Elements of the Conic Sections |
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Page 113
... meet CD in two points D , d . Describe , from the centre D , distance DF , another circle , which ( 3. 3. Elem . ) will pass through ... asymptotes . Cor . 1. The asymptotes of two opposite hyperbolas are BOOK III . 113 THE HYPERBOLA .
... meet CD in two points D , d . Describe , from the centre D , distance DF , another circle , which ( 3. 3. Elem . ) will pass through ... asymptotes . Cor . 1. The asymptotes of two opposite hyperbolas are BOOK III . 113 THE HYPERBOLA .
Page 114
... asymptotes , DA , AE are each of them equal and parallel to CB , half the second axis : and because DE , de are ... meeting the axis Aa in G ; and since the rectangle AGa is to the square of GF , as the square of CA is ( 7. 3. ) to ...
... asymptotes , DA , AE are each of them equal and parallel to CB , half the second axis : and because DE , de are ... meeting the axis Aa in G ; and since the rectangle AGa is to the square of GF , as the square of CA is ( 7. 3. ) to ...
Page 115
... meeting the asymptotes in the points K , L ; the rectangle KFL , is equal to the square of CB . Through the vertex A of the transverse axis draw DAE , meeting the asymptotes in the points D , E ; and let KL meet the same axis in G ...
... meeting the asymptotes in the points K , L ; the rectangle KFL , is equal to the square of CB . Through the vertex A of the transverse axis draw DAE , meeting the asymptotes in the points D , E ; and let KL meet the same axis in G ...
Page 116
... asymptotes , and parallel to the second axis , there be taken a point F , so situated , that the rectangle KFL may be equal to the square of the second axis ; that point is in the ... meeting the asymptotes in 116 CONIC SECTIONS .
... asymptotes , and parallel to the second axis , there be taken a point F , so situated , that the rectangle KFL may be equal to the square of the second axis ; that point is in the ... meeting the asymptotes in 116 CONIC SECTIONS .
Page 117
Robert Simson. to the second axis , and meeting the asymptotes in E , F end in G , H : and since , by the preceding ... meeting the same asymptote KC in C , O ; then CO , MN are equal . For let AB , LB meet the asymp- tote KP in the ...
Robert Simson. to the second axis , and meeting the asymptotes in E , F end in G , H : and since , by the preceding ... meeting the same asymptote KC in C , O ; then CO , MN are equal . For let AB , LB meet the asymp- tote KP in the ...
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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 AKB 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
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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.