A history of Greek mathematics - Wilbourhall.org

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THE COLLECTION. BOOK VIII 437
so that
or
PQ:QV=Q'W:PQ'
i
PQ.PQ'=QV.Q'W.
Thus P can be found, and similarly P'.
The conjugate diameter is found by virtue of the relation
(conjugate diam.) 2 : PP'
where p is the latus rectum to PP f
of the curve
f
,
2 = p
:
PF = AV'-.PV.VF
PP'.
determined by the property
Problem, Given tivo conjugate diameters of an ellipse,
to find the
axes.
Lastly, Pappus shows (Prop. 14, chap. 17) how, when we are
given two conjugate diameters, we can find the axes. The
construction is as follows.
(CD being the greater), E the centre.
Produce EA to Hso that
EA.AH=DE 2 .
Let A B, CD be conjugate diameters
Through A draw FG parallel to CD. Bisect EH in K, and
draw KL at right angles to EH meeting FG in L.
B
r*-^^ P\
M"\\V
,* ~y
^ -
l\\/> / N J/0
^^.a
/K F
With L as centre, and LE as radius, describe a circle cutting
GF in G, F.
Join EF, EG, and from A draw AM, AN parallel to EF, EG
respectively.