653327
[Commentary:
For a rough version of this page see Add MS
f. . ]
1.)
propositio
Si in centro circuli sit linea acta ad quodlibet punctum extra circulum
pro prima trium proportionalium: secunda sive media proportionalium
sit eiusdem lineæ pars quæ est semidiametro: tertia quæ minima
proportionalium sit etiam eiusdem pars a centro versus peripheriam, quæ
necessario terminabitur aliquod puncto intra circulum: deinde si a quodlibet
puncto in peripheria agantur duæ lineæ prima ad punctum extra
circulum, qui terminus est primæ proportionalis; altera ad punctum
intra cirulum, qui terminus est tertiæ proportionalis:
Tum duæ illæ lineæ eandem habebunt rationem quæ est
trium proportionalium:
Et a quovis puncto quod non est in peripheria, duæ lineæ
ita actæ, non habebunt illam
[Translation: If in the centre of a circle there is constructed a line to any point outside the circle for the first of three proportionals, let the second or mean proportional be part of the same line, which is the semidiameter, and let the third or least proportional be also part of the same line from the centre to the circumference, which necessarily ends at some 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 proportinonal, and the other to the point inside the circle, which is the end of the third proportional.
Then those two lines will have the same ratio as the three porportionals.
And from any point which is not on the circumference, two lines taken in this way will not have that ]
pro prima trium proportionalium: secunda sive media proportionalium
sit eiusdem lineæ pars quæ est semidiametro: tertia quæ minima
proportionalium sit etiam eiusdem pars a centro versus peripheriam, quæ
necessario terminabitur aliquod puncto intra circulum: deinde si a quodlibet
puncto in peripheria agantur duæ lineæ prima ad punctum extra
circulum, qui terminus est primæ proportionalis; altera ad punctum
intra cirulum, qui terminus est tertiæ proportionalis:
Tum duæ illæ lineæ eandem habebunt rationem quæ est
trium proportionalium:
Et a quovis puncto quod non est in peripheria, duæ lineæ
ita actæ, non habebunt illam
[Translation: If in the centre of a circle there is constructed a line to any point outside the circle for the first of three proportionals, let the second or mean proportional be part of the same line, which is the semidiameter, and let the third or least proportional be also part of the same line from the centre to the circumference, which necessarily ends at some 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 proportinonal, and the other to the point inside the circle, which is the end of the third proportional.
Then those two lines will have the same ratio as the three porportionals.
And from any point which is not on the circumference, two lines taken in this way will not have that ]
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