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wife drinks the barrel in an unknown number of days, “w,” so she drinks 1/w in one day. There-
fore 1/14 + 1/w = 1/10; solve for w, which turns out to be 35 days.
10. L. Carey Bolster et al.,
Invitation to Mathematics
(Glenview, IL: Scott, Foresman, 1987),
82 - 83.
11. Randall I. Charles et al.,
Scott Foresman-AddisonWesley Math
(Menlo Park, CA: Scott Foresman-
Addison Wesley, 1998), 186-187.
12. Timothy J. Reiss,
Knowledge, Discovery and Imagination in Early Modern Europe: The Rise of Aes-
thetic Rationalism
(Cambridge, UK: Cambridge University Press, 1997), 143-144. Reiss quotes
terminology from Erwin Panofsky,
Perspective as Symbolic Form
, trans. Christopher S. Wood (New
York: Zone, 1991), originally published as “Die Perspektive als 'symbolische Form,'”
Vortr ä ge der
Bibliothek Warburg
4 (1924-1925): 258-330. Panofsky's totalizing argument about perspective
has been the subject of extensive critique, notably in James Elkins,
The Poetics of Perspective
(Ithaca,
NY: Cornell University Press, 1994). The calculation of the volumes of nonstandard containers
was a widespread application of mathematics in early modern Europe undertaken by specialists
called “gagers” and for which there was a specialty mathematical literature. I only object to the
imposition of a culture of abstraction and generality when there is no evidence for it. For more
on gaging, see David Eugene Smith,
History of Mathematics
, vol. 2 (NewYork: Ginn, 1923-1925),
580 - 581.
13. “Recent” is an elastic term that takes in the last forty years. There are also some older
studies, from the beginning and middle of the twentieth century, that still deserve attention
today. See Denise Albanese, “Mathematics as Social Formation: Mapping the Early Modern
Universal, ” in
The Culture of Capital: Property, Cities, and Knowledge in Early Modern England
, ed.
Henry S. Turner (NewYork: Routledge, 2002), 255-273; Paula Blank, “Shakespeare's Equalities:
Checking the Math of
King Lear
, ”
Exemplaria
15 (2003): 473-508; Natalie Zemon Davis,
“Sixteenth-Century French Arithmetics on the Business Life,”
Journal of the History of Ideas
21
(1960): 18-48; Richard Goldthwaite, “Schools and Teachers of Commercial Arithmetic in
Renaissance Florence, ”
Journal of European Economic History
1 (1972): 418-433; Kenneth J.
Knoespel, “The Narrative Matter of Mathematics: John Dee's Preface to the
Elements of Euclid
of Megara
(1570), ”
Philological Quarterly
66 (1987): 27-46; Samuel Lilley, “Robert Recorde and
the Idea of Progress. A Hypothesis and Verification,”
Renaissance and Modern Studies
2 (1958):
3-37; Carla Mazzio, “The Three-Dimensional Self: Geometry, Melancholy, Drama,” in
Arts of
Calculation: Quantifying Thought in Early Modern Europe
, ed. David Glimp and Michelle R. Warren
(New York: Palgrave Macmillan, 2004), 39-65; Eugene Ostashevsky, “Crooked Figures: Zero
and Hindu-Arabic Notation in Shakespeare's
Henry V
, ” in
Arts of Calculation: Quantifying Thought
in Early Modern Europe
, ed. David Glimp and Michelle R. Warren (NewYork: Palgrave Macmillan,
2004), 205-228; Shankar Raman, “Death by Numbers: Counting and Accounting in
The Winter's
Tale
, ” in
Alternative Shakespeares 3
, ed. Diana E. Henderson (New York: Routledge, 2007),
158-180; Reiss,
Knowledge, Discovery and Imagination
; Smith, “On the Origin of Certain Typical
