2111
Datis duabus rectis inæqualibus ad angulos rectos positis:
e minore producta et maiore facere rectangulum tale
ut datarum maior ad diagonalem sit us minor ad
[Translation: Given two unequal straight lines supposed at right angles, from the lesser one extended and the greater construct a rectangle so that as the greater of the given lnes is to the diagonal so is the lesser line to the extended ]
e minore producta et maiore facere rectangulum tale
ut datarum maior ad diagonalem sit us minor ad
[Translation: Given two unequal straight lines supposed at right angles, from the lesser one extended and the greater construct a rectangle so that as the greater of the given lnes is to the diagonal so is the lesser line to the extended ]
Sint dataæ rectæ positæ ad
angulos rectos et .
sit maior, et minor
. Lineæ et a puncto
, agatur prallela
centro m et intervallo ,
agatur periferia quæ
secabit lineam in puncto .
a puncto , et lineæ
agatur parallela quæ
secabit productam in
puncto . Denique a puncto , et lineæ , agatur parallela
quæ secabit productam in puncto , et fit rectangulum .
Dico quod ut maior datarum ad , diagonalem; ita
minor ad . Est enim manifestum ut ad , ita
ad : sed linea , est æqualis . Ergo ad , est
ut ad . Est igitur factum quo
[Translation: Let the supposed given lines at right angles be et . Let be the greater one, and the lesser . From the point , let there be drawn a parallel to the line .
With centre and radius , let there be constructed the circumferene which will cut the line in the point . From the point let there be constructed the parallel to the line which will cut produced at the point . Then from the point , let there be constructed the parallel to the line which will cut produced in the point , and makes rectangule .
I say that as , the greater line, to , the diagonal, so it , the lesser line, to . For it is clear that as is to , so is to ; but the line is equal to . Therfore to is as to . It is therefore constructed, as required.
angulos rectos et .
sit maior, et minor
. Lineæ et a puncto
, agatur prallela
centro m et intervallo ,
agatur periferia quæ
secabit lineam in puncto .
a puncto , et lineæ
agatur parallela quæ
secabit productam in
puncto . Denique a puncto , et lineæ , agatur parallela
quæ secabit productam in puncto , et fit rectangulum .
Dico quod ut maior datarum ad , diagonalem; ita
minor ad . Est enim manifestum ut ad , ita
ad : sed linea , est æqualis . Ergo ad , est
ut ad . Est igitur factum quo
[Translation: Let the supposed given lines at right angles be et . Let be the greater one, and the lesser . From the point , let there be drawn a parallel to the line .
With centre and radius , let there be constructed the circumferene which will cut the line in the point . From the point let there be constructed the parallel to the line which will cut produced at the point . Then from the point , let there be constructed the parallel to the line which will cut produced in the point , and makes rectangule .
I say that as , the greater line, to , the diagonal, so it , the lesser line, to . For it is clear that as is to , so is to ; but the line is equal to . Therfore to is as to . It is therefore constructed, as required.
Eadem esset omnino constructio et demonstratio si problema
proponeretur universaliter in hunc
[Translation: It is the same in every construction and demonstration if the porblem us proposed generally in this ]
proponeretur universaliter in hunc
[Translation: It is the same in every construction and demonstration if the porblem us proposed generally in this ]
Datis duabus rectis inæqualibus et ad quamlibet inclinationem
positis: e minore aucta vel minuta vel insta et maiore facere
parallelorammum tale, ut datarum maior ad diagonalem sit ut
minor ad minorem auctam, vel nimutam, vel
[Translation: Given two unequal lines supposed at any inclination, and from the lesser one extended or decreased or as it stands and the greater one make a parallelogram so that the greater of the given lines to the diagonal is as the lesser to the lesser extended or decreased or as it ]
positis: e minore aucta vel minuta vel insta et maiore facere
parallelorammum tale, ut datarum maior ad diagonalem sit ut
minor ad minorem auctam, vel nimutam, vel
[Translation: Given two unequal lines supposed at any inclination, and from the lesser one extended or decreased or as it stands and the greater one make a parallelogram so that the greater of the given lines to the diagonal is as the lesser to the lesser extended or decreased or as it ]
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