Guevara, Giovanni di
,
In Aristotelis mechanicas commentarii
,
1627
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archimedes
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<
chap
id
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N10019
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N116B6
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main
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<
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pagenum
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45
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005/01/053.jpg
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proportionalis maiori A B C D, ac per motum proprium
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verſus B, ipſum punctum A peragrauerit quantum eſt vſque
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ad E; & per motum totius lineæ A B, verſus lineam C D,
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peragrauerit quantum eſt ab A, vſque ad F, ſeruata eadem
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proportione ipſorum laterum; certe punctum A reperiri non
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poſſet in E, neque in F; ſiquidem non fuiſſet latum duabus
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lationibus, nec peragraſſet ſpacium ſecundum vtramque po
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ſitionem, ſimul accedendo quantum fieri poteſt ad B & ad
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C; ſed vna tantùm latione, alterum ſolum ſpacium percur
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riſſet. </
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<
s
id
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N11712
">Reperietur ergo ipſum. </
s
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<
s
id
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N11715
">punctum A vbi vtraque pro
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greſſio poteſt verificari, vt in puncto G. </
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<
s
id
="
N1171B
">Quia nimirum F G
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eſt æqualis ipſi A E, & E G æqualis ipſi A F, cum ſint latera
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oppoſita eiuſdem rectanguli, vt patet per 34. primi Elemen
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torum Euclidis. </
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>
<
s
id
="
N11725
">Sed punctum G non poteſt eſſe niſi in recta
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A D, quæ eſt vtriuſque rectanguli diameter, vt patet per 26.
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ſexti, & eodem modo quodlibet aliud punctum, in quo vtra
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que latio ac latera depræhendantur eadem proportione pro
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portionalia, vt in H, reſpectu I & K: igitur punctum A, dua
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bus lationibus proportionalibus latum, neceſſariò mouebi
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tur ſuper rectam A D, quod erat probandum. </
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</
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<
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id
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type
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<
s
id
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N11736
">Quod quidem clarius adhuc probari poſſet exemplo hu
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ius quadrati A B C D, cuius latera diuiſa ſint in quatuor par
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tes æquales,
<
expan
abbr
="
efficiantq.
">efficiantque</
expan
>
ex illis minora quadrata contenta in
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maiori. </
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<
s
id
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N11743
">Nam ſi ſup
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number
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<
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ponatur punctum A ex
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ſe moueri tanquam na
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turali ac proprio motu
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verſus B, ſuper rectam
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A B, & eodem tempo
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re ſimul cum ipſa A B,
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quaſi motu alieno de
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ſcendere verſus C D,
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ac ſeruata eadem pro
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portione vtriuſque mo
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tus, quæ ſit æqualita
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tis: abſque dubio, eo-</
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