Harriot, Thomas - Mss. 6782

736368

Ratio
[Translation: The ratio of ]

Let Achilles be

A

Testudo

B

[Translation: The tortoise

B

. The Motion of Achilles from

A

B

in the time

e f

. of Testudo from

B

C

in the same time fgWhich let be the
half parte of the time ef Which
space of

B C

let be the tenth parte
of

A B

Now the quaestion is,
both these motions being continued in the same proportion as 10 to 1.
where & when shall

A

overtake

B

. Suppose at d.
At some point or other it must really Suppose that X

d

There must be

A

B

, [???] at the same instant of And therefore the time wherein
that

A

hath moved to

d

must be the same wherein

B

hath moved to

d

But the space

A d

B d

must be as 10 to
Now by the supposition it must follow (because these motions be proportionall (as 10 to 1))
* As

A B

B C

. so:

A d

B d

. which same termes
proportionall call by these same letters & in the same

β

is known to be 1.

γ

\frac{1}{10}

β + α

is unknown. & so is

α

.
yet this is known that. is æquall to

ɛ

* Now what other proportion is this than if a man
should say as all the first to the second so
all the antecedents to all the consequents which
in this be infinite in

X To find that poynt geometrically is set downe
in my other papers de infinitis
[Translation: on ]

501 (251)	502 (251v)
503 (252)	504 (252v)
505 (253)	506 (253v)
507 (254)	508 (254v)
509 (255)	510 (255v)

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