821411
[Translation: ]
Si aggregatum linearum inæqualium æqueretur
aggregato tot æqualium: Magnitudo facta &
[Translation: If the sum of the unnequal lines is equal to the sum of as many equals, the size of the product ]
[Translation: ]
plana facta ab inæqualibus
minora sunt quaduratis
facta ab
[Translation: planes made from unequals are less than squares made from ]
[Commentary:
Here and on folio Add MS
f. , Harriot shows that the product of two or three unequal parts is always less than the product of the same number of equal parts. ]
1o. de
[Translation: 1. on ]
[Translation: 1. on ]
Sit: tota linea. .
vel duæ æquales partes. .
magnitudo facta ab illis
erit quadratum
[Translation: Let the total line be
or two equal parts ,
the size of their product will be the square .
Sint inæquales partes.
et:
[Translation: Let there be unequal parts and .
magnitudo facta:
[Translation: the size of the product is .
vel duæ æquales partes. .
magnitudo facta ab illis
erit quadratum
[Translation: Let the total line be
or two equal parts ,
the size of their product will be the square .
Sint inæquales partes.
et:
[Translation: Let there be unequal parts and .
magnitudo facta:
[Translation: the size of the product is .
Si linea dividatur utcunque in tot
partes inæquales, quot æquales:
Magnitudo facta ab inæquali-
bus, minor est illa quæ facta
ab
[Translation: If a line is divided in any way into as many unequal parts as equal parts, the size of the product of the unequal parts is less than the product of the equal parts.
partes inæquales, quot æquales:
Magnitudo facta ab inæquali-
bus, minor est illa quæ facta
ab
[Translation: If a line is divided in any way into as many unequal parts as equal parts, the size of the product of the unequal parts is less than the product of the equal parts.
[Translation: ]
Si aggregatum linearum inæqualium æqueretur
aggregato tot æqualium: Magnitudo facta &
[Translation: If the sum of the unnequal lines is equal to the sum of as many equals, the size of the product ]
[Translation: ]
plana facta ab inæqualibus
minora sunt quaduratis
facta ab
[Translation: planes made from unequals are less than squares made from ]
2o. De sectione in tres
[Translation: 2. On sectioning into three ]
[Translation: 2. On sectioning into three ]
Casus
[Translation: First ]
Sint tres inæquales
[Translation: Let there be three ]
magnitudo facta:
[Translation: the size of the product is .
[Translation: First ]
Sint tres inæquales
[Translation: Let there be three ]
magnitudo facta:
[Translation: the size of the product is .
Tres æquales
[Translation: Three equal ]
magnitudo facta
quæ cubus.
[Translation: the size of the product which is a cube is .
[Translation: Three equal ]
magnitudo facta
quæ cubus.
[Translation: the size of the product which is a cube is .
Casus 2a
[Translation: Case ]
Sint tres inæquales
[Translation: Let there be three unequal ]
magnitudo facta.
[Translation: the size of the product is .
[Translation: Case ]
Sint tres inæquales
[Translation: Let there be three unequal ]
magnitudo facta.
[Translation: the size of the product is .
Tres æquales
[Translation: Three equal ]
magnitudo facta
quæ cubus.
[Translation: the size of the product which is a cube is .
[Translation: Three equal ]
magnitudo facta
quæ cubus.
[Translation: the size of the product which is a cube is .