De arithmetica.
The Nature of Number
Hugh introduces arithmetic as the study of even and odd numbers, distinguishing each by their divisibility by two.
Arithmetic deals with even numbers and odd numbers. An even number is one thing when it divides evenly by two, and another when it doesn't divide evenly; an odd number is one thing when it leaves an even remainder, and another when it leaves an odd remainder.1
The Three Kinds of Odd Number
Odd numbers are divided into three kinds: the prime, the composite, and the number that is composite in itself yet prime in relation to others.
An odd number also comes in three kinds. The first kind is the first number itself, which is prime and uncomposed; the second is the second number, which is composite; the third is the second number in itself and composite, but when compared to others is the first and uncomposed.2
Read the original Latin
Arithmetica materiam habet parem et imparem numerum. par numerus alius est pariter par, alius pariter impar, alius impariter par. impar quoque numerus tres habet species. prima est primus et incompositus, secunda secundus et compositus, tertia per se secundus et compositus, ad alios comparatus primus et incompositus.
Notes
- 1 ↩The Latin plays on par/impar (even/odd) and pariter/impariter (evenly/unevenly) to classify numbers by their behavior under division. The glosses suggest pariter par means 'evenly (divisible,) even' and pariter impar means 'evenly (divisible,) odd' — i.e., divisible by two but yielding an odd quotient. The third clause, impariter par, means 'oddly (divisible,) even' — i.e., not cleanly divisible by two but yielding an even quotient. The translation renders the sense of these three classes in plain terms.
- 2 ↩The Latin uses substantivized ordinals (prima, secunda, tertia) for the three species, paired with adjectives (primus/incompositus, secundus/compositus). The third species is described as 'per se secundus et compositus, ad alios comparatus primus et incompositus' — a number that is composite in itself but prime relative to other numbers. The translation renders 'incompositus' as 'prime and uncomposed' and 'compositus' as 'composite' to preserve the mathematical sense.
Didascalicon de Studio Legendi (On the Study of Reading) companion
Hugh said begin with small daily portions. Start tomorrow.
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