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[Commentary:
On this page, Harriot examines Problem IX from Apollonius Gallus
(Viete 1600a, Prob .
Problema IX.
Datis duobus circulis, & puncto, per datum punctum circulum describere quem duo dati circuli contingat.
IX. Given two circles and a point, through the given point describe a circle that touches the two given ]
Problema IX.
Datis duobus circulis, & puncto, per datum punctum circulum describere quem duo dati circuli contingat.
IX. Given two circles and a point, through the given point describe a circle that touches the two given ]
Appoll. Gall. problema. 9.
Casus.
[Translation: Apollonius Gallus, Problem IX, case ]
Casus.
[Translation: Apollonius Gallus, Problem IX, case ]
In isto casu:
Si punctum datum sit extra
circulum circa , et intra
tangentes ad partes :
vel extra eundem circulum et
intra tangentes ad partes . .
Duo circuli possunt
tangere duos
[Translation: In this case, if the point is outside the circle around , and inside the tangents on the side of , or outside the same circle and inside the tangents on the sides of and , then two circles can touch the two given.
Si punctum datum sit extra
circulum circa , et intra
tangentes ad partes :
vel extra eundem circulum et
intra tangentes ad partes . .
Duo circuli possunt
tangere duos
[Translation: In this case, if the point is outside the circle around , and inside the tangents on the side of , or outside the same circle and inside the tangents on the sides of and , then two circles can touch the two given.
Punctum non dabiter in circulis
et , neque in spatio intra
illos circulos vidilicet
et intra tangentes.
Alias utercunque: et unus tantum
circulus tangens describitur nisi in
locis supra
[Translation: The point will not be given in the circles and , nor in the space inside those circles, namely , and inside the tangents. Any other way, and one such tangent circle will be described unless in the places delineated above.
et , neque in spatio intra
illos circulos vidilicet
et intra tangentes.
Alias utercunque: et unus tantum
circulus tangens describitur nisi in
locis supra
[Translation: The point will not be given in the circles and , nor in the space inside those circles, namely , and inside the tangents. Any other way, and one such tangent circle will be described unless in the places delineated above.