10553
[Commentary:
On this page, Harriot examines Problem VI from Apollonius Gallus
(Viete 1600a, Prob , noting cases that were missed by Viète.
Problema VI.
Datis puncto, linea recta, & circulo, per datum punctam describere circulum, quem data linea recta & datus circulus
VI. Given a point, a line, and a circle, through the given point describe a circle that touches the given line and the given circle.]
Problema VI.
Datis puncto, linea recta, & circulo, per datum punctam describere circulum, quem data linea recta & datus circulus
VI. Given a point, a line, and a circle, through the given point describe a circle that touches the given line and the given circle.]
(. – o) Apoll: Gallus. prob.
[Translation: Apollonius Gallus, Problem ]
[Translation: Apollonius Gallus, Problem ]
alius casus:
a Vieta
[Translation: another case, missed by ]
a Vieta
[Translation: another case, missed by ]
Data.
punctum,
linea
circulum
Quæsitum. .
[Translation: Given:
the point ,
the line ,
the circle .
Sought: the circle .
punctum,
linea
circulum
Quæsitum. .
[Translation: Given:
the point ,
the line ,
the circle .
Sought: the circle .
Casus
1. . Vieta.
2. .
3. .
4. .
[Translation: Cases:
1. , in Viète.
2. .
3. .
4. , in Viète.
1. . Vieta.
2. .
3. .
4. .
[Translation: Cases:
1. , in Viète.
2. .
3. .
4. , in Viète.
alter casus:
a Vieta
[Translation: another case missed by ]
a Vieta
[Translation: another case missed by ]
In tribus prioribus
casibus
punctum () datum, est extra
datum circulum, et punctum
est ad easdem partes lineæ datæ.
cum () puncto seu cum circulo
[Translation: In the three previous cases, the point is outside the given circle, and the point is on the same side of the given line as the point or as the given circle.
casibus
punctum () datum, est extra
datum circulum, et punctum
est ad easdem partes lineæ datæ.
cum () puncto seu cum circulo
[Translation: In the three previous cases, the point is outside the given circle, and the point is on the same side of the given line as the point or as the given circle.
In 4o casu, punctum () datum
est intra datum circulum
et , , sunt ad partes
[Translation: In the 4th case, the given point is inside the given circle, and and are on opposite sides.
est intra datum circulum
et , , sunt ad partes
[Translation: In the 4th case, the given point is inside the given circle, and and are on opposite sides.