Visibility of Luna and Lunar Crescent

wA diislaled by S. Oddz 6 Crlr of Moituntd.s, Boot Thr4, treatite Eigtu,
SmdiJicdtion ol the Nee M@a Yelc Judaic. Seris, volh. XI, Yatc Univesity pE$,
No Hav6 CT, 1956). Maimodidcs mrk w studi.d by von Lifl.ow in
SiEunghberichk da Wiehu Altd.nie, Math-Natrre, Cl6e,lxvi, (1872), pp.459-480,
ln his *ort Maimonides nak6 rh. snalLsl visible phe ofthc M@n depqdenr on trc
variables, as claimed by Forh€.in8hd. Th.se veiables bave ben tem€d ss rr? rr€
etonAorion otthe Moon a\d tle aplbre.t ahgle of tision - F6\.noghe slarcs rhal if
by hgk ofrision Mai1onides m.es the diffeEncc of the Sun md the Moon in rc.irh
dirlaccs then th. nle of Mainoid6 .nd his om rule for hinimlm visibt. pb4 of
Moon ae n€dly the enc Howevcr he f!fther says lhat Maimonides rute sivcs slidrly
lower oininun alliludes that could be duc tc, b.(.r ob$fring condirio.s in Jeruslem
lh& in Atbos. Unfodu.alely Fohednghah .dmik that hc could not sumcienrly
undedand Maimodis' dithmdiol nelhod dd has not giecn a dchited @ounl of rb.
same (Foihciinsham, l9l0).
Lder, Bruin(Bruin. 1977)gives a moe debiled eounrof any medievalatenpr
ol solving fie probl€n of findin8 sronomi€al €onditiotu for thc fi6t visibility of
crsc€nl. De$ribinglhe Isl.mic astonomical procedurcs Btuin says $a1Al-Khurizini
gives mathenadcal rules and rablcs lor pedicling thc new cre$e.t where6 AlBamni
peeds a conplerc soludon. He aho nenlions lh€ lato accounl ofMo$s ber Madoon
lnd clains rhst ibn Mamoon larsely follos Al Balloi. One oflhe nost inponanl dp.cl
ofBruin's accounr ofrhc eflods oftbe bedicval era is rhar Anbs^rulins orthis ea had
olEady rcaliz€d rhe sienitlcece of cE$cnr widrh. This inpoiant aFcl enaincd
hissins frem all th. najor cooiribudons of lw.ntietn century bcloE Bruin. Bed on this
d€scription ed thc modein loowl.dge in ihis work lhe sme h6 been explocd dor.
.xlecively od is pEsnt d latu id the chaPler.
lilcatue that app.ared duing 2od c.nrury lhe gencral rule of
Babylods for first visibilily ofnew lunecresc€nlis:
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