Harriot, Thomas - Mss. 6782

537269

De compositio rationum.
[Translation: On the composition of ratios. A ]

Composita ratio fit ex simplicibus duabus vel pluribus quotcunque.
Simplex ratio est ut

b

c

. Hoc est ut numerus ad numerum
vel: ut linea ad
[Translation: Let a ratio be composed from two simple ones or from more, however many.
The simple ratio is as

b

c

. That is, as a number to a number, or as a line to a line.

Composita ratio
ex duabus est

[Translation: The ratio composed from two is ]

hoc est, si quantitates sunt numeri
ut

b

d

multiplicata ad

c

f

[Translation: That is, if the quantities are numbers, as

b d

c f

Si autem lineæ. Ut parallegrammum

b d

: ad parallelogrammum

c f

. Sed
parallelogramma sunt intelligenda
æqualium
[Translation: And if lines, as the parallelogram

b d

to the parallelogram

c f

. But the parallelograms are understood to have equal angles.

Et ita enunciatur:
ratio

x

y

: componitur
ex ratione,

b

c

,
et ex ratione

d

f

[Translation: And it is conveyed thus:
the ratio

x

y

is composed from the ratios

b

c

and from the ratio

d

f

Composita ratio ex tribus
est ut:

b

c

d

f

g

h

[Translation: A ratio composed from three is ]

hoc est: si numeri:
ut

b d g

multiplicati: ad

c f h

multip.
si lineæ: ut solidum

b d g

ad solidum
ex

c f h

: sed intelligenda sunt
æqualium
[Translation: That is, if numbers, as

b d g

c f h

. If lines, as the solid

b d g

to the solid from

c f h

, but they must be understood as equiangular.

Et ita enunciatur:
ratio;

x

y

: componitur
ex ratione,

b

c

d

f

g

h

[Translation: And it is conveyed thus: the ratio

x

y

is composed from the ratios

b

c

d

f

g

h

Instar plurium: fit ratio composita ex quinque, ut
[Translation: It stands thus for more: let a ratio be composed from five, as follows.

Hoc est, ratio:

y

z

: æqualis est
compositæ
[Translation: That is, the ratio

y

z

is equal to that composed from:

hoc est:

y

z

b d g m o

c f h n p

[Translation: That is,

y : z = b d g m o : c f h n p

[Translation: Turn ]

511 (256)	512 (256v)
513 (257)	514 (257v)
515 (258)	516 (258v)
517 (259)	518 (259v)
519 (260)	520 (260v)

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