379190
De
[Translation: On ]
[Translation: On ]
Ex Linea Quadrataria producta.
Consequentiones quædam
[Translation: From the production of a quadrate line,
certain marvellous ]
Consequentiones quædam
[Translation: From the production of a quadrate line,
certain marvellous ]
* Eadem evenient si motus
BD sit in maior vel
minori
[Translation: The same hapapens if the motion of BD is in a greater or smaller ]
BD sit in maior vel
minori
[Translation: The same hapapens if the motion of BD is in a greater or smaller ]
* Si ponatur BD movendi
ad situm CE in spacio unius
horæ: ac etiam eodem tempore
AB producta movendi ad
situm AK per
[Translation: If it is supposed that BD moves towards the position of CE in the space of one hour, and also in the same time that AB produced moves towards the position of AK by circulation.
Haec
[Translation: These things ]
ad situm CE in spacio unius
horæ: ac etiam eodem tempore
AB producta movendi ad
situm AK per
[Translation: If it is supposed that BD moves towards the position of CE in the space of one hour, and also in the same time that AB produced moves towards the position of AK by circulation.
Haec
[Translation: These things ]
1. Ex communi sectione duarum
linearum dictarum sit curva
linea infinita BFGH &c.
acta designata in termino
illius
[Translation: 1. From the point of intersection of the two said lines comes the infnite curved line BFGH etc. and the path is traced out in one hour.
linearum dictarum sit curva
linea infinita BFGH &c.
acta designata in termino
illius
[Translation: 1. From the point of intersection of the two said lines comes the infnite curved line BFGH etc. and the path is traced out in one hour.
2. Illa curva cum linea CE
non concurrebat ante terminum
horæ: et in ipse termino
concurrit: et si dicti motus
continuentur, ultra terminum
horæ non fit ulterior productio
nec
[Translation: 2. The curve and the line CE do not meet before the end of one hour; and at the end they do meet; and if the said motions are continued, beyond the end of the hour there will be no further lengthening or ]
non concurrebat ante terminum
horæ: et in ipse termino
concurrit: et si dicti motus
continuentur, ultra terminum
horæ non fit ulterior productio
nec
[Translation: 2. The curve and the line CE do not meet before the end of one hour; and at the end they do meet; and if the said motions are continued, beyond the end of the hour there will be no further lengthening or ]
3. Eodem instanti scilicet
termino horæ, AB mota et
in termino motus: tum secat
lineam CE: cum habet situ
AK scilicet parallelum ad
[Translation: 3. In that same instant at the end of the hour, AB is moving and at the end of its motion; then it cuts the line CE; while of course the position of AK is parallel to CE. Ita ut re hac racionatione sequitur duas
lineas parallelas in infinite distantia
[Translation: Thus by this reasoning it follows that two parallel lines cut at an infinite ]
termino horæ, AB mota et
in termino motus: tum secat
lineam CE: cum habet situ
AK scilicet parallelum ad
[Translation: 3. In that same instant at the end of the hour, AB is moving and at the end of its motion; then it cuts the line CE; while of course the position of AK is parallel to CE. Ita ut re hac racionatione sequitur duas
lineas parallelas in infinite distantia
[Translation: Thus by this reasoning it follows that two parallel lines cut at an infinite ]
Et hoc mirandum quod [???]dum generatur illa curva terminus in acta
productionis magis ac magis distantia linea AK, et in termino horæ
habet suam maximam distantia ac etiam concursum cum AK et
[Translation: And this is marvellous, that while the end of the curve is generated, in the act of production it becomes more and more distant from the line AK, and at the end of the hour has its maximum distance and yet meets with AK and ]
productionis magis ac magis distantia linea AK, et in termino horæ
habet suam maximam distantia ac etiam concursum cum AK et
[Translation: And this is marvellous, that while the end of the curve is generated, in the act of production it becomes more and more distant from the line AK, and at the end of the hour has its maximum distance and yet meets with AK and ]
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