS, or, the hero of two legends connected with the part of the Roman forum called the Lacus Curtius, which appears to have once been a marsh, and where sacrifices were regularly offered. The first legend makes him the leader of the Sabine army in a battle with the Romans under Tullus Hostilius. To escape from the attack of the Romans he was forced to ride into a swamp which occupied the spot, hence called the Lacus Curtius. The second legend, which is dated, tells how a gulf suddenly appeared in the forum, according to one account riven by a thunder-bolt, and the aruspices declared that it would never close till what was dearest to Rome was thrown therein. At this announcement a noble youth, Mettus Curtius, came forward, declaring that her citizens were the most valuable possessions of the city ; and, armed and on horseback, he leapt into the chasm, which forthwith closed over his head.  CURTIUS,, the celebrated biographer of Alexander the Great. Of his personal history nothing whatever is known with certainty, some fixing his epoch in the, others as far down as the mediaeval age, but most critics in the time of Vespasian. Niebuhr held him to be a contemporary of Septimius Severus. His work originally consisted of ten books, but the first two of these are entirely lost, and the remaining eight are incomplete. The best modern editions of the text are those of Zunq-fc, Baumstark, and Miitzell.

1em  

   

 HIS subject is treated here from an historical point of view, for the purpose of showing how the different leading ideas in the theory were successively arrived at and developed. A curve is a line, or continuous singly infinite system of points. We consider in the first instance, and chiefly, a plane curve described according to a law. Such a curve may be regarded geometrically as actually described, or kinematically as in course of description by the motion of a point ; in the former point of view, it is the locus of all the points which satisfy n given condition ; in the latter, it is the locus of a point moving subject to a given condi tion. Thus the most simple and earliest known curve, the circle, is the locus of all the points at a given distance from a fixed centre, or else the locus of a point moving so as to be always at a given distance from a fixed centre. (The straight line and the point are not for the moment regarded as curves.) Next to the circle we have the conic sections, the inven tion of them attributed to Plato (who lived to ); the original definition of them as the sections of a cone was by the Greek geometers who studied them soon replaced by a proper definition in piano like that for the circle, viz., a conic section (or as we now say a &quot; conic &quot;) is the locus of a point sush that its distance from a given point, the focus, is in a given ratio to its (perpendicular) distance from a given line, the directrix ; or it is the locus of a point which moves so as always to satisfy the foregoing condition. Similarly any other property might be used as a definition ; an ellipse is the locus of a point such that the sum of its distances from two fixed points (the foci) is con stant, &c., ckc. The Greek geometers invented other curves; in parti-, cular, the &quot; conchoid,&quot; which is the locus of a point such that its distance from a given line, measured along the line drawn through it to a fixed point, is constant; and the &quot; cissoid &quot; which is the locus of a point such that its dis tance from a fixed point is always equal to the intercept (on the line through the fixed point) between a circle passing through the fixed point and the tangent to the circle at the point opposite to the fixed point. Obviously the number of such geometrical or kinematical definitions is infinite. In a machine of any kind, each point describes a curve ; a simple but important instance is the &quot; three-bar curve,&quot; or locus of a point in or rigidly connected with a bar pivotted on to two other bars which rotate about fixed centres respectively. Every curve thus arbitrarily defined has its own properties ; and there was not any principle of classification. The principle of classification first presented itself in the Geometrie of Descartes (1637). The idea was to represent any curve whatever by means of a relation be tween the coordinates (x, y] of a point of the curve, or .&amp;lt; ay to represent the curve by means of its equation.

Descartes takes two lines xx, yy , called axes of co ordinates, intersecting at a point O called the origin (the axes are usually at right angles to each other, and for the present they are considered as being so) ; and he determines the position of a point P by means of its distances OM (or <section end="CURVE" />