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1. ———. “Notes linguistiques et critiques sur le Livre II des
Coniques d’Apollonius de Pergè (Première partie).” Revue des
Études Grecques 112 (1999): 409–443.
———. “Notes linguistiques et critiques sur le Livre II des
Coniques d’Apollonius de Pergè (Deuxième partie).” Revue des
Études Grecques 113 (2000): 359–391.
———. “Notes linguistiques et critiques sur le Livre III des
Coniques d’Apollonius de Pergè (Première partie).” Revue des
Études Grecques 115 (2002): 110–148.
Fried, Michael N., and Sabetai Unguru. Apollonius of Perga’s
Conica: Text, Context, Subtext. Leiden: Brill, 2001. An overall
assessment of the Conics that tries to explain and interpret the
text without resorting to modern conceptions and notation.
The book offers a remarkable overview of Apollonius’
masterly mathematical insight, pinpoints features of his
geometrical approach to conic sections that were completely
neglected by previous scholars, and firmly places his work in
the Euclidean tradition.
Knorr, Wilbur R. “The Hyperbola-Construction in the Conics,
Book II: Ancient Variations on a Theorem of Apollonius.”
Centaurus 25 (1982): 253–291. The article shows that a
theorem in the extant version of the Conics is a later addition.
———. The Ancient Tradition of Geometric Problems.
Cambridge, MA: Birkhäuser, 1985. On pp. 293–338 of this
book, a thorough analysis is developed of some among
Apollonius’ most remarkable achievements.
Pappus of Alexandria. Book 7 of the Collection, 2 vols. Edited,
translated, and with commentary by Alexander Jones. New
York: Springer-Verlag, 1986. On pp. 510–546, an account is
offered of Apollonius’s lost works. A translation of a part of
the Arabic text of Apollonius’s Cutting off of a Ratio is given
on pp. 606–619.
Saito, Ken. “Compounded Ratio in Euclid and Apollonius.”
Historia Scientiarum 31 (1986): 25–59. A study of a
mathematical tool widely employed by Apollonius.
Unguru, S. “A Very Early Acquaintance with Apollonius of
Perga’s Treatise on Conic Sections in the Latin West.”
Centaurus 20 (1976): 112–128. The author shows that a
detailed knowledge of the Conics is exhibited in Witelo’s
Perspectiva, surmising that this derives from a very early,
otherwise unattested, Latin translation of the Apollonian
treatise.
Fabio Acerbi
ARCHIMEDES (b. Syracuse, 287 BCE, d. Syra-
cuse, 212 BCE), mathematics, physics, pneumatics,
mechanics. For the original article on Archimedes see DSB,
vol. 1.
The major contribution to Archimedean studies in
the second half of the twentieth century is M. Clagett’s
Archimedes in the Middle Ages. Other contributions have
touched on partial or minor points, and the overall pic-
ture presented in the original article is by and large
unchanged. The points emphasized in the present post-
script are the alleged formation of Archimedes in Alexan-
dria, his concern with astronomical matters, recent
advances concerning transmission and authenticity of
some of his treatises, the additional information gained by
a new reading of the Archimedean palimpsest, a more sat-
isfactory edition of the Arabic tract containing the con-
struction of the regular heptagon ascribed to Archimedes,
the edited tract On mutually tangent circles, and finally, the
approximation for (3.
Archimedes and Alexandria. It is usually assumed that
Archimedes studied in Alexandria. However, no source
asserts this and a critical assessment of the evidence com-
monly adduced suggests the contrary. Diodorus Siculus
(Bibliotheca Historica, V.37.3) wrote that Archimedes
invented the cochlias when he was in Egypt. As
Archimedes wrote a treatise On spirals and the device was
in fact extensively used in Egypt, the Diodorean claim is
more likely his or others’ inference conflating two well-
known facts, and at any rate it entails nothing about
Archimedes’s studies in Alexandria. It is positively known
that Archimedes addressed some of his works to Alexan-
drian scholars: Eratosthenes, Conon, and Dositheus.
Eratosthenes was born in Cyrene, studied in Athens, and
went to Alexandria not before 246 BCE. As a conse-
quence, Archimedes could not have met him during his
alleged Alexandrian formation: He simply addressed him
as a personality of high institutional and scientific rank.
Conon was very likely older than Archimedes and per-
formed astrometeorological observations in Sicily, as
Ptolemy’s Phaseis attests. Because Archimedes’s father was
an astronomer, as noted in the prefatory letter of the
Sand-reckoner, it is more likely that Conon and
Archimedes were personally acquainted, if this ever hap-
pened, on the occasion of Conon’s stay in Sicily than dur-
ing a hypothetical Alexandrian sojourn of Archimedes.
Dositheus, whose observations too are recorded in
Ptolemy’s Phaseis, was merely a substitute addressee after
Conon’s death, and Archimedes’s prefatory letters appear
to imply that he never met Dositheus. Finally, no sources
at all support the commonly held view that some form of
public or private teaching was established in Alexandria in
connection with the activities of the museum.
Archimedes and Astronomical Matters. Archimedes’s use
in the Sand-reckoner of Aristarchus’s model is well known,
as well as his attested interest in constructing a model
planetarium. In the Sand-reckoner a remarkable feature is
the estimate of the change in the apparent solar diameter
when the observer shifts from the center to the surface of
Earth. Two other items deserve mention. In Almagest III.1
Ptolemy quoted Hipparchus’s references to solstice obser-
vation reports by him and Archimedes that were suppos-
edly accurate to the quarter-day. In the context it is clear
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3. that Hipparchus was talking about multiple observations.
This would make Archimedes the first known Greek to
have recorded solstice dates and times in successive years,
not just in one particular calendrically significant epoch
year as Meton and Aristarchus did. In Hippolytus’s Refu-
tation of all Heresies, numbers are ascribed to Archimedes
for the following:
1. intervals between successive cosmic bodies, from
Earth to the zodiac;
2. the circumference of the zodiac;
3. the radius of Earth;
4. distances of cosmic bodies from the surface of Earth,
the Moon and the zodiac being excluded.
The numerals in the text are fairly corrupted and do
not match, and the issue is complicated by the fact that
the ordering of the series of cosmic bodies in (1) and (4)
do not agree; Hippolytus surely drew from earlier epito-
mes. In fact, after suitable emendations, the two sequences
of numbers in (1) and (4) can be made to agree and (1)
has the form ma + nb, where m, n are integers and a, b are
fixed lengths. The actual values of n suggest that
Archimedes took up a pre-existing model, presumably of
late Pythagorean origin, of cosmic distances arranged
according to a musical scale, and adapted it to his own
purposes, about which only conjectures can be made. A
mark of Archimedean origin is that the numbers are
named in accordance with the system of octads developed
in the Sand-reckoner.
Textual Tradition and Authenticity. Refined criteria
suited to establish a chronological ordering of the
Archimedean works have been proposed by Wilbur R.
Knorr. The criteria are:
1. The form of exhaustion procedure employed: The
passage from the “approximation” form (allegedly
the one at work in Elements XII) to the “difference”
form and finally to the “ratio” form are successive
refinements. This is the main criterion.
2. The proportion theory employed: A pre-Euclidean
proportion theory is at work in early works, whereas
in Spiral lines the theory of Elements V is applied.
3. The so-called lemma of Archimedes: It is introduced
only in later works, whereas juvenile essays rest on
the bisection principle implicit in Elements XII and
later justified by Elements X.1.
4. Resorting to mechanical methods as an heuristic
background: This is typical of later works.
5. The degree of formal precision in a proof: This
increases after Conon’s death.
Knorr’s main underlying assumption is that variations in
the above usages should receive an historical and not a
technical explanation. Terminological arguments have
been developed by Tohru Sato supporting to some extent
Knorr’s reconstruction. A distinction between an early
and a mature group of works results. The former includes,
in this order, Measurement of the Circle, Sand-reckoner,
Quadrature of Parabola Props. 18 to 24, and Plane Equi-
libria I and II. Most of the mature treatises are ordered by
internal references; the first and the last work in the series,
which escape cross-referencing, would be respectively
Quadrature of Parabola, Props. 4 to 17, and the Method.
No one of the above criteria is conclusive, and the num-
ber of ad hoc assumptions and adjustments necessary to
make the proposal a coherent whole reduces it merely to a
plausible guess.
Other scholarly contribution to problems of authen-
ticity and transmission of the Archimedean corpus
include:
1. Knorr’s tentative reconstruction of the original text
of the Measurement of the Circle, with particular
emphasis on Alexandrian and late ancient editions
and epitomes, and on the transmission of the
resulting corpus of writings through antiquity and
the Middle Ages;
2. John Berggren’s analysis, based on internal
consistency and mathematical relevance, of the
spurious theorems in the Equilibria of Planes;
3. Knorr’s reconstruction of a lost Archimedean treatise
on the center of gravity of solids, with reduction to
Archimedean sources of the whole extant tradition
on the balance;
4. by the same author, an assessment in the negative of
the evidence about an Archimedean Catoptrics.
The Archimedean Palimpsest. The Archimedean
palimpsest reappeared in 1998 after it was stolen in the
years around World War I. The considerable gain offered
by the digital techniques employed in reading the under-
lying writing is balanced, at times overbalanced, by the
dramatic decay of the material conditions of the manu-
script. The very good photographic plates taken at the
time of the discovery of the palimpsest, preserved at the
Royal Danish Library in Copenhagen, Ms. Phot. 38, and
covering about two thirds of the relevant folia, are still an
indispensable piece of evidence, as they portray the man-
uscript in a decidedly more acceptable state of conserva-
tion. It appears that the transcription of the first editor
was fairly accurate: It is in principle to be expected that
the text he procured will need only marginal corrections.
Real advances can be hoped for only for those portions of
text that were left unread by the first transcription.
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4. Only two, very short, fragments from the palimpsest
have been edited so far, Proposition 14 of the Method and
what remains of the Stomachion, and these provisional
texts do not clearly distinguish the parts coming from a
really new reading of the manuscripts from those in which
resort to the photographs or to Johan Ludvig Heiberg’s
text was necessary. A new edition of the Arabic fragment
of the Stomachion is a desideratum. What remains of this
work appears to refer to a square ADGB divided into 14
parts (see Figure 1, taken from the Arabic fragment),
where E, H, M, N, C are middle points of BG, BE, AL,
DG, ZG, respectively, EZ and HT are drawn perpendicu-
lar, A belongs to HK produced and O to BC produced.
The Arabic fragment simply gives the values of the areas
of the fourteen parts as fractions of the area of the whole
square. Such areas turn out to be unit fractions of the
whole; the only exception, the area of HEFLT, is written
as a sum of unit fractions. The Greek fragment amounts
to a short, initial introduction and to a partial con-
struction of the diagram (the one implied by the Greek
text actually makes AZEB a square). As a preliminary
result it is proved that AB >BL, and as a consequence
∠AMB > ∠LMB, but then the text breaks off. The aim,
stated by Archimedes in the introduction, is “finding out
the fitting-together of the arising figures.” Just after that,
Archimedes asserts that
there is not a small multitude of figures made of
them, because of it being possible to take them
(the text is here hardly readable) into another place
of an equal and equiangular figure, transposed to
hold another position; and again also with two
figures, taken together, being equal and similar to
a single figure, and two figures taken together
being equal and similar to two figures taken
together-[then], out of the transposition, many
figures are put together. (Netx, Acerbi, and Wil-
son, 2004, p. 93)
One speculative possibility is that the Stomachion
contained a first application of combinatorial techniques:
to count in how many ways the initial configuration can
be broken off into its constituent pieces and then recom-
posed, with the pieces arranged in a different way.
In Method 14, a passage unread by Heiberg, within a
column of text that requires extensive restoration, reveals
that Archimedes handles infinite multitudes of mathemat-
ical entities by setting them in one-to-one correspon-
dence. One should not attach too much importance to
this move as if it was an anticipation of modern set-theo-
retic treatment of infinities. The move adds nothing to the
explicit character of Method 14, and in any case analogous
features can be found outside Archimedes, for instance in
Pappus, Collectio IV.34.
The Regular Heptagon and Other Arabic Sources. A
new edition of the Arabic treatise makes it possible to
write in a correct form some passages in the construction
of the regular heptagon ascribed to Archimedes. What fol-
lows should replace the text from “HD = DB” to “arc AH
= 2 arc HB” in Proposition 17 (lines 14–33 of the second
column on p. 225 of the original DSB article):
Since ∠CHD = ∠DBT, and ∠CDH = ∠TDB, and
HD = DB, then CD = DT, CH = TB and one cir-
cle contains the four points B, H, C, T. [Actually
the equality CH = TB is of no subsequent use and
the last statement follows directly from the equal-
ity of angles CHD and DBT.] Since CB·DB = AC2
= HC2
, and CB = TH, while DB = DH, TH·HD
= HC2
, and ∆ THC ~ ∆ CHD. So ∠DCH =
∠HTC. But ∠DCH = 2∠CAH, so ∠CTH
= 2∠CAH. But ∠CTD = ∠DBH, so ∠DBH =
2∠CAH, and arc AH = 2 arc HB.
It may be added that the neusis involved in the con-
struction of the heptagon can be solved in a straightfor-
ward way by a simple adaptation of the solution of the
neusis reported in Pappus, Collectio IV.60, as a preliminary
to the angle trisection. It turns out that the construction,
by intersection of two hyperbolas, is identical with the one
proposed by the Arabic mathematician al-Saghânî. The
proof, if framed in analogy with Pappus, that the con-
struction really solves the neusis is considerably simpler
than that in al- Saghânî.
Archimedes Archimedes
Figure 1.
A Z D
M
O
N
C
Q
F
L
T
K
B H E G
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5. The short Arabic treatise On mutually tangent circles,
ascribed to Archimedes in the title, is a collection of fif-
teen lemmas concerning circles rather than a work with a
discernible aim; only seven lemmas out of fifteen involve
mutually tangent circles. If the original really dates back to
Archimedes, what is read is most likely an epitome, possi-
bly containing some accretions. A similar assessment
should be extended to other compilations ascribed to
Archimedes and redacted in the format of “Books of Lem-
mas,” such as the Liber assumptorum or the shorter version
of the so-called Book of Lemmas whose longer version is
credited to a certain Aqâtun in the transmitted Arabic ver-
sion Two propositions of some interest can be singled out
from On mutually tangent circles. The first is lemma 12
(see Fig. 2, representing one possible configuration). Two
tangents AB and AG are drawn to the same circle, and the
points of tangency B and G are joined by a straight line.
From point D on that line another tangent is drawn,
touching the circle at Z and intersecting the other two
tangents at E and H. To prove that HD : DE = HZ : ZE.
The easy proof draws the parallel ET to AB and argues by
similar triangles and from the equality of tangents to a cir-
cle drawn from the same point.
One interesting feature is that the lemma holds also
when the two initial tangents are parallel: In this case the
text displays two letters A denoting different points. The
fact that Apollonius proposed similar theorems for conic
sections in Conics III might be taken as supporting the
Archimedean origin of lemma 12, because Apollonius
shaped his Conics as a system of scholarly references to
preceding authors. The second result is lemma 15, quoted
also by al-Bírúní and assigned by him to “Archimedes in
the Book of Circles.” A broken line AGB, with AG >BG,
is inscribed in a segment of circle (see Figure 3); bisect arc
AB at D and drop perpendicular DE from D on to AG.
To prove that AE = EG + GB three proofs are given, the
first of which runs as follows. Take arc HD = arc DG and
EZ = EG; join DG, DZ, DA, DH, HA. A rather involved
but elementary argument shows that ∆ AZD = ∆ AHD.
Hence AZ = (AH =) BG. Summing EZ = EG to this equal-
ity, what is required is obtained.
A very similar theorem is proven by Ptolemy in
Almagest I.10 in order to calculate the chord of the half-
angle. Because the latter result can be easily derived from
the so-called Ptolemy’s theorem, the fact that Ptolemy
himself does not do that suggests that the alternative
approach he reports was the basis of earlier chord tables.
Simplified variants of the same theorem as in Almagest
I.10 are Prop. 14 of the treatise, ascribed to Archimedes,
having the above-mentioned construction of the regular
heptagon as Prop. 17, and lemma 3 of the Liber assump-
torum. It is likely that both the theorem in the Almagest
and lemma 15 were different cases of a more comprehen-
sive Archimedean proposition; however, it is not said that
he devised such a proposition for trigonometric purposes.
Approximation for ÷3. The approximation 1351-780
>√3 >265/153 found in Measurement of the Circle, Prop.
3, appears to have received a fairly satisfactory explanation
in the remark that the successive convergent fractions of
the development in continued fraction of √27, when
divided by 3, are 5/3, 26/15, 265/153, 1351/780. The
approximated value ascribed to Archimedes in Diophanes
20a (Diophantus, p. 22.16 Tannery) and implied for
instance in Hero’s calculations in Metrica I.17 is 26-15. As
these values can be obtained by a procedure of successive
reciprocal subtractions, traces of which can be found in
the Greek mathematical corpus, it is likely that the
approximations at issue were obtained in that way.
Archimedes Archimedes
Figure 2.
H
B
A
B
D
A
T
E
Z
H
G
Z
G
T
E
D
Figure 3.
A
H
D
G
B
Z
E
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6. S U P P L E M E N TA RY B I B L I O G R A P H Y
WORKS BY ARCHIMEDES
“On mutually tangent circles.” In Archimedis Opera Omnia, cum
Commentariis Eutocii: vol. IV: Über einander berührende
Kreise. Edited by I.L. Heiberg. Translated from the Arabic
into German and with notes by Y. Dold-Samplonius, H.
Hermelink und M. Schramm. Stuttgart, Germany: B.G.
Teubner, 1975. The Arabic translation of the a tract ascribed
to Archimedes. The edition proposes a German translation
and a facsimile reproduction of the unique manuscript
Bankipore 2468 rather than a critical text and apparatus.
Dold-Samplonius, Yvonne, ed. “Book of Lemmas.” In Book of
Assumptions by Aqâtun. Ph.D. diss., University of
Amsterdam, 1977.
Netz, Reviel, Fabio Acerbi, and Nigel Wilson. “Towards a
Reconstruction of Archimedes’s Stomachion,” SCIAMVS 5
(2004): 67–99.
New editions of fragments from the Palimpsest are
available in the following articles.
Netz, Reviel, Ken Saito, and Natalie Tchernetska. “A New
Reading of Method Proposition 14: Preliminary Evidence
from the Archimedes Palimpsest (Part 1).” SCIAMVS 2
(2001): 9–29.
———. “A New Reading of Method Proposition 14: Preliminary
Evidence from the Archimedes Palimpsest (Part 2).”
SCIAMVS 3 (2002): 109–125.
OTHER SOURCES
Berggren, John L. “A Lacuna in Book I of Archimedes’ Sphere
and Cylinder.” Historia Mathematica 4 (1977): 1–5. A
discussion of a specific problem in Archimedes’s writings is
found here.
———. “Spurious Theorems in Archimedes’ Equilibria of
Planes.” Archive for History of Exact Sciences 16 (1977):
87–103. See this text about some problems of authenticity in
the Archimedean corpus.
Clagett, Marshall. Archimedes in the Middle Ages. Vol. 1. The
Arabo-Latin Tradition. Madison: The University of Wisconsin
Press, 1964; Vol. 2. The Translations from the Greek by
William of Moerbeke. Memoirs 117. 2 tomes; Vol. 3. The Fate
of the Medieval Archimedes 1300–1565. Memoirs 125. 3
tomes; Vol. 4. A Supplement on the Medieval Latin Traditions
of Conic Sections (1150–1566). Memoirs 137. 2 tomes; Vol.
5. Quasi-Archimedean Geometry in the Thirteenth Century.
Memoirs 157. 2 tomes. Philadelphia: American Philosophical
Society, 1976–1984. The entire mediaeval Archimedean
tradition is now available in this masterful edition.
Hogendijk, Jan P. “Greek and Arabic Constructions of the
Regular Heptagon.” Archive for History of Exact Sciences 30
(1984): 197–330. The Archimedean tract on the regular
heptagon is best read in this edition. The proposed
translation is from p. 289.
Knorr, Wilbur R. “Archimedes and the Elements: Proposal for a
revised Chronological Ordering of the Archimedean
Corpus.” Archive for History of Exact Sciences 19 (1978):
211–290. The new chronological ordering of Archimedes’s
works was proposed here.
———. “Archimedes’ Lost Treatise on the Centers of Gravity of
Solids.” Mathematical Intelligencer 1 (1978): 102–109.
———.“Archimedes’ Neusis-Constructions in Spiral Lines.”
Centaurus 22 (1978): 77–98.
———. “Archimedes and the Pre-Euclidean Proportion
Theory.” Archives internationales d’histoire des sciences 28
(1978): 183–244. This article corrects in fact “Archimedes
and the Elements,” which mainly focused on exhaustion
procedures, so that what in the latter paper is adherence to
Euclidean methods becomes in the present one a mark of
pre-Euclidean provenance. Such a move is possible once
entire portions of the Elements, for instance book XII, are
regarded as simply reporting Eudoxean elaborations.
———. “Archimedes and the Spirals: The Heuristic
Background.” Historia Mathematica 5 (1978): 43–75.
———. Ancient Sources of the Medieval Tradition of Mechanics.
Greek, Arabic and Latin Studies on the Balance. Supplemento
agli Annali dell’Istituto e Museo di Storia della Scienza, 1982,
Fasc. 2. The reduction to non-extant Archimedean sources of
the whole extant tradition on the balance is argued at length
here.
———. “Archimedes and the Pseudo-Euclidean Catoptrics: Early
Stages. In the Ancient Geometric Theory of Mirrors.”
Archives internationales d’histoire des sciences 35 (1985):
28–105. The nonexistence of an Archimedean Catoptrics,
although attested by a number of sources, is argued in detail
in this work.
———. “Archimedes after Dijksterhuis: A Guide to Recent
Studies.” In Archimedes. Princeton, NJ: Princeton University
Press, 1987. A complete bibliography updated to 1987 can
be found here.
———. “On Archimedes’ Construction of the Regular
Heptagon.” Centaurus 32 (1989): 257–271.
———. Textual Studies in Ancient and Medieval Geometry.
Boston, MA: Birkhäuser, 1989. Part III of this book presents
a very ambitious reconstruction of the textual tradition of the
Archimedean text Measurement of the Circle.
——— “On an Alleged Error in Archimedes’ Conoids, Prop. 1.”
Historia Mathematica 20 (1993): 193–197. A discussions of a
very specific problem in Archimedes’ writings is found here.
———. The Ancient Tradition of Geometric Problems. Boston,
MA: Birkhäuser 1986. Reprint, New York: Dover 1993.
Knorr offers a very good account of Archimedes’
mathematical techniques.
Netz, Reviel. The Works of Archimedes: Translated into English,
together with Eutocius’ Commentaries, with Commentary, and
Critical Edition of the Diagrams. Vol. 1: The Two Books On the
Sphere and the Cylinder. Cambridge, U.K.: Cambridge
University Press, 2004. This is the first volume of a new
English translation of Archimedes’s works.
Neugebauer, Otto. A History of Ancient Mathematical Astronomy.
3 vols. Berlin: Springer, 1975. Neugebauer offered the first
discussion of the problem of the numbers for the distances of
the cosmic bodies.
Osborne, Catherine. “Archimedes on the Dimensions of the
Cosmos.” Isis 74 (1983): 234–242. The difficult problem of
the numbers for the distances of the cosmic bodies is tackled
here.
Archimedes Archimedes
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7. Schneider, Ivo. Archimedes: Ingenieur, Naturwissenschaftler und
Mathematiker. Darmstadt, Germany: Wissenschaftliche
Buchgesellschaft, 1979. The best overall account of
Archimedes’s life and works after Dijksterhuis’s book.
Sezgin, Fuat. Geschichte des Arabischen Schrifttums. Band V,
Mathematik bis c. 430 H. Leiden: E.J. Brill, 1974. A fairly
complete account of the Arabic Archimedes with detailed list
of manuscripts is available here.
Taisbak, Christian M. “An Archimedean Proof of Heron’s
Formula for the Area of a Triangle; Reconstructed.”
Centaurus 24 (1980): 110–116.
———. “Analysis of the So-called “Lemma of Archimedes” for
Constructing a Regular Heptagon.” Centaurus 36 (1993):
191–199. This analysis of the Archimedean tract on the
regular heptagon is very helpful.
Tohru Sato.“ Archimedes’ On the Measurement of a Circle
Proposition 1: An Attempt at a Reconstruction.” Japanese
Studies in the History of Science 18 (1979): 83–99. It is argued
that the extant Latin translation by Gerard of Cremona was
based on a better text than the extant Greek.
———. “Archimedes’ Lost Works on the Center of Gravity of
Solids, Plane Figures, and Magnitudes.” Historia Scientiarum
20 (1981): 1–41. Sato presents a different view from Knorr
on reduction to non-extant Archimedean sources of the
extant tradition on the balance.
———. “A Reconstruction of The Method 17, and the
Development of Archimedes’ Thought on Quadrature. Part
One.” Historia Scientiarum 31 (1986): 61–86. Linguistic
arguments supporting the ordering proposed by Knorr are
offered here and in the following article.
———. “A Reconstruction of The Method 17, and the
Development of Archimedes’ Thought on Quadrature. Part
Two.” Historia Scientiarum 32 (1987): 75–142. The article
also contains a reconstruction of a lost Archimedean
proposition.
Vitrac, Bernard. “A propos de la chronologie des œuvres
d’Archimède.” In Mathématiques dans l’Antiquité, edited by
J.Y. Guillaumin. Saint-Étienne, France: Publications de
l’Université de Saint-Étienne 1992. Knorr’s unstated
presuppositions and methods in establishing the
Archimedean chronology are criticized in this work.
Fabio Acerbi
ARCONVILLE, MARIE GENEVIÈVE
CHARLOTTE THIROUX D’ (b. Paris [?],
France, 17 October 1720; d. Paris [?], 23 December
1805), chemistry, anatomy, translation.
Madame d’Arconville was one of the very few
eighteenth-century women who not only undertook
translations of scientific works, but also carried out her
own long-lasting program of experiments. A prolific
author, she wrote or translated anonymously dozens of
texts on scientific matters, as well as literature, morality,
and history.
Life and Education. Marie Geneviève was daughter of
André Guillaume d’Arlus or Darlus, a wealthy farmer-
general. When she was only fourteen years old, she
married Louis Lazare Thiroux d’Arconville, a councillor—
later a president—at the Paris parliament, and brought
him a 350,000-French-pound endowment. The eldest of
their three sons, Louis Thiroux de Crosne, became an
intendant—a royal administrator in the province—then
the Paris lieutenant general of the police; he was eventu-
ally beheaded during the Terror (in 1794), while his
mother spent a few months in jail.
Being disfigured by smallpox at age twenty-two,
Madame d’Arconville chose an austere life thereafter and
professed Jansenist morals. She also founded a charitable
institution close to her country house at Meudon, near
Paris on the road to Versailles. But she mainly devoted her
time to reading—including Voltaire and Jean-Jacques
Rousseau—and attending courses, as well as to writing
and conducting experiments in botany and chemistry.
Not only was she able to translate English and Italian, she
also learned several sciences, notably those taught in pub-
lic courses at the Jardin du Roi (King’s Garden), and she
practiced botany, agriculture, and chemistry. In her thir-
ties, she took up the pen and started publishing transla-
tions; from the 1760s, she produced original works as
well. She translated numerous novels, plays, and poems,
and she wrote essays on morals, then biographies of late-
sixteenth- and early-seventeenth-century French figures,
including Cardinal Arnaud d’Ossat, King Francis II, and
Queen Marie de Médicis. She is even said to have written
the Essai sur l’amour-propre envisagé comme principe de
morale (Essay on Self-respect as Principle of Morals), which
King Frederick II read at the Berlin Academy in 1770. At
her death, she left a twelve-volume manuscript of miscel-
lanea, which was lost and then rediscovered at the end of
the twentieth century. Although she avoided Parisian soci-
ety, she received into her home and met many of the great
authors and scientists of her time, including Voltaire,
Denis Diderot, Bernard de Jussieu, Guillaume-Chrétien
Lamoignon de Malesherbes, Pierre-Joseph Macquer, and
Antoine-Laurent Lavoisier.
Scientific Writings. In 1759 Madame d’Arconville, in col-
laboration with anatomist Jean-Joseph Süe, published a
French edition of Alexander Monro’s Anatomy of the
Human Bones (1726). She added a few personal observa-
tions in footnotes and a preface, which reveals a profound
admiration for Jacques Bénigne Winslow, and, most sig-
nificantly, a volume of plates (Monro’s original was not
illustrated, and the author stated that illustrations gave a
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