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From Man or Angel
the great
Architect
Did
wisely to conceal,
and not divulge,
His secrets, to be
scanned by them who
ought
Rather
admire. Or, if they
list to try
Conjecture, he his
fabric of the
Heavens
Hath
left to their
disputes -- perhaps
to move
His
laughter at their
quaint opinions
wide
Hereafter,
when they come to
model Heaven
And calculate the
stars: how they will
wield
The
mighty frame: how
build, unbuild,
contrive
To
save appearances;
how gird the
Sphere
With
Centric and
Eccentric scribbled
o'er,
Cycle and
Epicycle, Orb in
Orb.
[From
Paradise
Lost]
Paradise Lost.
Loci: Convergence
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Van Schooten's Ruler Constructions
Conclusions
We can only speculate why van Schooten wanted to study constructions that did not use a compass. It seems unlikely that he really mistrusted the accuracy or truth of a compass construction more than he mistrusted making marks on a ruler. So, it may be that he simply relished the intellectual challenge of using different geometric tools. Whatever his reasons, we can be grateful for these delightful nuggets of geometry from so long ago.