Multiplying fractions: a worked check of 3/4 x 2/3
The product 8/9 is rejected and a second working gives 6/9, that is 2/3
This page works a small problem in the multiplication of fractions. The writer first gives 3/4 times 2/3 as 8/9, rejects it - arguing that a product cannot exceed the quantity being multiplied and that 8/9 is more than 2/3 - and then prefers a second working that yields 6/9, that is 2/3. The block opens with a fragmentary note linking Acquapendente and Orvieto, echoing the distance notes on the nearby folios. The Italian is written in mirror script.
On this page
A product of fractions rejected as false
The writer first sets 3/4 times 2/3 as making 8/9, then strikes it down: since 8/9 is greater than 2/3, and - he reasons - in dividing fractions the product can never exceed the quantity multiplied, the answer must be wrong.
The preferred working, giving 6/9 = 2/3
He then sets the same 3/4 times 2/3 and makes 6/9, judging this second way better because it renders what it comes to, namely 6/9, that is 2/3. The reasoning is worked in his own idiosyncratic manner rather than by the modern rule.
An opening note on Acquapendente and Orvieto
The block begins with a fragmentary note that Acquapendente is [reckoned] to Orvieto, tying the arithmetic to the distance and itinerary notes of the surrounding folios. The reading of the phrase is uncertain.