11156
[Commentary:
On this page, Harriot examines Problem VIII from Apollonius GallusApollonius Gallus
(Viete 1600a, Prob .
Problema VIII.
Datis duobus punctis, & circulo, per data duo puncta circulum describere, qui datum
VIII. Given two points and a circle, through the two given points describe a circle that touches the given ]
Problema VIII.
Datis duobus punctis, & circulo, per data duo puncta circulum describere, qui datum
VIII. Given two points and a circle, through the two given points describe a circle that touches the given ]
Apoll: Gallus. prob.
[Translation: Apollonius Gallus, Problem ]
[Translation: Apollonius Gallus, Problem ]
Desirit Duo casus (et alij)
in Vieta:
[Translation: There are two cases missing in Viète, ]
in Vieta:
[Translation: There are two cases missing in Viète, ]
Datis duobus puncti , .
Et circulo, :
per datum, circulum contingentem
[Translation: Given the two points and , and the circle , describe a circle through the given points, touching the circle.
Sit iam factum:
Et sit contactus in
agantur rectæ , , ,
arcus , et sunt similes
ita , et . contingentium.
[Translation: And let it be done thus:
And let it meet in .
Connect the lines , , , .
The arcs and are simlar, thus and , touching .
Et circulo, :
per datum, circulum contingentem
[Translation: Given the two points and , and the circle , describe a circle through the given points, touching the circle.
Sit iam factum:
Et sit contactus in
agantur rectæ , , ,
arcus , et sunt similes
ita , et . contingentium.
[Translation: And let it be done thus:
And let it meet in .
Connect the lines , , , .
The arcs and are simlar, thus and , touching .
Datur latera triangulorum ,
est distantia
[Translation: Given the sides of triangles and , The distance to the vertex is .
In alia charta
modus
[Translation: The method of investigation is in another ]
Si linea a , per se vel producta non secat circulum
datum: fierunt duo circuli
[Translation: If the lines from and , either in themselves or produced, do not cut the given circle, then there will arise two touching circles.
Si unum punctum sit intra alterum extra
circulum datum: casus
[Translation: If one point is inside, the other outside, the given circle, the case is ]
Si ab uno datorum punctum
sint duæ tangentes
circulum: et altera fit:
extra
[Translation: If from one of the given points there are two tangents to the circle, and the other is constructed
outside
]
est distantia
[Translation: Given the sides of triangles and , The distance to the vertex is .
In alia charta
modus
[Translation: The method of investigation is in another ]
Si linea a , per se vel producta non secat circulum
datum: fierunt duo circuli
[Translation: If the lines from and , either in themselves or produced, do not cut the given circle, then there will arise two touching circles.
Si unum punctum sit intra alterum extra
circulum datum: casus
[Translation: If one point is inside, the other outside, the given circle, the case is ]
Si ab uno datorum punctum
sint duæ tangentes
circulum: et altera fit:
extra
[Translation: If from one of the given points there are two tangents to the circle, and the other is constructed
outside
]