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on the rule of three). Knowing something about our reading, our rigor, and their rigor
should allow us to determine something about their reading. “Something” is enough
for an argument of plausibility such as this one, but that something must still be
accurate. What if the three “knowns” are radically different from what we think them
to be? This is where reading and rigor begin to be related. The assumption, which I
now disown, that their rigor and our rigor are even similar, let alone identical, is a
claim that materially informs our methodology of reading. In other terms, our assump-
tions about how and with what accuracy early modern readers solved arithmetic
problems fundamentally affects our ability to understand how and why early modern
readers read their own cultures' arithmetic texts. To put it yet another way, the assump-
tion that our rigor was their rigor allows our reading to ignore the procedures and
accuracy of their arithmetic because it can be assumed that they are the same: that
their procedures are ours and that they always got the answers right, just as we assume
we would do. If our reading does not do the mathematics, it is because our rigor has
been assumed to be their rigor. This alters the data set and we therefore read what is
not there. Reading something that is not there is the same as failing to read in a manner
that is carefully and responsibly attentive to contemporary history and culture. Only
if our rigor was their rigor can their reading be our reading. I will take up later what
readings of ours might be mistaken for theirs, but first I will present some primary
examples of early modern arithmetic in order to examine the concept of rigor, and
its filiations as theirs and ours.
The Renaissance was familiar with many forms of rigor, including logic descended
from classical traditions and its medieval, scholastic evolution, and the exact, accretive
forms of proof associated with classical Greek geometry.
3
In the essay “ Of Studies, ”
Francis Bacon recommends mathematics “if a man's wit be wandering” in order to make
them “subtle,” “for in demonstrations, if his wit be called away never so little, he must
begin again. ”
4
The Renaissance also experimented with conflations of certain knowledge
and probable knowledge, syllogism and enthymeme, and logic and rhetoric in the intel-
lectual movements we variously call humanism, Ramism, and the scientific revolution.
Renaissance printing not only produced important editions of Euclid, particularly in
vernacular languages, but also the “informal” geometries, by Robert Recorde, Petrus
Ramus, and others, which present theorems and diagrams and informal discussion but
avoid reproduction of Euclidean proofs.
5
These innovations in geometry proceeded from
a relatively stable (and authoritative) tradition that had no counterpart in arithmetic.
Both the form of numeration (Hindu-Arabic numbering, including its zero) and the
