 | Mathematics - 1862 - 282 pages
...tangent lines parallel to a is = 0. XXVII. To study the nature of the surface more closely, let us find the locus of the middle points of a system of parallel chords. Let them be parallel to a, then, if ts be the vector of the middle point of one of them, ts + xa. and... | |
 | John Hunter (of Uxbridge.) - 1866 - 104 pages
...to a circle is always perpendicular to the radius passing through the point of contact. 31. To find the locus of the middle points of a system of parallel chords. Let PP' be one of the chords ; «f, y' the coordinates of P ; and x", y" those of P'. f. The equation... | |
 | William Peveril Turnbull - Geometry, Analytic - 1867 - 298 pages
...— 90, 92, 100 may be slightly altered so as to suit the parabola.) 113. A diameter of a curve is the locus of the middle points of a system of parallel chords. For example, in the circle a diameter is, according to this definition, a straight line drawn through... | |
 | Peter Guthrie Tait - 1867 - 364 pages
...by tangent lines parallel to a is 254. To study the nature of the surface more closely, let us find the locus of the middle points of a system of parallel chords. Let them be parallel to a, then, if is be the vector of the middle point of one of them, w+xa and *s—xa.... | |
 | W. P. Turnbull - Geometry, Analytic - 1867 - 276 pages
...— 90, 92, 100 may be slightly altered so as to suit the parabola.) 113. A diameter of a curve is the locus of the middle points of a system of parallel chords. For example, in the circle a diameter is, according to this definition, a straight line drawn through... | |
 | Peter Guthrie Tait - Quaternions - 1867 - 366 pages
...(SpQp— l)Sa<f>a — (Sp>pa)1 = 0. 254. To study the nature of the surface more closely, let us f'nd the locus of the middle points of a system of parallel chords. Let them be parallel to a, then, if sr be the vector of the middle point of one of them, w+xa and tsr—xa.... | |
 | William Henry Besant - Conic sections - 1869 - 304 pages
...article contains a proof of the theorem which includes all the three cases. 177. PROP. II. To find the locus of the middle points of a system of parallel chords. Let P'P one of the chords be produced to meet the directrix in F, draw Ax parallel to FP, and divide... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...number of parallel chords all lie in the same diameter perpendicular to the chords. In other words, the locus of the middle points of a system of parallel chords is the diameter perpendicular to these chords. PROPOSITION VIII.— THEOREM. 18. In the same circle,... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...number of parallel chords all lie in the same diameter perpendicular to the chords. In other words, the locus of the middle points of a system of parallel chords is the diameter perpendicular to these chords. PROPOSITION VIII.— THEOREM. 18. In the same circle,... | |
 | William Steadman Aldis - Geometry, Analytic - 1873 - 240 pages
...assume the form where B and C' have the same or opposite signs according as B and C have. 82. To find the locus of the middle points of a system of parallel chords in any quadric. Let the equation of the surface be Ay? + By' + <7z 2 + 2A'yz + ZB'zx + 2 Gxy + 2A"x+2B"y... | |
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The locus of the middle points of a system of parallel chords in a parabola is called a diameter. 
