393197
6) De
[Translation: On ]
[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 ]
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 ,
, , sese mutuo contingentes
in punctis , , . cuius centra , , .
Agatur recta in continuum
[…]
Agatur recta contingens
circulum in puncto .
Agatur recta in continuum quæ secabit
circulum cuius centrum in puncto.
fiat, recta, parallela .
Et ad lineam productam sint per-
pendicularis ,
[Translation: Let the three given circles be , , , mutually touching at the points , , , whose centres are , , .
There is constructed the extended line .
There is constructed the line touching the circle at the point .
There is constructed the extended line which will cut the circule whose centre is in the point .
Let the line be parallel to .
And to the extended line let there be perpendiculars and .
, , sese mutuo contingentes
in punctis , , . cuius centra , , .
Agatur recta in continuum
[…]
Agatur recta contingens
circulum in puncto .
Agatur recta in continuum quæ secabit
circulum cuius centrum in puncto.
fiat, recta, parallela .
Et ad lineam productam sint per-
pendicularis ,
[Translation: Let the three given circles be , , , mutually touching at the points , , , whose centres are , , .
There is constructed the extended line .
There is constructed the line touching the circle at the point .
There is constructed the extended line which will cut the circule whose centre is in the point .
Let the line be parallel to .
And to the extended line let there be perpendiculars and .
Bissecetur in puncto .
Centro , intervallo ,
describatur circulus.
Dico quod: ille est circulus quæsitus
et contingit tres datos
in puncto , ,
[Translation: Let the line be bisected at the point .
With centre , radius , there is drawn a circle.
I say that this is the circle sought, and that it touches the three given circles at the points , , .
Centro , intervallo ,
describatur circulus.
Dico quod: ille est circulus quæsitus
et contingit tres datos
in puncto , ,
[Translation: Let the line be bisected at the point .
With centre , radius , there is drawn a circle.
I say that this is the circle sought, and that it touches the three given circles at the points , , .