## Elements of the Conic Sections |

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### Common terms and phrases

abscissa bola centre common section cone Conic Sections conical surface conjugate diameters conjugate hyperbolas consequently diam directrix drawn parallel Elem equiangular excess foci focus given in position greater axis half the second hyper hyperbola fig intercepted join latus rectum let it meet line be drawn lines ordinately applied lipsis meet the hyperbola meeting the asymptotes opposite hyperbolas parallelogram passes perbola perpendicular plane point D point G point of contact PROP proportionals rectangle AMB rectangle contained right angles second axis second diameter conjugate segments semidiameter square of CB straight line AE straight line drawn straight line parallel straight line touching straight lines ordinately tangent tangle THEOR touches the ellipsis touches the hyperbola touches the parabola transverse diameter triangle vertex vertices

### Popular passages

Page 2 - Co. of the said district, have deposited in this office the title of a book, the right whereof they claim as proprietors, in the words following, to wit : " Tadeuskund, the Last King of the Lenape. An Historical Tale." In conformity to the Act of the Congress of the United States...

Page 2 - An Act supplementary to an Act, entitled " An Act for the Encouragement of Learning, by securing the copies of Maps, Charts, and Books, to the authors and proprietors of such copies during the time* therein mentioned," and extending the benefits thereof to the arts of designing, engraving, and etching historical and other prints.

Page 163 - ... upon geometrical loci ; give me leave to present one to your notice, to which I should like to have your demonstration, to compare with my own. ***** When a circle and a right line are given in position, can you determine a point in the circumference of the circle, from which a tangent being drawn ; the segment of the tangent intercepted between the point of contact, and the line shall be given in length ? The enunciation you will excuse, provided you can comprehend me ; we may sometimes dispense...

Page 96 - A and base the circle BF, and let it be cut by a plane through the axis, and let the section so made be the...

Page 2 - District of Pennsylvania, to wit : BE IT REMEMBERED, that on the eighteenth day of May, in the thirty-third year of the Independence of the United States of America, AD 1809, Kimber &.

Page 109 - If from any point G of the Inperbola there is drawn a right line parallel to the transverse axis A a, meeting the second axis in N ; the square of the second axis shall be, to the square of the transverse, as the sum of the squares of the halt...

Page 7 - EF is equal to the length of the string FGC : take away the common part FG, and the remainder EG will be equal to the remainder GC. COROLLARY. »Hence that segment of the axis which is intercepted between the focus and the directrix, is bisected in the vertex of the axis. Thus CB is bisected in H. PROP. II. THEOR. If the distance of any point from the focus of a parabola be equal to the: perpendicular drawn from the same point to the directrix, that point is in the parabola.

Page 37 - ... the surface generated is called a conic surface, and the solid terminated by the surface is called a cone. II. The point is called the vertex, and the circle the base of the cone. The straight line drawn from the vertex to the centre of the circle, is called the axis. If the axis be perpendicular to the plane of the base, the cone is said to be right. III. If the generating line be produced indefinitely in both directions, it is evident that the surface will extend indefinitely both above and...

Page 20 - If from a point without a circle there be drawn two straight lines, one of which is perpendicular to a diameter, and the other cuts the circle; the square of the perpendicular is equal to the rectangle contained by the whole cutting line and the part without the circle, together with .the rectangle contained by the segments of the diameter.

Page 77 - The squares of straight lines ordinately applied to the same diameter, are to one another as the rectangles contained by the segments of that diameter, as was demonstrated (1.