Harriot, Thomas - Mss. 6784

393197

6) De
[Translation: On ]

problema.
Datis tribus circulis
sese mutuo contingentibus:
invenire quartum circulum
qui mutus tangetur in
[Translation: Problem.
Given three circles, mutually touching, to find a fourth circle that is mutually touched by those ]

Sint tres dati circuli

b r d

r t h

h u e

, sese mutuo contingentes
in punctis

r

h

e

. cuius centra

z

p

a

.
Agatur recta

a p

in continuum
[…]
Agatur

f b

recta contingens
circulum

b r d

in puncto

b

.
Agatur recta

b z

in continuum quæ secabit
circulum cuius centrum

z

d

puncto.
fiat,

u a i

recta, parallela

b z

.
Et ad lineam

b z

productam sint per-
pendicularis

u q

i l

[Translation: Let the three given circles be

b r d

r t h

h u e

, mutually touching at the points

r

h

e

, whose centres are

z

p

a

.
There is constructed the extended line

a p

.

There is constructed the line

f b

touching the circle

b r d

at the point

b

.
There is constructed the extended line

b z

which will cut the circule whose centre is

z

in the point

d

.
Let the line

u a i

be parallel to

b z

.
And to the extended line

b z

let there be perpendiculars

u q

and

i l

Bissecetur

b c

in puncto

y

.
Centro

y

, intervallo

y b

,
describatur circulus.
Dico quod: ille est circulus quæsitus
et contingit tres datos
in puncto

b

t

g

[Translation: Let the line

b c

be bisected at the point

y

.
With centre

y

, radius

y b

, there is drawn a circle.
I say that this is the circle sought, and that it touches the three given circles at the points

b

t

g

401 (201)	402 (201v)
403 (202)	404 (202v)
405 (203)	406 (203v)
407 (204)	408 (204v)
409 (205)	410 (205v)

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