EXPLANATION OF SCIENTIFIC TERMS. 



side A B at D, were the cone extended in 

 size downwards, and the ellipsis would 

 be completed as in the dotted part of the 

 figure. 



2. If the cone (fig. 4.) be cut by a plane 

 a i, parallel to one of the sides A B, the 

 outline of the Fig. 4. 



section will 

 be a Parabola. 

 This curve 

 never returns 

 upon itself; 

 that is, it ne- 

 ver completes 

 its round like 

 the circle and 

 ellipsis. On 

 the contra- 

 ry, it would 

 spread out 

 wider and 

 wider, were 

 the cone ex- 

 tended ; because, the plane being parallel 

 to A B, will always cut the diameter of the 

 base at an equal distance from the side. 



Fiff. 5. 



3. If the cone ABC 

 (fig. 5.) be cut by a 

 plane a b, which, if 

 extended, would cut 

 the opposite cone 

 A D E in c, passing 

 through to d, the 

 sections of both 

 cones will exhibit 

 curves expanding 

 continually, like the 

 parabola, but with 

 different properties. 

 They are termed 

 Hyperbolas. 



II. The distinc- 

 tion between those 

 curves will be more 

 easily perceived, B 

 when they are ex- 

 hibited on a plane, ndependently of the 

 cone. 



1. Fig. 6. is an ellipsis, of which the 

 Fig. 6. 



lines are at right angles to each other; 

 are both equally divided at the centre C, 

 and cut the ellipsis into four equal and 

 similar portions : they are also termed the 

 greater and. the lesser Axis. Any other line 

 (as q s) which passes through the centre 

 C, and terminates in opposite points of 

 the circumference, is also said to be a 

 diameter. The two points, g and /i, in 

 the transverse diameter, equally distant 

 from its ends, A and B, are called the 

 Foci, each being a Focus ; and these points 

 are so situated, that, if we take any point 

 m, in the circumference of the ellipsis, 

 and draw the lines mg and m h from that 

 point to the two foci, the length of these 

 lines, when joined together, will always 

 be the same, at whatever part of the cir- 

 cumference the point m may be taken. 

 Any line, nop, drawn across the ellipsis, 

 parallel to C D, is a double Or dinette, its 

 half, p o, or o n, being called an Ordinate , 

 and the part A o, which the ordinate cuts 

 oif from the greater axis AB, is an Ab- 

 scissa. 



2. In the parabola (fig. 7.), the line 

 A B, which, passing through the vertex 

 A, divides the figure into two equal and 

 similar portions, is the axis of the para- 

 bola. Any line within the curve, drawn 

 parallel to the axis (as well as the axis 

 itself), is termed a diameter, and has its 

 vertex, where it meets the curve line. 



Fig. 7. 

 f> -v y 



I) 



2st diameter, A B, is called the 

 inverse diameter; and the shortest, 

 , is the Conjugate diameter. These 



The point F, in the axis A B, is the 

 focus of the curve; and a line, pq, at 

 right angles to the axis when produced 

 to a?, (the points x and F being equally 

 distant from the vertex A) is called the 

 Directrix. The focus, F, is so situate 1, 

 that, if we take any point, m, of the pa- 

 rabolic curve, and from that point draw 

 the right line m F, and also another 

 right line, m p, perpendicular to the di- 

 rectrix, and meeting it at ?), the two 

 lines, m F, and m p, will be always of 

 equal length. As in the ellipsis, any 

 straight line, m o , crossing the axis at 

 right angles, and terminating at both 

 ends in the curve, is a double ordinate ; 

 mo and on are ordinate s ; and A o, the 

 part of the axis which is cut oft', is the 

 abscissa, 



3. Fly. 8. shews two opposite hy- 



