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" PROPOSITION 5. The locus of a point, the ratio of whose distances from two given points is constant, is a circle*. "
Euclid's Elements of Geometry - Page 424
edited by - 1893 - 504 pages
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An Elementary Treatise on Quaternions

Peter Guthrie Tait - Quaternions - 1867 - 354 pages
...whether the spheres intersect or not. It is, in fact, what is called their Radical Plane. 221. Find the locus of a point the ratio of whose distances from two given points is constant. Let the given points be 0 and A, the extremities of the vector a. Also let P be the required point...
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An Elementary Treatise on Quaternions

Peter Guthrie Tait - Quaternions - 1867 - 364 pages
...whether the spheres intersect or not. It is, in fact, what is called their Radical Plane. 221. Find the locus of a point the ratio of whose distances from two given points is constant. Let the given points be 0 and A, the extremities of the vector a. Also let P be the required point...
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Introduction to quaternions, by P. Kelland and P.G. Tait

Philip Kelland - 1873
...whether the lines which join them form a hexagon or not. ADDITIONAL EXAMPLES то CHAP. VIII. 1. Find the locus of a point, the ratio of whose distances from two given straight lines is constant. 2. Find the locus of a point the square of whose distance from a given...
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Report of Her Majesty's Civil Service Commissioners: Together ..., Volume 21

1877 - 682 pages
...the vertical angle of u triangle divides the base produced into segments proportional to the sides. The locus of a point the ratio of whose distances from two fixed points is constant is a circle. 4. If a solid angle be contained by three plane angles, any two...
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The Civil service manual for 1879 Government appointments and how to obtain them

Edwin T. Olver - 1879
...the vertical angle of a triangle divides the base produced into segments proportional to the sides. The locus of a point the ratio of whose distances from two fixed points is constant is a circle. 4. If a solid angle be contained by three plane angles, any two...
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The Civil Service Manual for 1880-1881: Government Appointments and how to ...

1880 - 153 pages
...the vertical angle of a triangle divides the base produced into segments proportional to the sides. The locus of a point the ratio of whose distances from two fixed points is constant is a circle. (. If a solid angle be contained by three plane angles, any two...
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Elements of Quaternions

Arthur Sherburne Hardy - Quaternions - 1881 - 252 pages
...which is the equation of a sphere passing through o and having VfL — for a diameter. OD 15. To find the locus of a point the ratio of whose distances from two given points is constant. Let o and A be the two given points, OA = a, OR = p, R being a point of the locus. Then, by condition,...
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Elements of Quaternions

Arthur Sherburne Hardy - Quaternions - 1881 - 252 pages
...which is the equation of a sphere passing through o and having m OD — for a diameter. 15. To find the locus of a point the ratio of whose distances from two given po1nts is constant. Let o and A be the two given points, OA = a, OR = p, R being a point of the locus....
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Mathematical Questions and Solutions, from the "Educational Times.", Volume 44

1886 - 198 pages
...centres of the moon and earth, M, m the masses of ea,th and moon, R the radius of the earth. .. . But the locus of a point the ratio of whose distances from two points distant 8 apart is -S,c, is a circle of radius 5V* / I — K. 8189. (By Professor MATHEWS, MA)...
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Euclid's Elements of Geometry, Books 1-6; Book 11

Henry Martyn Taylor - Euclid's Elements - 1895 - 706 pages
...line is drawn cutting BC in D, and the angles BDA, CDA are bisected by straight lines cutting AB, AC m F, E respectively: prove that AD, BE, CF intersect...of the angle APB meeting AB in C and AB produced in D. CBD Because PC, PD are the bisectors of the angle APB, therefore the ratios of AC to CB and AD to...
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