. Haswell's engineers' and mechanics' pocket-book ... Make A B the transverse diameter, and C D, perpendicular to it,the conjugate. Bisect A B in 0, and from 0, with the radius O C or 0 D, de-scribe the circle D / c F, cutting A B produced in F and /, whichpoints will be the foci. In A B produced take any number of points, n n, &c., and fromF and /, as centres, with B 72, A tz, as radii, describe arcs, cuttingeach other in s s, &c. Through s 5, &c., draw the curve s B s, and it will be the hyper-bola ^ To describe hyperbolas by another metliod, see Gregorys Mathematics, p. 160. 56 C
. Haswell's engineers' and mechanics' pocket-book ... Make A B the transverse diameter, and C D, perpendicular to it,the conjugate. Bisect A B in 0, and from 0, with the radius O C or 0 D, de-scribe the circle D / c F, cutting A B produced in F and /, whichpoints will be the foci. In A B produced take any number of points, n n, &c., and fromF and /, as centres, with B 72, A tz, as radii, describe arcs, cuttingeach other in s s, &c. Through s 5, &c., draw the curve s B s, and it will be the hyper-bola ^ To describe hyperbolas by another metliod, see Gregorys Mathematics, p. 160. 56 CONIC SECTIONS. To find the length of the Ordinate, E F, of an Ellipse, the Transverse, AB, Conjugate, C D, and Abscissa, A F and F B, heing known—fig. 3. Rule.—As the transverse diameter is to the conjugate, so is thesquare root of the product of the abscissae to the ordinate whichdivides them. Example.—The transverse axis, A B, is 100; the conjugate, C D,is 60; one abscissa, B F, is 20 ; the other, A F, is (100—20) = 80. 100 : 60 : : v^OxSO : 24 Ans. The Transverse and Conjugate diameters, and an Ordinate heing known,to find the Ahscissce—fig. 3. Rule.—As the conjugate diameter is to the transverse, so is thesquare root of the difference of the squares of the ordinate and semi-conjugate to the distance between the ordinate and centre; andthis distance, being added to and subtracted from the semi-trans-verse, will give the abscissas required. Example.—The transverse diameter, A B, is 100 ;
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