 D are said to be harmonic conjugates of each other with respect to the points A and B, and AB is said to be harmonically divided by the points C and D. If C and D are harmonic with respect to A and B, then A and B are harmonic with respect to C and D....  A Syllabus of Modern Plane Geometry - Page 12by Association for the improvement of geometrical teaching - 1889 - 32 pagesFull view - About this book
 | Euclides - 1884 - 434 pages
...the line joining the two given points. Suppose A and B the given points, O the middle of AB. Since C and D are harmonic conjugates with respect to A and B, .-.AD:DB = AC:CB. " App. VI. Def. 3 Now if D be situated (as in figs. 1 and 2) to the right of 0, then... | |
 | George Bruce Halsted - Geometry - 1896 - 208 pages
...co-straight with them, be so taken that AC/BC=AD/DB, then the points A, C, B, D form a harmonic range; C and D are harmonic conjugates with respect to A and B : AC, AB, AD are said to be in harmonic progression : and AB is said to be a harmonic mean between... | |
 | Education - 1902 - 942 pages
...Define a Harmonic Range, and show that if 0 and D are harmonic conjugates with respect to A and /)', then A and B are harmonic conjugates with respect to C and D. « A circle is described touching a straight line All in <', and having its diameter a harmonic mean... | |
 | Education - 1915 - 412 pages
...Nesbitt's Question 17963.] 18061. (DAVID GREEN.) — Two conies have double contact at fixed points A, B. C and D are harmonic conjugates with respect to A and B. From C a tangent is drawn to one of the conies and from D a tangent is drawn to either conic. Then... | |
 | Marcel Berger - Mathematics - 1984 - 284 pages
...a,b] = -1; we say that the two pairs of points {a, b} and { c, d } are in harmonic division, and that a and b are harmonic conjugates with respect to c and d. For instance. \a, b, c, OOD] = - 1 is equivalent to c = (a + b)/2. ie r is the midpoint of a, h. Using... | |
 | Titu Andreescu, Zuming Feng - Mathematics - 2000 - 308 pages
...points A and B. and AB is said to be harmonically divided by the points C and D. If C and D are harmonic with respect to A and B, then A and B are harmonic with respective to C and D. Harmonic range The four points A, B, C, D are referred to as a harmonic... | |
 | Titu Andreescu, Zuming Feng - Mathematics - 2002 - 340 pages
...D. Harmonic range The four points A, B, C, D are referred to as a harmonic range, denoted by (ABCD), if C and D are harmonic conjugates with respect to A and B. Kelly's theorem If n > d and C\,...,Cn are convex subsets of Rd, each d + 1 of which have nonempty... | |
 | Titu Andreescu, Zuming Feng, George Lee - Education - 2003 - 296 pages
...points A and B, and AB is said to be harmonically divided by the points C and D. If C and D are harmonic with respect to A and B, then A and B are harmonic with respect to C and D. Harmonic range The four points A, B, C, D are referred to as a harmonic range,... | |
| |
