It
consists
of five books, of which the first
nisphaerium of Jordanus.
nisphaerium of Jordanus.
William Smith - 1844 - Dictionary of Greek and Roman Antiquities - c
In 1551 (Basle, folio)
that it bears internal marks of having been made he republished it as “. . . . omnia quae extant opera,
from the Arabic (as was indeed generally admitted), praeter Geographiam, quam non dissinili forma
and throws great light on the subsequent Greek (double column) nuperrimè ædidimus : summa cura
editions and versions. Next comes the version of et diligentia castigata ab Erasmo Oswaldo Schrek-
George of Trebizond, “ Ptolemaei Almagestum, ex henfuchsio . . . . " The contents are the same as
Versione Latina Georgii Trapezuntii,” Venice, in the former edition, with notes added by the
15:25, folio. (Fabricius, who is in doubt as to new editor. Erasmus Reinbold published the first
whether it were not 1527, and confounds it with book only (Gr. Lat with Scholia), Wittenberg,
the former version. ) From all we can collect, 1549, 8vo. (Lalande, who gives also 1560), and
however, no one asserts himself to have seen an also 1569 (Halina). S. Gracilis (Legrêle) pub-
earlier edition of the version of Trapezuntius than blished the second book in Latin, Paris, 1556,
that of Venice, 1528, folio (with a red lily in the 8vo. (Lal. Halm. ). J. B. Porta gave the first book
title page); and Hoffman sets down none earlier. in Latin, with Theon, Naples, 1588, 4to. (Lal. ),
Its title (from a copy before us) is “ Claudii Pto- and the first and second books in the same way,
lemaei Pheludiensis Alexandrini Almagestum. . . . Naples, 1605, 4to. (Lal. Halm. ).
latina donatum lingua ab Georgio Trapezuntio. . . . From the tinie of Galileo, at which we are now
anno salutis MDXXyni. labente. ” This version is arrived, we cannot find that any complete version
stated in the preface to have been made from the of the Almagest (Greek edition there certainly was
Greek: the editor was Lucas Gauricus. The none) was published until that of Halma, to which
nine books of astronomy by the Arab Gever, edited
We shall not attempt to describe
by Peter Apian, Nuremberg, 1534, folio, and often the dissertations by Delambre, Ideler, &c. , con-
set down as a commentary on, almost an edition tained in this splendid collection, but shall simply
of, the Almagest, have no right whatever to either note the contents of the first four volumes: for the
name, as we say from examination. Halma, ob- rest see Theon. Of the manuscripts we have
serving in the epitome of Purbach and Regiomon- already spoken. The descriptions are-Paris, 1813,
tanuis strong marks of Arabic origin, and taking 1816, 1819, 1820, quarto. The first two volumes
Geber to be in fact Ptolemy, concludes that the contain the Almagest, in Greek and French, with
epitome was made from Geber, and reproves them the various readings. The third contains the Karwy
for not naming their original. Halma must have Baoileiwv and the páoeis tûv år lavar of Ptolemy,
taken Geber's work to be actually the Almagest, for, and the works of GEMINUS. The fourth contains
with the above censure, he admits that the two the υποθέσεις των πλακωμένων and the άρχαι και
epitomists have caught the meaning and spirit of mobéoeis Madnuatınal of Ptolemy, and the upotú-
Ptolemy. It is worth while, therefore, to state, πωσεις of Proclus.
from examination of Geber (whom Halma had not The part of the Almagest which really concerns
seen), and comparison of it with the epitome in the modern astronomer, as part of the effective
question, that neither is Geber a commentary on records of his science, is the catalogue of stars in
the Almagest, nor the epitome formed from Geber. the seventh and eighth books. Of this catalogue
The first Greek text of the Almagest (as well as there have been several distinct editions. The
that of Euclid) was published by Symon Grynoeus, earliest (according to Lalande, not mentioned by
Basle, 1538, folio: “KA. Ntoneualov heykans ouv- Halma) is a Latin version by John Noviomagus,
Taféws Bien, sy'. . . . ” It is Greek only, and con- from Trapezuntius,“ . . . . Phaenomena stellarum
tains the Almagest, and the commentary of Theon 1022 fixarum ad hanc aetatem reducta . . . ," Co
[PAPPUs). Basle, 1541, folio. Jerome Gemusaeus logne, 1537, folio, with forty-eight drawings of the
published
omnis quae extant opera (Geogra- constellations by Albert Durer. The next (Baily)
is a Greek edition (stated to be furnished by
* It is a slight matter, but it is difficult to say Halley), at the end of the third of the four volumes
how small an error is not worth correcting when of Hudson's “ Geographiae veteris Scriptores Graeci
great names support it. Halma, followed by Baily, minores,” Oxford, 1698—1712, 8vo.
The next
says that Trapezuntius got his Greek manuscript (Halma) is a French version by Montignot, Nancy,
from a copy of one in the Vatican, made by order 1786, and Strasburg, 1787, 4to. , translated into
of the abbot Bartolini. But what Gauricus says is German by Bode, Berlin and Stettin, 1795, 8vo.
“ Georg. Trap. magnum hunc Astronomum . . . . e The last, and by far the best, is that given in
Graeca in Latinam transtulit linguam. Quem Lau- Greek) by the late Francis Brily, in his collection
rentius Bartolinus. . . . e Vaticano exemplari. . . . of the catalogues of Ptolemy, Ulugh Beigh, Tycho
transcribendum curavit. ” The quem seems to Brahé, Halley, and Hevelius, which forms volume
refer to Trapezuntius, who had long been dead : xiii. of the Memoirs of the Royal Astronomical
Gauricus explains how he came by a copy. Andrew Society, London, 1843, 4to. This edition of the
Trapezuntius, in his preface to his father's work
(which follows that of Gauricus), though dedicating + Mr. Baily, who closely examined all his edi.
to the pope, does not hint at the manuscript from tions, as will presently be noted, does not even
the pope's library, nor at any manuscript in par- give the name of this one, though to our know
ticular.
ledge it was one of those he tried to make use of.
## p. 572 (#588) ############################################
572
PTOLEMAEUS.
PTOLEMAEUS.
catalogue is the one which should be cited. It have been twice printed in Greek, and together ;
gives the readings of the Florence and Paris manu- first, by John Camerarius (Gr. Lat. ), Nuremberg.
scripts (from Halma), of the Greek of Grynoeus 1535, 410. ; secondly, with new Latin version and
and Halma, and of the Latin of Liechtenstein and preface, by Philip Melancthon, Basle, 1553, 8vo.
Trapezuntius, with corrections from our present (Fabricius, Hoffmann). Among the Latin editions,
astronomical knowledge very sparingly, and we over and above those already noted as accompany-
believe very judiciously, introduced. The astro-ing editions of the Almagest, Hain mentions two
nomer might easily make Ptolemy's catalogue what (of both works) of the fifteenth century ; one by
it ought to have been ; the scholar, from criticism Ratdolt, Venice, 1481, 4to. ; another by Bonetus
alone, would certainly place many stars where it is (with other astrological tracts), Venice, 1493, fol.
impossible Ptolemy could have recorded them as There is another, iranslated by Gogava, Louvain,
being. From frequent conversation with Mr. Baily | 1548, 4to. (Hoffınann, Lalande); and there is ano-
during the progress of his task, we can confidently ther attached to the collection made by Hervagius
say that he had no bias in favour of making his (which begins with Julius Firmicus, and ends with
text astronomically correct at the expense of cri- Manilius), Basle, 1533, folio ; and all except the
tical evidence ; but that he was as fully impressed Firmicus and Manilius seem to have been printed
with the necessity of producing Ptolemy's errors as before, Venice, 1519, folio (Lalande). There is
his truths.
mention of two other editions, of Basle and Venice,
Mr. Baily remarks, as to the catalogue, and the 1551 and 1597, including both Firmicus and Ma-
same appears as to other parts of the Almagest, that nilius (Lalande). The Centiloquium has been
Ilalma often gives in the text he has chosen read sometimes attributed to Hermes Trismegistus : but
ings different from those of all his principal subjects this last-named author had a Centiloquium of his
of collation. This means that he bas, in a consi- own, which is printed in the edition just described,
derable number of cases, either amended his text and is certainly not in matter the same as Pto-
conjecturally, or preferred the reading of some lemy's. Fabricius, mentioning the Centiloquium,
minor manuscript, without particular mention. says that Ptolemy de Electionibus, appeared (Lat. ),
This is no great harın, since, as the readings of all | Venice, 1509,- Perhaps this is the same
his great sources are always given, it amounts to hav- work as the one of the same title, afterwards pub-
ing one more choice from an unnamed quarter. But lished as that of the Arab Zahel. The English
it is important that the critical reader of the edition translation (1701) purporting to be from “ Pro-
should have notice of it ; and the more so, inas- lemy's Quadripartite” (Hoffmann), must be from
much as the readings are at the end of each the paraphrase by Proclus, as appears from its
volume, without* text-reference from the places in title-page containing the name of Leo Allatius, who
which they occur.
edited the latter. The usual Latin of the Centilo.
On the preceding summary of the bibliographical quium is by Jovius Pontanus: whether the Commen-
history of the Almagest, we shall remark that the turies attributed to him, printed, Basle, 1531, 4to.
reader is not to measure the currency of it by the (Lalande), &c. , are any thing more than the version,
number of its editions. It was the gold which lay we must leave to the professedly astrological biblio-
in the Bank, while paper circulated on its authority. grapher. It was printed without the Quadripar-
All the European books on astronomy were fa- titum several times, as at Cologne, 1514, 8vo. : and
shioned upon it, and it was only the more learned this is said to be with the comment of Trapezuntius,
astronomers who went to the common original. meaning probably the version. The commentaries
Euclid was actually read, and accordingly, as we or introductions, two in number, attributed to
have seen, the presses were crowded with editions Proclus and Porphyry, were printed (Gr. Lat. )
of the Elements. But Ptolemy, in his own words, Basle, 1559, folio (Lalande).
was better known by his astrology than by his as- 3. Kavwv Baouléwv. This is a catalogue of Assy-
tronomy. We now come to his other writings, on rian, Persian, Greek, and Roman sovereigns, with
which we have less to say.
the length of their reigns, several times referred to
2. Tetpábı6 os oúvtatis, generally called Tetra- by Syncellus, and found, with continuation, in
billon, or Quadripartitum de A potelesmatibus et Ju- Theon. It is considered an undoubted work of
diciis Astrorum. With this goes another small Ptolemy. It is a scrap which has been printed by
work, called kapids, or Fructus Librorum Suorum, Scaliger, Calvisius (who valued it highly), Petavius
often called Centiloquium, from its containing a and Dodwell ; but most formally by Bainbridge
'hundred aphorisms. Both of these works are as- (in the work presently cited), and by Halma, as
trological, and it has been doubted by some whether above noticed.
they be genuine. But the doubt merely arises 4. Φάσεις απλανών αστέρων και συναγωγή επιση-
from the feeling
that the contents are unworthy of Magelav, De Apparentiis et Significationibus inerran-
Ptolemy. The Tetrabiblon itself is, like the Alma- tium. This annual list of sidereal phaenomena has
gest and other writings, dedicated to his brother been printed three times in Greek: by Petavius,
Syrus: it refers, in the introduction, to another in his Uranologion, Paris, 1630, folio ; partially
work on the mathematical theory. Both works in Fabricius, but deferred by Harless to a supple-
mentary volume which did not appear ; and by
• If editors will put the various readings at the Halma, as above noticed. There are three other
end of their volumes, instead of at the bottom of works of the same name or character, which have
the pages, we should wish, when there are more been attributed to Ptolemy, and all three are given,
volumes than one, that the readings for one volume with the genuine one, by Petavius, as above. Twó
should be inserted at the end of another. It would of them are Roman calendars, not worth notice. The
then be practicable to have the text and its variations third was published, in Latin, from a Greek manu-
open before the reader at one and the same moment, script, by Nic. Leonicus, Venice, 1516, 8vo. (Fabri-
which, when two or three instances come close to cius): and this is reprinted in the collection begin-
gether, is very desirable.
ning with Julius Firmicus, above noticed. We have
## p. 573 (#589) ############################################
PTOLEMAEUS.
PTOLEMAEUS.
573
mentioned the versions of the genuine work which , works of Ptolemy is as follows :-From Simplicius,
are found with those of the Almagest.
Περί μετρησέως μονόβιβλος, to prove that there
5, 6. De Analemmate and Planisphaerium. can be only three dimensions of space ; Niepl poter
These works are obtained from the Arabic. Fa- Bubalov, mentioned also by Eutocius ; Etoixeia,
bricius, who had not seen them, conjectures that two books of hypotheses. From Suidas, three books
they are the same, which is not correct. The Mnxavikw. From Heliodorus and_Simplicius,
Analemma is a collection of graphical processes 'OTTIKT) #payuatela. From Tzetzes, lepinynous ;
for facilitating the construction of sun-dials, and from Stephen of Byzantium, nepitnous. There
grounded on what we now call the orthographic have been many modern forgeries in Ptolemy's
projection of the sphere, a perspective in which, name, mostly astrological.
mathematically speaking, the eye is at an infinite It must rest an unsettled question whether the
distance. The Planisphere is a description of the work written by Ptolemy on optics be lost or not.
stereographic projection, in which the eye is at The matter now stands thus : Alhazen, the principal
the pole of the circle on which the sphere is pro-Arab writer on optice, does not mention Ptolemy,
jected. Delambre seems to think, from the former nor indeed, any one else. Some passages from Roger
work, that Ptolemy knew the gnomonic projection, Bacon, taken to be opinions passed on a manu-
in which the eye is at the centre of the sphere: script purporting to be that of Ptolemy, led Mon-
but, though he uses some propositions which are tucla to speak highly of Ptolemy as an optical
closely connected with the theory of that projec-writer. This mention probably led Laplace to ex-
tion, we cannot find any thing which indicates dis- amine a Latin version from the Arabic, existing in
tinct knowledge of it. There is but one edition of the Royal Library at Paris, and purporting to be
the work De Analemmate, edited by Commandine, Ptolemy's treatise. The consequence was Laplace's
Rome, 1562, 4to. (Lalande says there is a Vene assertion that Ptolemy had given a detailed account
tian title of the same date. He also mentions of the phenomenon of astronomical refraction. This
another edition, Rome, 1572, 4to. , perhaps an error remark of Laplace led Humboldt to examine the
of copying). Nothing is told about the Arabic manuscript, and to call the attention of Delambre
original, or the translator. The Planisphaerium to it. Delambre accordingly gave a full account of
first appeared in print in the edition of the Geo the work in his Histoire de l'Astronomie Ancienne,
graphy, Rome (? ), 1507, fol. (Hoffmann); next vol. ii. pp. 411–431. The manuscript is headed
in Valder's collection, entitled “Sphaerae atque As- Incipit Liber Ptolemaei de Opticis sive Aspectibus
trorum Coelestium Ratio . . . . " Basle (? no place is translatus ab Ammiraco (or Ammirato] Eugenio
named), 1536, 4to. With this is joined the Pla-Siculo.
It consists of five books, of which the first
nisphaerium of Jordanus. There is also an edition is lost and the others somewhat defaced. It is said
of Toulouse, 1544, fol. (Hoffmann). . But the best there is in the Bodleian a manuscript with the
edition is that of Commandine, Venice, 1558, 4to. whole of five books of a similar title. The first
Lalande says it was reprinted in 1588. Suidas three books left give such a theory of vision as
records that Ptolemy wrote animous émipavelas might be expected from a writer who had the work
opalpas, which is commonly taken to be the work attributed to Euclid in his mind. But the fifth book
on the planisphere. Both the works are addressed does actually give an account of refraction, with ex-
to Syrus.
perimental tables upon glass, water, and air, and an
7. Tiepl útodégewv TV Flavwuévwy, De Planeta- account of the reason and quantity of astronomical
rum Hypothesibus. This is a brief statement of the refraction, in all respects better than those of Al-
principal hypotheses employed in the Almagest hazen and Tycho Brahé, or of any one before Cas-
(to which it refers in a preliminary address to sini. With regard to the genuineness of the book,
Syrus) for the explanation of the heavenly motions on the one hand there is its worthiness of Ptolemy
Simplícius refers to two books of hypotheses, of on the point of refraction, and the attribution of it
which we may suppose this is one. It was first to him. On the other hand, there is the absence of
printed (Gr. Lat. ) by Bainbridge, with the Sphere allusion, either to the Almagest in the book on
of Proclus and the canon above noted, London, optics, or to the subject of refraction in the Alma-
1620, 4to. , with a page of Bainbridge's corrections gest. Delambre, who appears convinced of the ge-
at the end; afterwards by Halma, as already de- nuineness, supposes that it was written after the Al-
scribed.
magest. But on this supposition, it must be supposed
8. 'Apuovikov Berla y. This treatise on the that Ptolemy, who does not unfrequently refer to
theory of the musical scale was first published the Almagest in his other writings, has omitted to
(Gr. Lat. ) in the collection of Greek musicians, by do so in this one, and that upon points which are
Gogavinus. Venice, 1562, 4to. (Fabricius). Next taken from the Almagest, as the assertion that the
by Wallis (Gr. Lat. ), Oxford, 1682, 4to. , with moon has a colour of its own, seen in eclipses. But
various readings and copious notes. This last what weighs most with us is the account which
edition was reprinted (with Porphyry's com- Delambre gives of the geometry of the author.
mentary, then first published) in the third volume Ptolemy was in geometry, perspicuous, elegant,
of Wallis's works, Oxford, 1699, folio.
profound, and powerful ; the author of the optics
9. Tepl xpirnplov kal meuovikoù, De Judicandi could not even succeed in being clear on the very
Facultate et Animi Principatu, a metaphysical points in which Euclid (or another, if it be not
work, attributed to Ptolemy. It was edited by Euclid) had been clear before him. Delambre ob-
Bouillaud (Gr. Lat. ), Paris, 1663, 4to. , and the serves, in two passages, “ La démonstration de
edition had a new title page (and nothing more) in Ptolémée est fort embrouillée ; celle d'Euclide est
1681.
et plus courte et plus claire,” “ Euclide avait
In Lalande we find attributed to Ptolemy, “Re-prouvé proposition 21 et 22, que les objets pa-
gulae Artis Mathematiche” (Gr. Lat. ),—1569, 8vo. , raissent diminués dans les miroirs convexes. On
with explanations by Erasmus Reinhold.
entrevoit que Ptolémée a voulu aussi démontrer les
The collection made by Fabricius of the lost mêmes propositions. " Again, the refraction apart,
1
## p. 574 (#590) ############################################
574
PTOLEMAEUS.
PTOLEMAEUS.
moon.
3
1
Delambre remarks of Alhazen that he is "plus these helps, if we were ignorant of refraction and
riche, plus savant, et plus géométre que Ptolemée. " of the true altitude of the pole, as to which, even
Taking all this with confidence, for Delambre, at Alexandria, and in spite of armillary circles of
though severe, was an excellent judge of relative every kind, an error of a quarter of a degree was
merit, we think the reader of the Almagest will committed. In our day we dispute about the frac
pause before be believes that the man who had tion of a second ; in that of Hipparchus they could
written this last work (which supposition is abso- not answer for the fraction of a degree ; they might
lutely necessary) became a poor geometer, on the mistake by as much as the diameter of the sun or
authority of one manuscript headed with his name. Let us rather turn our attention to the
The subject wants further investigation from such essential services rendered by Hipparchus to astra
sources as still exist : it is not unlikely that the nomy, of which he is the real founder. He is the
Arabic original may be found. Were we speaking first who gave and demonstrated the means of solv-
for Ptolemy, we should urge that a little diminu- ing all triangles, rectilinear and spherical, both.
tion of his fame as a mathematician would be well. He constructed a table of chords, of which he made
compensated by so splendid an addition to his ex- the same sort of use as we make of our sines. He
perimental character as the credit of a true theory made more observations than his predecessors, and
of refraction. But the question is, how stands the understood them better. He established the theory
fact ? and for our own parts, we cannot but suspend of the sun in such a manner that Ptolemy, 263
our opinion.
years afterwards, found nothing to change for the
We now come to speak of Ptolemy as an astro- better. It is true that he was mistaken in the
nomer, and of the contents of the Almagest. And amount of the sun's inequality ; but I have shown
with his name we must couple that of his great pre- that this arose from a mistake of half a day in the
decessor, Hipparchus. The latter was alive at B. C. time of the solstice. He himself admits that his
150, and the former at a. D. 150, which is of easy result may be wrong by a quarter of a day; and
remembrance. From the latter labours of Hip- we may always, without scruple, double the error
parchus to the earlier ones of Ptolemy, it is from supposed by any author, without doubting his good
250 to 260 years. Between the two there is faith, but only attributing self-delusion. He deter-
nothing to fill the gap : we cannot construct an in- mined the first inequality of the moon, and Ptolemy
termediate school out of the names of Geminus, changed nothing in it ; he gave the motion of the
Poseidonius, Theodosius, Sosigenes, Hyginus, Ma- moon, of her apogee and of her nodes, and Pto-
nilius, Seneca, Menelaus, Cleomedes, &c. : and we lemy's corrections are but slight and of more than
have no others. We must, therefore, regard P to doubtful goodness. He had a glimpse (il a entreru)
lemy as the first who appreciated Hipparchus, and of the second inequality ; he made all the observa-
followed in his steps. This is no small merit in tions necessary for a discovery the honour of which
itself.
was reserved for Ptolemy ; a discovery which per-
What Hipparchus did is to be collected mostly haps he had not time to finish, but for which he
from the writings of Ptolemy himself, who has had prepared every thing. He showed that all the
evidently intended that his predecessor should lose hypotheses of his predecessors were insufficient to
no fame in his hands. The historian who has taken explain the double inequality of the planets ; he
most pains to discriminate, and to separate what predicted that nothing would do except the combi-
is due to Hipparchus, is Delambre. If he should nation of the two hypotheses of the excentric and
be held rather too partial to the predecessor of epicycle. Observations were wanting to him, be-
Ptolemy, those who think so will be obliged to cause these demand intervals of time exceeding the
admit that he gives his verdict upon the evidence, duration of the longest life: he prepared them for
and not upon any prepossession gained before trial. his successors. We owe to his catalogue the im-
He is too much given, it may be, to try an old as- portant knowledge of the retrograde motion of the
tronomer by what he has done for us, but this does equinoctial points. We could, it is true, obtain
not often disturb his estimate of the relative merit this knowledge from much better observations,
of the ancients. And it is no small testimony that made during the last hundred years : but such ob-
an historian so deeply versed in modern practice, servations would not give proof that the motion is
80 conversant with ancient writings, so niggard of sensibly uniform for a long succession of centuries;
his praise, and so apt to deny it altogether to any and the observations of Hipparchus, by their num-
thing which has since been surpassed, cannot get ber and their antiquity, in spite of the errors
through his task without making it evident that which we cannot help finding in them, give us this
Hipparchus has become a chief favourite. The important confirmation of one of the fundamental
summing up on the merits of the true father of as- points of Astronomy. He was here the first dis-
tronomy, as the historian calls him, is the best coverer. He invented the planisphere, or the mode
enumeration of his services which we can make, of representing the starry heavens upon a plane,
and will save the citation of authorities. The fol-. and of producing the solutions of problems of
lowing is translated from the preliminary discourse spherical astronomy, in a manner often as exact as,
(which, it is important to remember, means the and more commodious than, the use of the globe
last part written) of the Histoire de l'Astronomie itself. He is also the father of true geography, by
Ancienne.
his happy idea of marking the position of spots on
• “Let no one be astonished at the errors of half
a degree with which we charge Hipparchus, perhaps The reader must not think that Delambre says
with an air of reproach. We must bear in mind the diameter of the sun is a degree, or near it. By
that his astrolabe was only an armillary sphere ; not answering for the fraction of a degree, he means
that its diameter was but moderate, the subdivisions. that they could be sure of no more than the nearest
of a degree hardly sensible ; and that he had | degree, which leaves them open to any error under
neither telescope, vernier, nor micrometer. What half a degree, which is about the diameter of the
could we do even now, if we were deprived of sun or moon.
## p. 575 (#591) ############################################
PTOLEMAEUS.
575
PTOLEMAEUS.
;
i
the earth, as was done with the stars, by circles as in many other instances, he shows no attempt to
drawn from the pole perpendicularly to the equator, judge a mathematical argument by any thing except
that is, by latitudes and longitudes. His method its result: had it been otherwise, the unity and
of eclipses was long the only one by which difference power of this chapter would have established a
of meridians could be determined; and it is by the strong presumption in favour of its originality.
projection of his invention that to this day we con- Though Hipparchus constructed chords, it is to be
struct our maps of the world and our best geogra- remembered we know nothing of his manner as a
phical charts. "
mathematician; nothing, indeed, except some re-
We shall now proceed to give a short synopsis sults. The next chapter is on the obliquity of
of the subjects treated in the Almagest: the reader the ecliptic as determined by observation. It is
will find a longer and better one in the second vo- followed by spherical geometry and trigonometry
lume of the work of Delambre just cited.
enough for the determination of the connection
The first book opens with some remarks on between the sun's right ascension, declination, and
theory and practice, on the division of the sciences, longitude, and for the forniation of a table of de-
and the certainty of mathematical knowledge : clinations to each degree of longitude. Delambre
this preamble concludes with an announcement of says he found both this and the table of chords
the author's intention to avail himself of his pre- very exact.
decessors, to run over all that has been sufficiently The second book is one of deduction from the
explained, and to dwell upon what has not been general doctrine of the sphere, on the effect of po-
done completely and well. ' It then describes as sition on the earth, the longest days, the determi-
the intention of the work to treat in order:- the nation of latitude, the points at which the sun is
relations of the earth and heaven; the effect of vertical, the equinoctial and solsticial shadows of
position upon the earth ; the theory of the sun and the gnomon, and other things which change with
moon, without which that of the stars cannot be the spectator's position. Also on the arcs of the
undertaken ; the sphere of the fixed stars, and ecliptic and equator which pass the horizon simul-
those of the five stars called planets. Arguments taneously, with tables for different climates, or
are then produced for the spherical form and motion parallels of latitude having longest days of given
of the heavens, for the sensibly spherical form of durations. This is followed by the consideration
the earth, for the earth being in the centre of the of oblique spherical problems, for the purpose of
heavens, for its being but a point in comparison calculating angles made by the ecliptic with the
with the distances of the stars, and its having no vertical, of which he gives tables,
motion of translation. Some, it is said, admitting The third book is on the length of the year, and
these reasons, nevertheless think that the earth may on the theory of the solar motion. Ptolemy in-
have a motion of rotation, which causes the (then) forms us of the manner in which Hipparchus made
only apparent motion of the heavens. Admiring the discovery of the precession of the equinoxes,
the simplicity of this solution, Ptolemy then gives by observation of the revolution from one equinox
his reasons why it cannot be. With these, as well to the same again being somewhat shorter than
as his preceding arguments, our readers are familiar. the actual revolution in the heavens. He discusses
Two circular celestial motions are then admitted : the reasons which induced his predecessor to think
one which all the stars have in common, another there was a small inequality in the length of the
which several of them have of their own. From year, decides that he was wrong, and produces the
several expressions here used, various writers have comparison of his own observations with those of
imagined that Ptolemy held the opinion maintained Hipparchus, to show that the latter had the true
by many of his followers, namely, that the celestial and constant value (one three-hundredth of a day
spheres are solid. Delambre inclines to the con- less than 3654 days). As this is more than six
trary, and we follow him. It seems to us that, minutes too great, and as the error, in the whole
though, as was natural, Ptolemy was led into the interval between the two, amounted to more than
phraseology of the solid-orb system, it is only in a day and a quarter, Delambre is surprised, and
the convenient mode which is common enough in with reason, that Ptolemy should not have detected
all systems. When a modern astronomer speaks it. He hints that Ptolemy's observations may
of the variation of the eccentricity of the moon's have been calculated from their required result ; on
orbit as producing a certain effect upon, say her which we shall presently speak. It must be re-
longitude, any one might suppose that this orbit membered that Delambre watches every process of
was a solid transparent tube, within which the Ptolemy with the eye of a lynx, to claim it for
moon is materially restrained to move. Had it not Hipparchus, if he can ; and when it is certain that
been for the notion of his successors, no one would the latter did not attain it, then he might have
have attributed the same to Ptolemy: and if the attained it, or would if he had lived, or at the least
literal meaning of phrases have weight, Copernicus it is to be matter of astonishment that he did not.
is at least as much open to a like conclusion as Ptolemy then begins to explain his mode of ap-
Ptolemy.
plying the celebrated theory of excentrics, or revo-
Then follows the geometrical exposition of the lutions in a circle which has the spectator out of its
mode of obtaining a table of chords, and the table centre ; of epicycles, or circles, the centres of which
itself to half degrees for the whole of the semi- revolve on other circles, &c. As we cannot here
circle, with differences for minutes, after the man- give mathematical explanations, we shall refer the
ner of recent modern tables. This morsel of reader to the general notion which he probably has
geometry is one of the most beautiful in the Greek on this subject, to Narrien's History of Astronomy,
writers: some propositions from it are added to or to Delambre himself. As to the solar theory, it
many editions of Euclid. Delambre, who thinks may be sufficient to say that Ptolemy explains the
as meanly as he can of Ptolemy on all occasions, one inequality then known, as Hipparchus did
mentions it with a doubt as to whether it is his before him, by the supposition that the circle of
own, or collected from his predecessors. In this, the sun is an excentric; and that he does not
1
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PTOLEMAEUS.
PTOLEMAEUS.
appear to have added to his predecessor at all, in given by Hipparchus as the least which couid be;
discovery at least.
some changes having also been made by Ptolemy's
On this theory of epicycles, we may say a word own observations. This catalogue is pretty weil
once for all. The common notion is that it was a shown by Delambre (who is mostly successful
cumbrous and useless apparatus, thrown away by when he attacks Ptolemy as an observer) to repre-
the moderns, and originating in the Ptolemaic, or sent the heaven of Hipparchus, altered by a wrong
rather Platonic, notion, that all celestial motions precession, better than the heaven of the time at
must either be circular and uniform motions, or which the catalogue was made. And it is observed
compounded of them. But on the contrary, it was that though Prolemy observed at Alexandria,
an elegant and most efficient mathematical instru- where certain stars are visible which are not visible
ment, which enabled Hipparchus and Ptolemy to at Rhodes (where Hipparchus observed), none of
represent and predict much better than their pre- those stars are in Ptolemy's catalogue. But it may
decessors had done ; and it was probably at least also be noticed, on the other hand, that one original
as good a theory as their instruments and capabi- mistake (in the equinox) would have the effect of
lities of observation required or deserved. And making all the longitudes wrong by the same
many readers will be surprised to hear that the quantity; and this one mistake might have oc-
modern astronomer to this day resolves the same curred, whether from observation or calculation, or
motions into epicyclic ones. When the latter ex- both, in such a manner as to give the suspicious
presses a result by series of sines and cosines appearances.
(especially when the angle is a mean motion or a The remainder of the thirteen books are devoted
multiple of it) he uses epicycles ; and for one to the planets, on which Hipparchus could do little,
which Ptolemy scribbled on the heavens, to use except observe, for want of long series of observa-
Milton's phrase, he scribbles twenty. The differ- tions. Whatever we may gather from scattered
ence is, that the ancient believed in the necessity hints, as to something having been done by Hip-
of these instruments, the modern only in their parchus himself, by Apollonius, or by any others,
convenience ; the former used those which do not towards an explanation of the great features of
sufficiently represent actual phenomena, the latter planetary motion, there can be no doubt that the
knows how to choose better; the former taking the iheory presented by Ptolemy is his own.
instruments to be the actual contrivances of nature, These are the main points of the Almagest, so
was obliged to make one set explain every thing, far as they are of general interest. Ptolemy ap-
the latter will adapt one set to latitude, another to pears in it a splendid mathematician, and an (at
longitude, another to distance. Difference enough, least) indifferent observer. It seems to us most
no doubt; but not the sort of difference which the likely that he knew his own deficiency, and that,
common notion supposes.
as has often happened in similar cases, there was
The fourth and fifth books are on the theory of on his mind a consciousness of the superiority of
the moon, and the sixth is on eclipses. As to the Hipparchus which biassed him to interpret all his
moon, Ptolemy explains the first inequality of the own results of observation into agreement with the
moon's motion, which answers to that of the sun, and predecessor from whom he feared, perhaps a great
by virtue of which (to use a mode of expression very deal more than he knew of, to differ. But nothing
common in astronomy, by which a word properly re- can prevent his being placed as a fourth geometer
presentative of a phenomenon is put for its cause) the with Euclid, Apollonius, and Archimedes. De-
motions of the sun and moon are below the average lambre has used him, perhaps, harshly ; being,
at their greatest distances from the earth, and certainly in one sense, perhaps in two, an indi:
above it at their least. This inequality was well ferent judge of the higher kinds of mathematical
known, and also the motion of the lunar apogee, as merit.
it is called ; that is, the gradual change of the As a literary work, the Almagest is entitled to
position of the point in the heavens at which the a praise which is rarely given ; and its author has
moon appears when her distance is greatest. Pto-shown abundant proofs of his conscientious fairness
lemy, probably more assisted by records of the ob- and nice sense of honour. It is pretty clear that
Bervations of Hipparchus than by his own, detected the writings of Hipparchus had never been public
that the single inequality above mentioned was not property: the astronomical works which intervene
bufficient, but that the lunar motions, as then known, between Hipparchus and Ptolemy are so poor as to
could not be explained without supposition of an make it evident that the spirit of the former had
other inequality, which has since been named the not infused itself into such a number of men as
evection. Its effect, at the new and full moon, is would justify us in saying astronomy had a scien-
to make the effect of the preceding inequality ap- tific school of followers. Under these circum-
pear different at different times; and it depends stances, it was open to Ptolemy, had it pleased
not only on the position of the sun and moon, but him, most materially to underrate, if not entirely to
on that of the moon's apogee. The disentangle- suppress, the labours of Hipparchus ; and without
ment of this inequality, the magnitude of which the fear of detection. Instead of this, it is from
depends upon three angles, and the adaptation of the former alone that we now chiefly know the
an epicyclic hypothesis to its explanation, is the latter, who is constantly cited as the authority,
greatest triumph of ancient astronomy.
and spoken of as the master. Such a spirit, shown
The seventh and eighth books are devoted to by Ptolemy, entitles us to infer that had he really
the stars. The celebrated catalogue (of which we used the catalogue of Hipparchus in the manner
have before spoken) gives the longitudes and lati- hinted at by Delambre, he would have avowed
tudes of 1022 stars, described by their positions what he had done ; still, under the circumstances
in the constellations. It seems not unlikely that of agreement noted above, we are not at liberty to
in the main this catalogue is really that of Hip- reject the suspicion. We imagine, then, that
parchus, altered to Ptolemy's own time by assum- Ptolemy was strongly biassed towards those me-
ing the value of the precession of the equinoxes (thods both of observation and interpretation, which
VANNI
ܪ
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PTOLEMAEUS.
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PTOLEMAEUS.
access to
would place him in agreement, or what he took for where, would avail himself of the rich materials
agreement, with the authority whom in his own collected by Greek investigators, especially from
mind he could not disbelieve. (IIalma and De- the time of Alexander ; and this presumption is
lambre, opp. citt. ; Weidler, Hist. Astron. ; La converted into a certainty by the information which
lande, Bibliogr. Astron. ; Hoffman, Lexic. Bibliogr. ; Ptolemy gives us respecting the Greek itineraries
the editions named, except when otherwise stated ; and peripluscs which Marinus had used as autho-
Fabric. Bibh Gracc. , &c. )
[A. De M. ] rities. The whole question is thoronghly discussed
by Hecren, in his Commentatio de Fontibus Gco-
THE GEUGRAPHICAL SYSTEM OF PTOLEMY. graphicorum Ptolemaci, Tabularumque iis anncx-
arum, Gotting. 1827, which is appended to the
The rewypadıkti Torymous of Ptolemy, in cight English translation of his Ideen (Asiatic Nations,
books, may be regarded as an exhibition of the vol. iii. Append. C. ). He shows that Brehmer has
final state of geographical knowledge among the greatly overrated the geographical knowledge of
ancients, in so far as geography is the science of the Phoenicians, and that his hypothesis is alto-
determining the positions of places on the earth's gether groundless.
surface ; for of the other branch of the science, the In examining the geographical system of Pto-
description of the objects of interest connected with lemy, it is convenient to speak separately of its
different countries and places, in which the work mathematical and historical portions; that is, of his
of Strabo is so rich, that of Ptolemy contains com- notions respecting the figure of the earth, and the
paratively nothing. With the exception of the mode of determining positions on its surface, and
introductory matter in the first book, and the latter his knowledge, derived from positive information, of
part of the work, it is a mere catalogue of the the form and extent of the different countries, and
names of places, with their longitudes and lati- the actual positions and distances of the various
tudes, and with a few incidental references to ob- places in the then known world.
jects of interest.
that it bears internal marks of having been made he republished it as “. . . . omnia quae extant opera,
from the Arabic (as was indeed generally admitted), praeter Geographiam, quam non dissinili forma
and throws great light on the subsequent Greek (double column) nuperrimè ædidimus : summa cura
editions and versions. Next comes the version of et diligentia castigata ab Erasmo Oswaldo Schrek-
George of Trebizond, “ Ptolemaei Almagestum, ex henfuchsio . . . . " The contents are the same as
Versione Latina Georgii Trapezuntii,” Venice, in the former edition, with notes added by the
15:25, folio. (Fabricius, who is in doubt as to new editor. Erasmus Reinbold published the first
whether it were not 1527, and confounds it with book only (Gr. Lat with Scholia), Wittenberg,
the former version. ) From all we can collect, 1549, 8vo. (Lalande, who gives also 1560), and
however, no one asserts himself to have seen an also 1569 (Halina). S. Gracilis (Legrêle) pub-
earlier edition of the version of Trapezuntius than blished the second book in Latin, Paris, 1556,
that of Venice, 1528, folio (with a red lily in the 8vo. (Lal. Halm. ). J. B. Porta gave the first book
title page); and Hoffman sets down none earlier. in Latin, with Theon, Naples, 1588, 4to. (Lal. ),
Its title (from a copy before us) is “ Claudii Pto- and the first and second books in the same way,
lemaei Pheludiensis Alexandrini Almagestum. . . . Naples, 1605, 4to. (Lal. Halm. ).
latina donatum lingua ab Georgio Trapezuntio. . . . From the tinie of Galileo, at which we are now
anno salutis MDXXyni. labente. ” This version is arrived, we cannot find that any complete version
stated in the preface to have been made from the of the Almagest (Greek edition there certainly was
Greek: the editor was Lucas Gauricus. The none) was published until that of Halma, to which
nine books of astronomy by the Arab Gever, edited
We shall not attempt to describe
by Peter Apian, Nuremberg, 1534, folio, and often the dissertations by Delambre, Ideler, &c. , con-
set down as a commentary on, almost an edition tained in this splendid collection, but shall simply
of, the Almagest, have no right whatever to either note the contents of the first four volumes: for the
name, as we say from examination. Halma, ob- rest see Theon. Of the manuscripts we have
serving in the epitome of Purbach and Regiomon- already spoken. The descriptions are-Paris, 1813,
tanuis strong marks of Arabic origin, and taking 1816, 1819, 1820, quarto. The first two volumes
Geber to be in fact Ptolemy, concludes that the contain the Almagest, in Greek and French, with
epitome was made from Geber, and reproves them the various readings. The third contains the Karwy
for not naming their original. Halma must have Baoileiwv and the páoeis tûv år lavar of Ptolemy,
taken Geber's work to be actually the Almagest, for, and the works of GEMINUS. The fourth contains
with the above censure, he admits that the two the υποθέσεις των πλακωμένων and the άρχαι και
epitomists have caught the meaning and spirit of mobéoeis Madnuatınal of Ptolemy, and the upotú-
Ptolemy. It is worth while, therefore, to state, πωσεις of Proclus.
from examination of Geber (whom Halma had not The part of the Almagest which really concerns
seen), and comparison of it with the epitome in the modern astronomer, as part of the effective
question, that neither is Geber a commentary on records of his science, is the catalogue of stars in
the Almagest, nor the epitome formed from Geber. the seventh and eighth books. Of this catalogue
The first Greek text of the Almagest (as well as there have been several distinct editions. The
that of Euclid) was published by Symon Grynoeus, earliest (according to Lalande, not mentioned by
Basle, 1538, folio: “KA. Ntoneualov heykans ouv- Halma) is a Latin version by John Noviomagus,
Taféws Bien, sy'. . . . ” It is Greek only, and con- from Trapezuntius,“ . . . . Phaenomena stellarum
tains the Almagest, and the commentary of Theon 1022 fixarum ad hanc aetatem reducta . . . ," Co
[PAPPUs). Basle, 1541, folio. Jerome Gemusaeus logne, 1537, folio, with forty-eight drawings of the
published
omnis quae extant opera (Geogra- constellations by Albert Durer. The next (Baily)
is a Greek edition (stated to be furnished by
* It is a slight matter, but it is difficult to say Halley), at the end of the third of the four volumes
how small an error is not worth correcting when of Hudson's “ Geographiae veteris Scriptores Graeci
great names support it. Halma, followed by Baily, minores,” Oxford, 1698—1712, 8vo.
The next
says that Trapezuntius got his Greek manuscript (Halma) is a French version by Montignot, Nancy,
from a copy of one in the Vatican, made by order 1786, and Strasburg, 1787, 4to. , translated into
of the abbot Bartolini. But what Gauricus says is German by Bode, Berlin and Stettin, 1795, 8vo.
“ Georg. Trap. magnum hunc Astronomum . . . . e The last, and by far the best, is that given in
Graeca in Latinam transtulit linguam. Quem Lau- Greek) by the late Francis Brily, in his collection
rentius Bartolinus. . . . e Vaticano exemplari. . . . of the catalogues of Ptolemy, Ulugh Beigh, Tycho
transcribendum curavit. ” The quem seems to Brahé, Halley, and Hevelius, which forms volume
refer to Trapezuntius, who had long been dead : xiii. of the Memoirs of the Royal Astronomical
Gauricus explains how he came by a copy. Andrew Society, London, 1843, 4to. This edition of the
Trapezuntius, in his preface to his father's work
(which follows that of Gauricus), though dedicating + Mr. Baily, who closely examined all his edi.
to the pope, does not hint at the manuscript from tions, as will presently be noted, does not even
the pope's library, nor at any manuscript in par- give the name of this one, though to our know
ticular.
ledge it was one of those he tried to make use of.
## p. 572 (#588) ############################################
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PTOLEMAEUS.
PTOLEMAEUS.
catalogue is the one which should be cited. It have been twice printed in Greek, and together ;
gives the readings of the Florence and Paris manu- first, by John Camerarius (Gr. Lat. ), Nuremberg.
scripts (from Halma), of the Greek of Grynoeus 1535, 410. ; secondly, with new Latin version and
and Halma, and of the Latin of Liechtenstein and preface, by Philip Melancthon, Basle, 1553, 8vo.
Trapezuntius, with corrections from our present (Fabricius, Hoffmann). Among the Latin editions,
astronomical knowledge very sparingly, and we over and above those already noted as accompany-
believe very judiciously, introduced. The astro-ing editions of the Almagest, Hain mentions two
nomer might easily make Ptolemy's catalogue what (of both works) of the fifteenth century ; one by
it ought to have been ; the scholar, from criticism Ratdolt, Venice, 1481, 4to. ; another by Bonetus
alone, would certainly place many stars where it is (with other astrological tracts), Venice, 1493, fol.
impossible Ptolemy could have recorded them as There is another, iranslated by Gogava, Louvain,
being. From frequent conversation with Mr. Baily | 1548, 4to. (Hoffınann, Lalande); and there is ano-
during the progress of his task, we can confidently ther attached to the collection made by Hervagius
say that he had no bias in favour of making his (which begins with Julius Firmicus, and ends with
text astronomically correct at the expense of cri- Manilius), Basle, 1533, folio ; and all except the
tical evidence ; but that he was as fully impressed Firmicus and Manilius seem to have been printed
with the necessity of producing Ptolemy's errors as before, Venice, 1519, folio (Lalande). There is
his truths.
mention of two other editions, of Basle and Venice,
Mr. Baily remarks, as to the catalogue, and the 1551 and 1597, including both Firmicus and Ma-
same appears as to other parts of the Almagest, that nilius (Lalande). The Centiloquium has been
Ilalma often gives in the text he has chosen read sometimes attributed to Hermes Trismegistus : but
ings different from those of all his principal subjects this last-named author had a Centiloquium of his
of collation. This means that he bas, in a consi- own, which is printed in the edition just described,
derable number of cases, either amended his text and is certainly not in matter the same as Pto-
conjecturally, or preferred the reading of some lemy's. Fabricius, mentioning the Centiloquium,
minor manuscript, without particular mention. says that Ptolemy de Electionibus, appeared (Lat. ),
This is no great harın, since, as the readings of all | Venice, 1509,- Perhaps this is the same
his great sources are always given, it amounts to hav- work as the one of the same title, afterwards pub-
ing one more choice from an unnamed quarter. But lished as that of the Arab Zahel. The English
it is important that the critical reader of the edition translation (1701) purporting to be from “ Pro-
should have notice of it ; and the more so, inas- lemy's Quadripartite” (Hoffmann), must be from
much as the readings are at the end of each the paraphrase by Proclus, as appears from its
volume, without* text-reference from the places in title-page containing the name of Leo Allatius, who
which they occur.
edited the latter. The usual Latin of the Centilo.
On the preceding summary of the bibliographical quium is by Jovius Pontanus: whether the Commen-
history of the Almagest, we shall remark that the turies attributed to him, printed, Basle, 1531, 4to.
reader is not to measure the currency of it by the (Lalande), &c. , are any thing more than the version,
number of its editions. It was the gold which lay we must leave to the professedly astrological biblio-
in the Bank, while paper circulated on its authority. grapher. It was printed without the Quadripar-
All the European books on astronomy were fa- titum several times, as at Cologne, 1514, 8vo. : and
shioned upon it, and it was only the more learned this is said to be with the comment of Trapezuntius,
astronomers who went to the common original. meaning probably the version. The commentaries
Euclid was actually read, and accordingly, as we or introductions, two in number, attributed to
have seen, the presses were crowded with editions Proclus and Porphyry, were printed (Gr. Lat. )
of the Elements. But Ptolemy, in his own words, Basle, 1559, folio (Lalande).
was better known by his astrology than by his as- 3. Kavwv Baouléwv. This is a catalogue of Assy-
tronomy. We now come to his other writings, on rian, Persian, Greek, and Roman sovereigns, with
which we have less to say.
the length of their reigns, several times referred to
2. Tetpábı6 os oúvtatis, generally called Tetra- by Syncellus, and found, with continuation, in
billon, or Quadripartitum de A potelesmatibus et Ju- Theon. It is considered an undoubted work of
diciis Astrorum. With this goes another small Ptolemy. It is a scrap which has been printed by
work, called kapids, or Fructus Librorum Suorum, Scaliger, Calvisius (who valued it highly), Petavius
often called Centiloquium, from its containing a and Dodwell ; but most formally by Bainbridge
'hundred aphorisms. Both of these works are as- (in the work presently cited), and by Halma, as
trological, and it has been doubted by some whether above noticed.
they be genuine. But the doubt merely arises 4. Φάσεις απλανών αστέρων και συναγωγή επιση-
from the feeling
that the contents are unworthy of Magelav, De Apparentiis et Significationibus inerran-
Ptolemy. The Tetrabiblon itself is, like the Alma- tium. This annual list of sidereal phaenomena has
gest and other writings, dedicated to his brother been printed three times in Greek: by Petavius,
Syrus: it refers, in the introduction, to another in his Uranologion, Paris, 1630, folio ; partially
work on the mathematical theory. Both works in Fabricius, but deferred by Harless to a supple-
mentary volume which did not appear ; and by
• If editors will put the various readings at the Halma, as above noticed. There are three other
end of their volumes, instead of at the bottom of works of the same name or character, which have
the pages, we should wish, when there are more been attributed to Ptolemy, and all three are given,
volumes than one, that the readings for one volume with the genuine one, by Petavius, as above. Twó
should be inserted at the end of another. It would of them are Roman calendars, not worth notice. The
then be practicable to have the text and its variations third was published, in Latin, from a Greek manu-
open before the reader at one and the same moment, script, by Nic. Leonicus, Venice, 1516, 8vo. (Fabri-
which, when two or three instances come close to cius): and this is reprinted in the collection begin-
gether, is very desirable.
ning with Julius Firmicus, above noticed. We have
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PTOLEMAEUS.
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573
mentioned the versions of the genuine work which , works of Ptolemy is as follows :-From Simplicius,
are found with those of the Almagest.
Περί μετρησέως μονόβιβλος, to prove that there
5, 6. De Analemmate and Planisphaerium. can be only three dimensions of space ; Niepl poter
These works are obtained from the Arabic. Fa- Bubalov, mentioned also by Eutocius ; Etoixeia,
bricius, who had not seen them, conjectures that two books of hypotheses. From Suidas, three books
they are the same, which is not correct. The Mnxavikw. From Heliodorus and_Simplicius,
Analemma is a collection of graphical processes 'OTTIKT) #payuatela. From Tzetzes, lepinynous ;
for facilitating the construction of sun-dials, and from Stephen of Byzantium, nepitnous. There
grounded on what we now call the orthographic have been many modern forgeries in Ptolemy's
projection of the sphere, a perspective in which, name, mostly astrological.
mathematically speaking, the eye is at an infinite It must rest an unsettled question whether the
distance. The Planisphere is a description of the work written by Ptolemy on optics be lost or not.
stereographic projection, in which the eye is at The matter now stands thus : Alhazen, the principal
the pole of the circle on which the sphere is pro-Arab writer on optice, does not mention Ptolemy,
jected. Delambre seems to think, from the former nor indeed, any one else. Some passages from Roger
work, that Ptolemy knew the gnomonic projection, Bacon, taken to be opinions passed on a manu-
in which the eye is at the centre of the sphere: script purporting to be that of Ptolemy, led Mon-
but, though he uses some propositions which are tucla to speak highly of Ptolemy as an optical
closely connected with the theory of that projec-writer. This mention probably led Laplace to ex-
tion, we cannot find any thing which indicates dis- amine a Latin version from the Arabic, existing in
tinct knowledge of it. There is but one edition of the Royal Library at Paris, and purporting to be
the work De Analemmate, edited by Commandine, Ptolemy's treatise. The consequence was Laplace's
Rome, 1562, 4to. (Lalande says there is a Vene assertion that Ptolemy had given a detailed account
tian title of the same date. He also mentions of the phenomenon of astronomical refraction. This
another edition, Rome, 1572, 4to. , perhaps an error remark of Laplace led Humboldt to examine the
of copying). Nothing is told about the Arabic manuscript, and to call the attention of Delambre
original, or the translator. The Planisphaerium to it. Delambre accordingly gave a full account of
first appeared in print in the edition of the Geo the work in his Histoire de l'Astronomie Ancienne,
graphy, Rome (? ), 1507, fol. (Hoffmann); next vol. ii. pp. 411–431. The manuscript is headed
in Valder's collection, entitled “Sphaerae atque As- Incipit Liber Ptolemaei de Opticis sive Aspectibus
trorum Coelestium Ratio . . . . " Basle (? no place is translatus ab Ammiraco (or Ammirato] Eugenio
named), 1536, 4to. With this is joined the Pla-Siculo.
It consists of five books, of which the first
nisphaerium of Jordanus. There is also an edition is lost and the others somewhat defaced. It is said
of Toulouse, 1544, fol. (Hoffmann). . But the best there is in the Bodleian a manuscript with the
edition is that of Commandine, Venice, 1558, 4to. whole of five books of a similar title. The first
Lalande says it was reprinted in 1588. Suidas three books left give such a theory of vision as
records that Ptolemy wrote animous émipavelas might be expected from a writer who had the work
opalpas, which is commonly taken to be the work attributed to Euclid in his mind. But the fifth book
on the planisphere. Both the works are addressed does actually give an account of refraction, with ex-
to Syrus.
perimental tables upon glass, water, and air, and an
7. Tiepl útodégewv TV Flavwuévwy, De Planeta- account of the reason and quantity of astronomical
rum Hypothesibus. This is a brief statement of the refraction, in all respects better than those of Al-
principal hypotheses employed in the Almagest hazen and Tycho Brahé, or of any one before Cas-
(to which it refers in a preliminary address to sini. With regard to the genuineness of the book,
Syrus) for the explanation of the heavenly motions on the one hand there is its worthiness of Ptolemy
Simplícius refers to two books of hypotheses, of on the point of refraction, and the attribution of it
which we may suppose this is one. It was first to him. On the other hand, there is the absence of
printed (Gr. Lat. ) by Bainbridge, with the Sphere allusion, either to the Almagest in the book on
of Proclus and the canon above noted, London, optics, or to the subject of refraction in the Alma-
1620, 4to. , with a page of Bainbridge's corrections gest. Delambre, who appears convinced of the ge-
at the end; afterwards by Halma, as already de- nuineness, supposes that it was written after the Al-
scribed.
magest. But on this supposition, it must be supposed
8. 'Apuovikov Berla y. This treatise on the that Ptolemy, who does not unfrequently refer to
theory of the musical scale was first published the Almagest in his other writings, has omitted to
(Gr. Lat. ) in the collection of Greek musicians, by do so in this one, and that upon points which are
Gogavinus. Venice, 1562, 4to. (Fabricius). Next taken from the Almagest, as the assertion that the
by Wallis (Gr. Lat. ), Oxford, 1682, 4to. , with moon has a colour of its own, seen in eclipses. But
various readings and copious notes. This last what weighs most with us is the account which
edition was reprinted (with Porphyry's com- Delambre gives of the geometry of the author.
mentary, then first published) in the third volume Ptolemy was in geometry, perspicuous, elegant,
of Wallis's works, Oxford, 1699, folio.
profound, and powerful ; the author of the optics
9. Tepl xpirnplov kal meuovikoù, De Judicandi could not even succeed in being clear on the very
Facultate et Animi Principatu, a metaphysical points in which Euclid (or another, if it be not
work, attributed to Ptolemy. It was edited by Euclid) had been clear before him. Delambre ob-
Bouillaud (Gr. Lat. ), Paris, 1663, 4to. , and the serves, in two passages, “ La démonstration de
edition had a new title page (and nothing more) in Ptolémée est fort embrouillée ; celle d'Euclide est
1681.
et plus courte et plus claire,” “ Euclide avait
In Lalande we find attributed to Ptolemy, “Re-prouvé proposition 21 et 22, que les objets pa-
gulae Artis Mathematiche” (Gr. Lat. ),—1569, 8vo. , raissent diminués dans les miroirs convexes. On
with explanations by Erasmus Reinhold.
entrevoit que Ptolémée a voulu aussi démontrer les
The collection made by Fabricius of the lost mêmes propositions. " Again, the refraction apart,
1
## p. 574 (#590) ############################################
574
PTOLEMAEUS.
PTOLEMAEUS.
moon.
3
1
Delambre remarks of Alhazen that he is "plus these helps, if we were ignorant of refraction and
riche, plus savant, et plus géométre que Ptolemée. " of the true altitude of the pole, as to which, even
Taking all this with confidence, for Delambre, at Alexandria, and in spite of armillary circles of
though severe, was an excellent judge of relative every kind, an error of a quarter of a degree was
merit, we think the reader of the Almagest will committed. In our day we dispute about the frac
pause before be believes that the man who had tion of a second ; in that of Hipparchus they could
written this last work (which supposition is abso- not answer for the fraction of a degree ; they might
lutely necessary) became a poor geometer, on the mistake by as much as the diameter of the sun or
authority of one manuscript headed with his name. Let us rather turn our attention to the
The subject wants further investigation from such essential services rendered by Hipparchus to astra
sources as still exist : it is not unlikely that the nomy, of which he is the real founder. He is the
Arabic original may be found. Were we speaking first who gave and demonstrated the means of solv-
for Ptolemy, we should urge that a little diminu- ing all triangles, rectilinear and spherical, both.
tion of his fame as a mathematician would be well. He constructed a table of chords, of which he made
compensated by so splendid an addition to his ex- the same sort of use as we make of our sines. He
perimental character as the credit of a true theory made more observations than his predecessors, and
of refraction. But the question is, how stands the understood them better. He established the theory
fact ? and for our own parts, we cannot but suspend of the sun in such a manner that Ptolemy, 263
our opinion.
years afterwards, found nothing to change for the
We now come to speak of Ptolemy as an astro- better. It is true that he was mistaken in the
nomer, and of the contents of the Almagest. And amount of the sun's inequality ; but I have shown
with his name we must couple that of his great pre- that this arose from a mistake of half a day in the
decessor, Hipparchus. The latter was alive at B. C. time of the solstice. He himself admits that his
150, and the former at a. D. 150, which is of easy result may be wrong by a quarter of a day; and
remembrance. From the latter labours of Hip- we may always, without scruple, double the error
parchus to the earlier ones of Ptolemy, it is from supposed by any author, without doubting his good
250 to 260 years. Between the two there is faith, but only attributing self-delusion. He deter-
nothing to fill the gap : we cannot construct an in- mined the first inequality of the moon, and Ptolemy
termediate school out of the names of Geminus, changed nothing in it ; he gave the motion of the
Poseidonius, Theodosius, Sosigenes, Hyginus, Ma- moon, of her apogee and of her nodes, and Pto-
nilius, Seneca, Menelaus, Cleomedes, &c. : and we lemy's corrections are but slight and of more than
have no others. We must, therefore, regard P to doubtful goodness. He had a glimpse (il a entreru)
lemy as the first who appreciated Hipparchus, and of the second inequality ; he made all the observa-
followed in his steps. This is no small merit in tions necessary for a discovery the honour of which
itself.
was reserved for Ptolemy ; a discovery which per-
What Hipparchus did is to be collected mostly haps he had not time to finish, but for which he
from the writings of Ptolemy himself, who has had prepared every thing. He showed that all the
evidently intended that his predecessor should lose hypotheses of his predecessors were insufficient to
no fame in his hands. The historian who has taken explain the double inequality of the planets ; he
most pains to discriminate, and to separate what predicted that nothing would do except the combi-
is due to Hipparchus, is Delambre. If he should nation of the two hypotheses of the excentric and
be held rather too partial to the predecessor of epicycle. Observations were wanting to him, be-
Ptolemy, those who think so will be obliged to cause these demand intervals of time exceeding the
admit that he gives his verdict upon the evidence, duration of the longest life: he prepared them for
and not upon any prepossession gained before trial. his successors. We owe to his catalogue the im-
He is too much given, it may be, to try an old as- portant knowledge of the retrograde motion of the
tronomer by what he has done for us, but this does equinoctial points. We could, it is true, obtain
not often disturb his estimate of the relative merit this knowledge from much better observations,
of the ancients. And it is no small testimony that made during the last hundred years : but such ob-
an historian so deeply versed in modern practice, servations would not give proof that the motion is
80 conversant with ancient writings, so niggard of sensibly uniform for a long succession of centuries;
his praise, and so apt to deny it altogether to any and the observations of Hipparchus, by their num-
thing which has since been surpassed, cannot get ber and their antiquity, in spite of the errors
through his task without making it evident that which we cannot help finding in them, give us this
Hipparchus has become a chief favourite. The important confirmation of one of the fundamental
summing up on the merits of the true father of as- points of Astronomy. He was here the first dis-
tronomy, as the historian calls him, is the best coverer. He invented the planisphere, or the mode
enumeration of his services which we can make, of representing the starry heavens upon a plane,
and will save the citation of authorities. The fol-. and of producing the solutions of problems of
lowing is translated from the preliminary discourse spherical astronomy, in a manner often as exact as,
(which, it is important to remember, means the and more commodious than, the use of the globe
last part written) of the Histoire de l'Astronomie itself. He is also the father of true geography, by
Ancienne.
his happy idea of marking the position of spots on
• “Let no one be astonished at the errors of half
a degree with which we charge Hipparchus, perhaps The reader must not think that Delambre says
with an air of reproach. We must bear in mind the diameter of the sun is a degree, or near it. By
that his astrolabe was only an armillary sphere ; not answering for the fraction of a degree, he means
that its diameter was but moderate, the subdivisions. that they could be sure of no more than the nearest
of a degree hardly sensible ; and that he had | degree, which leaves them open to any error under
neither telescope, vernier, nor micrometer. What half a degree, which is about the diameter of the
could we do even now, if we were deprived of sun or moon.
## p. 575 (#591) ############################################
PTOLEMAEUS.
575
PTOLEMAEUS.
;
i
the earth, as was done with the stars, by circles as in many other instances, he shows no attempt to
drawn from the pole perpendicularly to the equator, judge a mathematical argument by any thing except
that is, by latitudes and longitudes. His method its result: had it been otherwise, the unity and
of eclipses was long the only one by which difference power of this chapter would have established a
of meridians could be determined; and it is by the strong presumption in favour of its originality.
projection of his invention that to this day we con- Though Hipparchus constructed chords, it is to be
struct our maps of the world and our best geogra- remembered we know nothing of his manner as a
phical charts. "
mathematician; nothing, indeed, except some re-
We shall now proceed to give a short synopsis sults. The next chapter is on the obliquity of
of the subjects treated in the Almagest: the reader the ecliptic as determined by observation. It is
will find a longer and better one in the second vo- followed by spherical geometry and trigonometry
lume of the work of Delambre just cited.
enough for the determination of the connection
The first book opens with some remarks on between the sun's right ascension, declination, and
theory and practice, on the division of the sciences, longitude, and for the forniation of a table of de-
and the certainty of mathematical knowledge : clinations to each degree of longitude. Delambre
this preamble concludes with an announcement of says he found both this and the table of chords
the author's intention to avail himself of his pre- very exact.
decessors, to run over all that has been sufficiently The second book is one of deduction from the
explained, and to dwell upon what has not been general doctrine of the sphere, on the effect of po-
done completely and well. ' It then describes as sition on the earth, the longest days, the determi-
the intention of the work to treat in order:- the nation of latitude, the points at which the sun is
relations of the earth and heaven; the effect of vertical, the equinoctial and solsticial shadows of
position upon the earth ; the theory of the sun and the gnomon, and other things which change with
moon, without which that of the stars cannot be the spectator's position. Also on the arcs of the
undertaken ; the sphere of the fixed stars, and ecliptic and equator which pass the horizon simul-
those of the five stars called planets. Arguments taneously, with tables for different climates, or
are then produced for the spherical form and motion parallels of latitude having longest days of given
of the heavens, for the sensibly spherical form of durations. This is followed by the consideration
the earth, for the earth being in the centre of the of oblique spherical problems, for the purpose of
heavens, for its being but a point in comparison calculating angles made by the ecliptic with the
with the distances of the stars, and its having no vertical, of which he gives tables,
motion of translation. Some, it is said, admitting The third book is on the length of the year, and
these reasons, nevertheless think that the earth may on the theory of the solar motion. Ptolemy in-
have a motion of rotation, which causes the (then) forms us of the manner in which Hipparchus made
only apparent motion of the heavens. Admiring the discovery of the precession of the equinoxes,
the simplicity of this solution, Ptolemy then gives by observation of the revolution from one equinox
his reasons why it cannot be. With these, as well to the same again being somewhat shorter than
as his preceding arguments, our readers are familiar. the actual revolution in the heavens. He discusses
Two circular celestial motions are then admitted : the reasons which induced his predecessor to think
one which all the stars have in common, another there was a small inequality in the length of the
which several of them have of their own. From year, decides that he was wrong, and produces the
several expressions here used, various writers have comparison of his own observations with those of
imagined that Ptolemy held the opinion maintained Hipparchus, to show that the latter had the true
by many of his followers, namely, that the celestial and constant value (one three-hundredth of a day
spheres are solid. Delambre inclines to the con- less than 3654 days). As this is more than six
trary, and we follow him. It seems to us that, minutes too great, and as the error, in the whole
though, as was natural, Ptolemy was led into the interval between the two, amounted to more than
phraseology of the solid-orb system, it is only in a day and a quarter, Delambre is surprised, and
the convenient mode which is common enough in with reason, that Ptolemy should not have detected
all systems. When a modern astronomer speaks it. He hints that Ptolemy's observations may
of the variation of the eccentricity of the moon's have been calculated from their required result ; on
orbit as producing a certain effect upon, say her which we shall presently speak. It must be re-
longitude, any one might suppose that this orbit membered that Delambre watches every process of
was a solid transparent tube, within which the Ptolemy with the eye of a lynx, to claim it for
moon is materially restrained to move. Had it not Hipparchus, if he can ; and when it is certain that
been for the notion of his successors, no one would the latter did not attain it, then he might have
have attributed the same to Ptolemy: and if the attained it, or would if he had lived, or at the least
literal meaning of phrases have weight, Copernicus it is to be matter of astonishment that he did not.
is at least as much open to a like conclusion as Ptolemy then begins to explain his mode of ap-
Ptolemy.
plying the celebrated theory of excentrics, or revo-
Then follows the geometrical exposition of the lutions in a circle which has the spectator out of its
mode of obtaining a table of chords, and the table centre ; of epicycles, or circles, the centres of which
itself to half degrees for the whole of the semi- revolve on other circles, &c. As we cannot here
circle, with differences for minutes, after the man- give mathematical explanations, we shall refer the
ner of recent modern tables. This morsel of reader to the general notion which he probably has
geometry is one of the most beautiful in the Greek on this subject, to Narrien's History of Astronomy,
writers: some propositions from it are added to or to Delambre himself. As to the solar theory, it
many editions of Euclid. Delambre, who thinks may be sufficient to say that Ptolemy explains the
as meanly as he can of Ptolemy on all occasions, one inequality then known, as Hipparchus did
mentions it with a doubt as to whether it is his before him, by the supposition that the circle of
own, or collected from his predecessors. In this, the sun is an excentric; and that he does not
1
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1,76
PTOLEMAEUS.
PTOLEMAEUS.
appear to have added to his predecessor at all, in given by Hipparchus as the least which couid be;
discovery at least.
some changes having also been made by Ptolemy's
On this theory of epicycles, we may say a word own observations. This catalogue is pretty weil
once for all. The common notion is that it was a shown by Delambre (who is mostly successful
cumbrous and useless apparatus, thrown away by when he attacks Ptolemy as an observer) to repre-
the moderns, and originating in the Ptolemaic, or sent the heaven of Hipparchus, altered by a wrong
rather Platonic, notion, that all celestial motions precession, better than the heaven of the time at
must either be circular and uniform motions, or which the catalogue was made. And it is observed
compounded of them. But on the contrary, it was that though Prolemy observed at Alexandria,
an elegant and most efficient mathematical instru- where certain stars are visible which are not visible
ment, which enabled Hipparchus and Ptolemy to at Rhodes (where Hipparchus observed), none of
represent and predict much better than their pre- those stars are in Ptolemy's catalogue. But it may
decessors had done ; and it was probably at least also be noticed, on the other hand, that one original
as good a theory as their instruments and capabi- mistake (in the equinox) would have the effect of
lities of observation required or deserved. And making all the longitudes wrong by the same
many readers will be surprised to hear that the quantity; and this one mistake might have oc-
modern astronomer to this day resolves the same curred, whether from observation or calculation, or
motions into epicyclic ones. When the latter ex- both, in such a manner as to give the suspicious
presses a result by series of sines and cosines appearances.
(especially when the angle is a mean motion or a The remainder of the thirteen books are devoted
multiple of it) he uses epicycles ; and for one to the planets, on which Hipparchus could do little,
which Ptolemy scribbled on the heavens, to use except observe, for want of long series of observa-
Milton's phrase, he scribbles twenty. The differ- tions. Whatever we may gather from scattered
ence is, that the ancient believed in the necessity hints, as to something having been done by Hip-
of these instruments, the modern only in their parchus himself, by Apollonius, or by any others,
convenience ; the former used those which do not towards an explanation of the great features of
sufficiently represent actual phenomena, the latter planetary motion, there can be no doubt that the
knows how to choose better; the former taking the iheory presented by Ptolemy is his own.
instruments to be the actual contrivances of nature, These are the main points of the Almagest, so
was obliged to make one set explain every thing, far as they are of general interest. Ptolemy ap-
the latter will adapt one set to latitude, another to pears in it a splendid mathematician, and an (at
longitude, another to distance. Difference enough, least) indifferent observer. It seems to us most
no doubt; but not the sort of difference which the likely that he knew his own deficiency, and that,
common notion supposes.
as has often happened in similar cases, there was
The fourth and fifth books are on the theory of on his mind a consciousness of the superiority of
the moon, and the sixth is on eclipses. As to the Hipparchus which biassed him to interpret all his
moon, Ptolemy explains the first inequality of the own results of observation into agreement with the
moon's motion, which answers to that of the sun, and predecessor from whom he feared, perhaps a great
by virtue of which (to use a mode of expression very deal more than he knew of, to differ. But nothing
common in astronomy, by which a word properly re- can prevent his being placed as a fourth geometer
presentative of a phenomenon is put for its cause) the with Euclid, Apollonius, and Archimedes. De-
motions of the sun and moon are below the average lambre has used him, perhaps, harshly ; being,
at their greatest distances from the earth, and certainly in one sense, perhaps in two, an indi:
above it at their least. This inequality was well ferent judge of the higher kinds of mathematical
known, and also the motion of the lunar apogee, as merit.
it is called ; that is, the gradual change of the As a literary work, the Almagest is entitled to
position of the point in the heavens at which the a praise which is rarely given ; and its author has
moon appears when her distance is greatest. Pto-shown abundant proofs of his conscientious fairness
lemy, probably more assisted by records of the ob- and nice sense of honour. It is pretty clear that
Bervations of Hipparchus than by his own, detected the writings of Hipparchus had never been public
that the single inequality above mentioned was not property: the astronomical works which intervene
bufficient, but that the lunar motions, as then known, between Hipparchus and Ptolemy are so poor as to
could not be explained without supposition of an make it evident that the spirit of the former had
other inequality, which has since been named the not infused itself into such a number of men as
evection. Its effect, at the new and full moon, is would justify us in saying astronomy had a scien-
to make the effect of the preceding inequality ap- tific school of followers. Under these circum-
pear different at different times; and it depends stances, it was open to Ptolemy, had it pleased
not only on the position of the sun and moon, but him, most materially to underrate, if not entirely to
on that of the moon's apogee. The disentangle- suppress, the labours of Hipparchus ; and without
ment of this inequality, the magnitude of which the fear of detection. Instead of this, it is from
depends upon three angles, and the adaptation of the former alone that we now chiefly know the
an epicyclic hypothesis to its explanation, is the latter, who is constantly cited as the authority,
greatest triumph of ancient astronomy.
and spoken of as the master. Such a spirit, shown
The seventh and eighth books are devoted to by Ptolemy, entitles us to infer that had he really
the stars. The celebrated catalogue (of which we used the catalogue of Hipparchus in the manner
have before spoken) gives the longitudes and lati- hinted at by Delambre, he would have avowed
tudes of 1022 stars, described by their positions what he had done ; still, under the circumstances
in the constellations. It seems not unlikely that of agreement noted above, we are not at liberty to
in the main this catalogue is really that of Hip- reject the suspicion. We imagine, then, that
parchus, altered to Ptolemy's own time by assum- Ptolemy was strongly biassed towards those me-
ing the value of the precession of the equinoxes (thods both of observation and interpretation, which
VANNI
ܪ
## p. 577 (#593) ############################################
PTOLEMAEUS.
577
PTOLEMAEUS.
access to
would place him in agreement, or what he took for where, would avail himself of the rich materials
agreement, with the authority whom in his own collected by Greek investigators, especially from
mind he could not disbelieve. (IIalma and De- the time of Alexander ; and this presumption is
lambre, opp. citt. ; Weidler, Hist. Astron. ; La converted into a certainty by the information which
lande, Bibliogr. Astron. ; Hoffman, Lexic. Bibliogr. ; Ptolemy gives us respecting the Greek itineraries
the editions named, except when otherwise stated ; and peripluscs which Marinus had used as autho-
Fabric. Bibh Gracc. , &c. )
[A. De M. ] rities. The whole question is thoronghly discussed
by Hecren, in his Commentatio de Fontibus Gco-
THE GEUGRAPHICAL SYSTEM OF PTOLEMY. graphicorum Ptolemaci, Tabularumque iis anncx-
arum, Gotting. 1827, which is appended to the
The rewypadıkti Torymous of Ptolemy, in cight English translation of his Ideen (Asiatic Nations,
books, may be regarded as an exhibition of the vol. iii. Append. C. ). He shows that Brehmer has
final state of geographical knowledge among the greatly overrated the geographical knowledge of
ancients, in so far as geography is the science of the Phoenicians, and that his hypothesis is alto-
determining the positions of places on the earth's gether groundless.
surface ; for of the other branch of the science, the In examining the geographical system of Pto-
description of the objects of interest connected with lemy, it is convenient to speak separately of its
different countries and places, in which the work mathematical and historical portions; that is, of his
of Strabo is so rich, that of Ptolemy contains com- notions respecting the figure of the earth, and the
paratively nothing. With the exception of the mode of determining positions on its surface, and
introductory matter in the first book, and the latter his knowledge, derived from positive information, of
part of the work, it is a mere catalogue of the the form and extent of the different countries, and
names of places, with their longitudes and lati- the actual positions and distances of the various
tudes, and with a few incidental references to ob- places in the then known world.
jects of interest.
