21v
[Translation: ]
[Commentary:
The examples of addition are continued from those on the first page (Add MS
f. ).
The examples are followed by some notes on plane, solid, and plano-plane numbers; Harriot's notation from the earlier working has been inserted into the translation at the relevant places.]
The examples are followed by some notes on plane, solid, and plano-plane numbers; Harriot's notation from the earlier working has been inserted into the translation at the relevant places.]
[Translation: ]
Si duo numeri sint similes plani; factus ex illis est quadratus,
cuius radix est medium proportionalis, inter
[Translation: If two numbers [bcdd, bcff] are similar planes, their product is a square whose root [bcdf] is the mean proportional between the given numbers.
Si similes plani dividantur per maximum communem divisor,
quoti sunt
[Translation: If similar plane numbers [bcdd, bcff] are divided by their greatest common divisor, the quotients are squares.
cuius radix est medium proportionalis, inter
[Translation: If two numbers [bcdd, bcff] are similar planes, their product is a square whose root [bcdf] is the mean proportional between the given numbers.
Si similes plani dividantur per maximum communem divisor,
quoti sunt
[Translation: If similar plane numbers [bcdd, bcff] are divided by their greatest common divisor, the quotients are squares.
Si duo numeri sint similes solidi; factus e quadrato unius per alterum,
est cubus; cuius radix est una medium videlicet inter datos
et proxima ad illum numerum qui factus fuit
[Translation: If two numbers [bcdfff, bcdggg] are similar solids, the product of the square of one with the other is a cube, whose root [bcdffg] is one mean proportional beteen the two given numbers, and nearest to that number that was made a square.
Si similes solidi dividantur per maximum communem divisor,
quoti sunt
[Translation: If similar solid numbers [bcdfff, bcdggg] are divided by their greatest common divisor, the quotients are cubes.
est cubus; cuius radix est una medium videlicet inter datos
et proxima ad illum numerum qui factus fuit
[Translation: If two numbers [bcdfff, bcdggg] are similar solids, the product of the square of one with the other is a cube, whose root [bcdffg] is one mean proportional beteen the two given numbers, and nearest to that number that was made a square.
Si similes solidi dividantur per maximum communem divisor,
quoti sunt
[Translation: If similar solid numbers [bcdfff, bcdggg] are divided by their greatest common divisor, the quotients are cubes.
Si duo numeri sint similes planoplani; factus e cubo primi
per secundum est primum quadrato-quadratum cuius radix est primum
medium proportionalis, inter
[Translation: If two numbers are similar plano-planes [bcdfgggg, bcdfhhhh], the product of the cube of the first with the second is a square-square, whose side [bcdfgggh] is the first mean proportional between the given ]
Si similes plano-plani dividantur per maximum communem divisor,
quoti sunt
[Translation: If similar plano-plane numbers [bcdfgggg, bcdfhhhh] are divided by their greatest commmon divisor, the quotients are square-squares.
per secundum est primum quadrato-quadratum cuius radix est primum
medium proportionalis, inter
[Translation: If two numbers are similar plano-planes [bcdfgggg, bcdfhhhh], the product of the cube of the first with the second is a square-square, whose side [bcdfgggh] is the first mean proportional between the given ]
Si similes plano-plani dividantur per maximum communem divisor,
quoti sunt
[Translation: If similar plano-plane numbers [bcdfgggg, bcdfhhhh] are divided by their greatest commmon divisor, the quotients are square-squares.