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Libros Libros 11 a 20 de 126 sobre To prove that the locus of the middle points of a system of parallel chords of a...
" To prove that the locus of the middle points of a system of parallel chords of a parabola is a straight line parallel to the axis of the parabola. "
A Treatise on Infinitesimal Calculus: The dynamics of material systems. 1862 - Página 13
1862
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An easy introduction to the higher treatises on the conic sections. [With] Key

John Hunter (of Uxbridge.) - 1866
...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...
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An Elementary Treatise on Quaternions

Peter Guthrie Tait - 1867 - 320 páginas
...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....
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An Elementary Treatise on Quaternions

Peter Guthrie Tait - 1867 - 320 páginas
...(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....
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AN INTRODUCTION TO ANALYTICAL PLANE GEOMETRY

W. P. TURNBULL, M.A. - 1867
...— 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...
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An Introduction to Analytical Plane Geometry

W. P. Turnbull - 1867 - 272 páginas
...— 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...
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Examination Papers for Science Schools and Classes

1869
...that — Cos i(A+B) Cos?= Cos l(a+i)Sin2 • -, mm 2 Cos i(AB) Sin|= Sin l(a+i)Sin° (lg } e. Prove that the locus of the middle points of a system of parallel chords of a parabola is a straight line which meets the parabola in one point only. (10.) f. Find the equation...
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Conic Sections treated Geometrically

1869 - 253 páginas
...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...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - 1871 - 368 páginas
...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, or...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - 1872 - 368 páginas
...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, or...
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An Elementary Treatise on Solid Geometry

William Steadman Aldis - 1873 - 208 páginas
...is therefore the area required. 81. It can be shewn by an investigation similar to that in Art. 71, that the locus of the middle points of a system of parallel chords of the surface By'+Cz' = x, whose direction-cosines are l, m, n, is Also the equation of the surface,...
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