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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

An Elementary Treatise on Quaternions

Peter Guthrie Tait - History - 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...

An elementary treatise on quaternions

Peter Guthrie Tait - 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...

Introduction to quaternions, by P. Kelland and P.G. Tait

Philip Kelland - 1873 - 248 pages
...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...

Report of Her Majesty's Civil Service Commissioners: Together ..., Volume 21

1877 - 678 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...

The Civil service manual for 1879 Government appointments and how to obtain them

Edwin T. Olver - 1879 - 158 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. 4. If a solid angle be contained by three plane angles, any two...

The Civil Service Manual for 1880-1881: Government Appointments and how to ...

1880 - 186 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...

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,...

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....