About 3,770 results
|Pappus-Guldinus Theorem Pappus's Hexagon Theorem 2131 Casey, J. A |
Sequel to the First Six Books of the ... See also CEVA'S THEOREM, HARMONIC
RANGE, MENE- LAUS- THEOREM References Coxeter, H. S. M. and Greitzer,
S. L. ...
|It is also the case that Pappus's theorem implies Desargues' – a result known as |
Hessenberg's theorem after its discoverer, ... Moulton implies no fourth harmonic
point, so the theorem of the fourth harmonic point implies that the plane is not a ...
|From Pappus' theorem follow the other theorems: This means (Fig. ... In particular|
, four harmonic lines of a pencil intersect any line, not through the vertex, in four
harmonic points, and any four lines connecting a point not on a given line with ...
|... 978, 979 Fermat's Theorem on Local Extrema, 830 Fibonacci sequence, A 1 6 |
first octant, 666 first-order approximation, ... 959-960 grid lines: in polar
coordinates, 623 Guldin's Rule, see Pappus's Theorem harmonic functions, 828
|... 3 theorem, 81–84, 88 Euler theorem, 66 Fermat general form, 3 Young, 27 |
point, 90, 92 Function concave, 23 convex, ... 95, 98 H ̈older, 27 generalized, 32
Pappus harmonic mean–geometric theorem, 80 mean, 8 Pedal helpful, 34
|In Book III, Pappus also describes the theory of means and gives an attractive |
construction that includes the arithmetic, the geometric, and ... 8.15) one has DB
L AC and BF J_ OD, then DO is the arithmetic mean, DB the geometric mean, and
DF the harmonic mean of the ... In many cases, the novelties take the form of
generalizations of earlier theorems, and a couple of these instances appear in
|10 — 12 First properties of the harmonic relation ..... 12 — 14 An ... 16, 17 A |
theorem in regard to a chain of perspectivities ; reduction to two links 17, 18 Proof
for the case of ranges on skew lines . ... Pappus' theorem Preliminary remarks .
|In proposition 145 Pappus shows that harmonic sets are invariant under |
projection and section. Proposition 130 gives us, though in a language different
from that of today, the theorem of Desargues on the involution determined by a
|Then P, Q, R are collinear, and Pappus' Theorem is true without any further |
condition. Suppose, next, that the line joining ... If CC' meets AA' in V2, OV2 is the
harmonic conjugate of OQ with respect to I and I'. Hence OV3 = OV2, and
Peter Hertling, Christoph M. Hoffmann, Wolfram Luther - 2008 - Preview
|Theorem 1 (Harmonic conjugate, Fig. 1, left). Let A,B,X be 3 ... X iscalled the |
harmonicconjugate of X relatively to A, B.The harmoniccon- jugate of X is X.
Theorem 2 (Desargues theorem, Fig. 1, right). ... Theorem 3 (Pappus theorem,
Fig. 2, left).