665333
[Commentary:
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Si a centro circuli sit linea recta ducta quælibet punctum extra circulum
prima trium proportionalium: secundum sit sive media proportionalium sit eiusdem
lineæ pars quæ est semidiameter: tertia quæ minima proportionalium
sit eiusdem pars a versus circumferentiam quæ necessario terminabitur [???]ad punctam intra deinde si a qualibet
puncto in periferia agantur duæ lineæ, una prima ad punctum extra circulum
(qui terminus est primæ proportionalis:) altera ad punctum intra circulum,
qui terminus est tertiæ proportionalis,) Tum duæ illæ lineæ eandem habent
rationem quæ est trium proportionalium.
Et a quovis puncto quæ non est in periferia
duæ lineæ ita actæ, non habent eandem
[Translation: If from the centre of a circle let a straight line be drawn to any point outside the circle as the first of three proportinals. Let the second or mean proportional be part of the same line, which is the semidiamater. The third or least proportional is part of the same line from the centre towards the circumference, which necessarily will terminate at a point inside the circle. Then from any point on the circumference there are constructed two lines, the first to the point outside the circle (which is the end of the first proportional), the other to the point inside the circle (which is the end of the third proportional). Then those two lines have the same ratio as the three proportionals.
And from any point which is not on the circumference, two lines constructed in this way do not have the same ratio.
prima trium proportionalium: secundum sit sive media proportionalium sit eiusdem
lineæ pars quæ est semidiameter: tertia quæ minima proportionalium
sit eiusdem pars a versus circumferentiam quæ necessario terminabitur [???]ad punctam intra deinde si a qualibet
puncto in periferia agantur duæ lineæ, una prima ad punctum extra circulum
(qui terminus est primæ proportionalis:) altera ad punctum intra circulum,
qui terminus est tertiæ proportionalis,) Tum duæ illæ lineæ eandem habent
rationem quæ est trium proportionalium.
Et a quovis puncto quæ non est in periferia
duæ lineæ ita actæ, non habent eandem
[Translation: If from the centre of a circle let a straight line be drawn to any point outside the circle as the first of three proportinals. Let the second or mean proportional be part of the same line, which is the semidiamater. The third or least proportional is part of the same line from the centre towards the circumference, which necessarily will terminate at a point inside the circle. Then from any point on the circumference there are constructed two lines, the first to the point outside the circle (which is the end of the first proportional), the other to the point inside the circle (which is the end of the third proportional). Then those two lines have the same ratio as the three proportionals.
And from any point which is not on the circumference, two lines constructed in this way do not have the same ratio.
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