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R I C H A R D C. R A M E R
Special List 542
Mathematics
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r i c h a r d c . r a m e r
R I C H A R D C . R A M E R
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Special List 542
Mathematics
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Special List 542
Mathematics
*1. ALMEIDA, A.[ntónio] A.[ugusto] Marques de. Aritmética como
descrição do real (1519-1679): contributos para a formação da mentalidade
moderna em Portugal. 2 volumes. Lisbon: Comissão Nacional para as
Comemorações dos Descobrimentos Portugueses / Imprensa Nacional,
1994. Mare Liberum. Large 8°, original illustrated wrappers. As new.
325 pp., (1 l.); 451 pp., (1 l.). One of 800 copies. ISBN: 972-27-0523-7.
2 volumes.
$90.00
FIRST and ONLY EDITION of this authoritative work, with an extensive bibliogra-
phy, indexes of authors, places, and subjects, and a preface by Joaquim Veríssimo Serrão.
Rebirth of the Study of Mathematics and Engineering in Portugal and the
Reflection of this Movement in Brazil:
Second Book on Military Engineering Written in Brazil and
Second Such Book Written by a Brazilian,
Dedicated to Gomes Freire de Andrade—With 20 Folding Engraved Plates
2. ALPOIM, José Fernandes Pinto de. Exame de bombeiros, que com-
prehende dez tratados .... Madrid: En la O�cina de Francisco Martinez
Abad, 1748. 4°, contemporary sheep (chafed, upper joint cracking),
spine gilt with raised bands in �ve compartments (upper compartment
defective), crimson leather lettering piece in second compartment from
head (slightly defective), text-block edges sprinkled. Title page in red
and black. Engraved allegorical vignette on f. *3r. Engraved portrait
of Gomes Freire de Andrade laid in: trimmed, with small piece miss-
ing from frame at lower edge, and with traces of glue on verso. Plate
XVI somewhat browned, plate XVIII dampstained. In good condition.
Lithograph bookplate: “EMMANVEL” in a circle around a �ve-pointed
star. Engraved portrait, (20 ll.), 444 pp. [i.e., 442; pagination skips from
372 to 375], 20 folding engraved plates and 1 folding table. $4,000.00
FIRST and ONLY EDITION. This work and Alpoim’s Exame de artilheiros, Lisbon
1744, are “proofs of the rebirth of the study of mathematics and engineering in Portugal
and the re�ection of this movement in Brazil, and they symbolize a Luso-Brazilian con-
tribution to this movement. They are, in short, the �rst two books on military engineering
written in Brazil and the �rst two ‘textbooks’ of this kind by a Brazilian author” (Borba
de Moraes I, 26).
The Exame de bombeiros is a comprehensive textbook on military bombardment.
Written in dialogue form, the Exame �rst covers the mathematics necessary for plotting
trajectories, proceeds to a long discussion of mortars and how to use them most e�ec-
tively, describes more recent inventions such as the howitzer and the petard, and closes
with a long treatise on the many types of incendiary shells and their proper use. The text
is enhanced with frequent references to the contributions of other military engineers,
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including Galileo and Vauban, and historical notes on how bombardment had contrib-
uted to the success or failure of various military campaigns. The plates depict mortars,
projectiles, and incendiary shells, many shown in cross section.
Borba de Moraes devotes three pages to unraveling the “veritable bibliographic
puzzle” of the printing of this work, and to dispelling the myth that it and/or Alpoim’s
Exame de artilheiros were printed in Rio de Janeiro by Antonio Isidoro da Fonseca in
1747—a theory �rst suggested by Varnhagen. Since the Exame de artilheiros was banned
by a decree of 15 July 1744 (for not adhering to the rules for the use of military titles),
Varnhagen thought Fonseca might not have wished to publish it under his own imprint.
To support his theory, Varnhagen cited the facts that Alpoim was a native of Brazil, that
the work was written there and dedicated to Gomes Freire de Andrade, Governor of
Brazil, and that the letters to the author in the preliminary leaves are from Brazilians. The
most puzzling evidence of all is plate XVII, which has “Rio 1749” engraved in the lower
right-hand corner. If this plate was engraved and printed in Brazil, it would be the earliest
extant Brazilian engraving. Even Borba de Moraes, who argues strongly that the Exame
de bombeiros and Exame de artilheiros were printed in Madrid and Lisbon, as their respec-
tive title-pages state, could give no convincing explanation of the plate XVII inscription.
Alpoim was born in Rio de Janeiro and served as professor at the Aula de Forti�cação
in Rio de Janeiro; at his death in 1770 he held the rank of Brigadier.
The engraved portrait of Gomes Freire de Andrade is signed by Olivarius Cor.
Soares notes that nothing is known of this artist except that he worked in Portugal from
1744-1748, and may have been one of the foreigners invited by D. João V.
The other plates, which illustrate geometric �gures, cross-sections of cannons, and
ballistics, are signed by José Francisco Chaves, about whom Soares had no biographical
information.
❊ Borba de Moraes (1983) I, 25-7: “famous and rare”; Período colonial 9-10. Alden
& Landis 748/2. Sacramento Blake IV, 422. Innocêncio IV, 326. Pinto de Mattos (1970) p.
505. Carvalho, Dicionário bibliográ�co militar portugues I, 58-9. Soares, História da gravura
artística em Portugal 499-500. Bosch 194 (cf. 187). Mindlin, Highlights 384. Indiana Univer-
sity, Lilly Library, Brazil 48. Not in Rodrigues. On Olivarius Cor, see Soares, História da
gravura artística em Portugal I, 171, nº 499 (under Chaves); on Olivarius Cor, see I, 180-185
(this work not listed). NUC: DLC-P4, ICN. OCLC: 35175211 (Catholic University-Oliveira
Lima Library, Library of Congress, Newberry Library, Brown University); 18678333
(Arizona Historical Society, University of Michigan, University of Mississippi); 79814401
(John Carter Brown Library); 257680375 (Universität Göttingen); 433371703 (Biblioteca
Nacional de España). Porbase lists a copy at the Biblioteca Nacional de Portugal, and
another copy there with the imprint “Lisboa: Imp. Regia 174?” Not located in Jisc. KVK
(51 databases searched) repeats Porbase.
3. BARBOSA, Francisco de Villela, later 1.º Visconde and still later 1.º
Marquês de Paranaguá. Breve tratado de geometria spherica … em addita-
mento aos seus Elementos de geometria. Lisbon: Typ. da Academia Real
das Sciencias, 1817. 8°, later wrappers (slightly soiled, chipped along
spine). Title page slightly soiled; uncut and partially unopened. Overall
in very good condition. 30 pp., 1 folding engraved plate of diagrams.
Lacks the three unumbered advertisement leaves at the end. $150.00
FIRST EDITION. It was later reprinted as part of the author’s Elementos de geometria
(�rst published in 1816? see Borba de Moraes), which was widely used as a geometry
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textbook in Portugal and Brazil through the nineteenth century. Villela Barbosa (1769-
1846), a native of Rio de Janeiro, taught mathematics at the Academia Real de Marinha
and was an o�cer of the Academia Real das Sciencias. Having served in the 1821 Côrtes,
he returned to Brazil in 1823 at the conclusion of that Parliament, and was one of the
three negotiators who concluded the 1825 treaty by which Portugal recognized Brazilian
independence. He later held high government o�ces in Brazil. Created 1.º Visconde de
Paranaguá by the Brazilian Emperor D. Pedro I in 1825, and 1.º Marquês in 1826, Vil-
lela Barbosa is better known for his poetry, e.g., Poemas, Coimbra, 1794, and Primavera,
Lisbon 1821.
❊ Borba de Moraes (1983) I, 75: collating as our copy; Período colonial p. 54. Innocêncio
III, 81-2: calling for only 28 pp. and 1 plate. Sacramento Blake III, 134-7: also calling for
28 pp. Not in JCB, Portuguese and Brazilian Books (but JCB has this according to Josiah).
W. Martins, História da inteligência brasileira II, 5-7 (“um árcade retardatário, um clássico
extemporâneao e um mau poeta”), 177, 212. Veríssimo, História da literatura brasileira
(1969) pp. 87, 113, 119. Not located in NUC.
*4. CANGALHAS, João Pedro Ferreira. Opusculos de arithmetica uni-
versal, publicados com a protecção da Academia Real das Sciencias e dedicados
ao … D. Francisco Benedicto de Sousa Lancastre, e Noronha, nono Conde do
Prado, e sexto Marquez das Minas. 3 volumes in 1. Lisbon: Na O�cina da
Mesma Academia [Real das Sciencias], 1795. Large 4° (27.2 x 20 cm.),
contemporary tree sheep (minor wear to corners, some worm damage
near head of spine), �at spine, gilt, green and crimson morocco lettering
pieces, gilt letter, triple gilt �llets in rectangle along borders of covers,
gilt tooling to edges of covers and spine. Woodcut device of Academia
Real das Sciencias on title pages. Mathematical equations, symbols and
tables in text. A large-paper copy, clean, crip[] sp, in near-�ne condition;
�ne to very �ne internally. (8 ll.), 285 pp.; (4 ll.), 158 pp.
3 volumes in 1. $1,200.00
FIRST EDITION, �rst (?) issue, with the original leaves Aa3 in volume I, and B4,
C1, C4, D1 in volume II, as opposed to the cancel leaves present in most copies. Writing
in 1934, Francisco Gomes Teixeira stated that aspects of this comprehensive algebra text-
book were still of use (História das matemáticas em Portugal, p. 235). The work consists of
2 volumes of Opusculos, in which algebraic concepts are de�ned and illustrated through
sample problems, and a third volume titled Taboada de quadrados dos numeros naturaes,
publicadas com a protecção da Academia Real das Sciencias, which lists the square of all whole
numbers from 1 to 8,699.
Each of the three title pages bears the imprint Lisboa: na O�cina da mesma Aca-
demia, 1795. There are four Opusculos in the �rst volume, two in the second. They are:
I. “Theoria preliminar dos numeros inteiros”; II. “Das equaçoens indeterminadas do
primeiro grão”; III. “Instrucção às equaçoens indeterminadas do segundo grão”; IV.
“Introdução ás fracçoens continuas”; V. “Introdução a diversas theorias dos numeros
inteiros”; and VI. “Das fracçoens decimaes periodicas”.
The chainlines run horizontally throughout in the present copy, as opposed to
the normal-size copy we have, which is a bibliographical curiosity, with the chainlines
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