Vitruvius
,
De architectura libri decem
,
1567
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514.01.310
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310
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LIBER
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cunda proprietaseſt: </
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>
<
s
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"
xml:space
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">Quod ſi inter regulam a b. </
s
>
<
s
xml:id
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"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s21061
"
xml:space
="
preserve
">flexam lineam ducetur linea, illa tandem flexam ſeca-
<
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/>
bit. </
s
>
<
s
xml:id
="
echoid-s21062
"
xml:space
="
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">Eſto ergo regula a b. </
s
>
<
s
xml:id
="
echoid-s21063
"
xml:space
="
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">polus c. </
s
>
<
s
xml:id
="
echoid-s21064
"
xml:space
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">atque in interuallo d e.</
s
>
<
s
xml:id
="
echoid-s21065
"
xml:space
="
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">deſcribatur flexa,quæ conchoides dicitur. </
s
>
<
s
xml:id
="
echoid-s21066
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s21067
"
xml:space
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">
<
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/>
inter hanc & </
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>
<
s
xml:id
="
echoid-s21068
"
xml:space
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">regulam a b. </
s
>
<
s
xml:id
="
echoid-s21069
"
xml:space
="
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">ducatur recta f g h. </
s
>
<
s
xml:id
="
echoid-s21070
"
xml:space
="
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">dico f g h. </
s
>
<
s
xml:id
="
echoid-s21071
"
xml:space
="
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">flexam lineam ſecaturam. </
s
>
<
s
xml:id
="
echoid-s21072
"
xml:space
="
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">ſit f g h.
<
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/>
</
s
>
<
s
xml:id
="
echoid-s21073
"
xml:space
="
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">æque diſtans lineæ a b. </
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>
<
s
xml:id
="
echoid-s21074
"
xml:space
="
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">aut non ſit. </
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>
<
s
xml:id
="
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"
xml:space
="
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">poſito ergo prius quod ſit & </
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>
<
s
xml:id
="
echoid-s21076
"
xml:space
="
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">fiat, ut ſicut ſe habet d g. </
s
>
<
s
xml:id
="
echoid-s21077
"
xml:space
="
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">ad g c. </
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>
<
s
xml:id
="
echoid-s21078
"
xml:space
="
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">ita
<
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/>
ſe habeat d e. </
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>
<
s
xml:id
="
echoid-s21079
"
xml:space
="
preserve
">ad alium, puta k. </
s
>
<
s
xml:id
="
echoid-s21080
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s21081
"
xml:space
="
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">constituto centro c. </
s
>
<
s
xml:id
="
echoid-s21082
"
xml:space
="
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">interuallo k. </
s
>
<
s
xml:id
="
echoid-s21083
"
xml:space
="
preserve
">ſecet circunferentiam deſcriptã
<
lb
/>
in f. </
s
>
<
s
xml:id
="
echoid-s21084
"
xml:space
="
preserve
">atque iungatur c f. </
s
>
<
s
xml:id
="
echoid-s21085
"
xml:space
="
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">quæ ſecet ab in l. </
s
>
<
s
xml:id
="
echoid-s21086
"
xml:space
="
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">erit ergo ut ſicut d g. </
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>
<
s
xml:id
="
echoid-s21087
"
xml:space
="
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">ſe habet ad g c. </
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>
<
s
xml:id
="
echoid-s21088
"
xml:space
="
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">ita ſe habent l
<
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/>
f. </
s
>
<
s
xml:id
="
echoid-s21089
"
xml:space
="
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">ad f c. </
s
>
<
s
xml:id
="
echoid-s21090
"
xml:space
="
preserve
">Sedſicut eſt d g. </
s
>
<
s
xml:id
="
echoid-s21091
"
xml:space
="
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">ad g c. </
s
>
<
s
xml:id
="
echoid-s21092
"
xml:space
="
preserve
">ita ſe habebat d e. </
s
>
<
s
xml:id
="
echoid-s21093
"
xml:space
="
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">ad k. </
s
>
<
s
xml:id
="
echoid-s21094
"
xml:space
="
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">ideſt ad c f. </
s
>
<
s
xml:id
="
echoid-s21095
"
xml:space
="
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">ergo d e. </
s
>
<
s
xml:id
="
echoid-s21096
"
xml:space
="
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">inuenietur
<
lb
/>
æ qualis ipſi l f. </
s
>
<
s
xml:id
="
echoid-s21097
"
xml:space
="
preserve
">quod fieri non potest, ita enim pars æqualis toti eſſet, quod manifeſtum fit producta linea
<
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/>
c f. </
s
>
<
s
xml:id
="
echoid-s21098
"
xml:space
="
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">donec ſecet flexam lineam per e in o. </
s
>
<
s
xml:id
="
echoid-s21099
"
xml:space
="
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">quoniam l f o. </
s
>
<
s
xml:id
="
echoid-s21100
"
xml:space
="
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">recta æ qualis est ipſi de ex diſſinitione con-
<
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/>
choidis. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Reliquum igitur est, quod recta f g h. </
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>
<
s
xml:id
="
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"
xml:space
="
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">ſecet flexam lineam modo ad eaſdem partes ducatur. </
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>
<
s
xml:id
="
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xml:space
="
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">Ve-
<
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<
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xlink:label
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note-514.01.310-01
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="
note-514.01.310-01a
"
xml:space
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">10</
note
>
rum æ quediſtet linea illa, quæ inter a b. </
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>
<
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xml:space
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">& </
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>
<
s
xml:id
="
echoid-s21105
"
xml:space
="
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">flexam producetur, & </
s
>
<
s
xml:id
="
echoid-s21106
"
xml:space
="
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">ſit ea m g n, ducaturq́; </
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>
<
s
xml:id
="
echoid-s21107
"
xml:space
="
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">per g. </
s
>
<
s
xml:id
="
echoid-s21108
"
xml:space
="
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">æ que-
<
lb
/>
diſtans f g. </
s
>
<
s
xml:id
="
echoid-s21109
"
xml:space
="
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">regulæ a b. </
s
>
<
s
xml:id
="
echoid-s21110
"
xml:space
="
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">ergo f g. </
s
>
<
s
xml:id
="
echoid-s21111
"
xml:space
="
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">concurret cum flexa, & </
s
>
<
s
xml:id
="
echoid-s21112
"
xml:space
="
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">ideo multo magis concurret m n. </
s
>
<
s
xml:id
="
echoid-s21113
"
xml:space
="
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">Cum
<
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/>
ergo huiuſmodi proprietates organo collectæ fuerint, uſus eius ad propoſitũ oſtẽdendus erit modo terti a proprie
<
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/>
tas adducatur, quæ est huiuſmodi. </
s
>
<
s
xml:id
="
echoid-s21114
"
xml:space
="
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">Recta a b. </
s
>
<
s
xml:id
="
echoid-s21115
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s21116
"
xml:space
="
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">prima flexa conchoides cum deſcripta illa nunquam con-
<
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/>
current, etiam ſi in infinitum protrahantur, hoc facile innoteſcet, ſi ad formam organi attendatur, quoniam in
<
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/>
eadem forma, linea media regulæ e f. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">in deſcribenda flexa ſecat ſemper lineam a b. </
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>
<
s
xml:id
="
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"
xml:space
="
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">in e. </
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>
<
s
xml:id
="
echoid-s21119
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xml:space
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">quo fit ut nota
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k. </
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<
s
xml:id
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xml:space
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">nunquam perueniet ad ab. </
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>
<
s
xml:id
="
echoid-s21121
"
xml:space
="
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">licet ad eam continenter accedat, per primam prædictam proprietatem.
<
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/>
</
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>
<
s
xml:id
="
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"
xml:space
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">Hoc Nicomedis aſſumptum utile es̃t demonſtrationi ſequenti. </
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>
<
s
xml:id
="
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xml:space
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">Si angulus fiet ad rectam quæ altera par-
<
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te in infinitum tendat, & </
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>
<
s
xml:id
="
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"
xml:space
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">ſi a puncto extra dato ducatur linea, quæ circa eundem angulum ſecet duas
<
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/>
rectas, cuius rectæ lineæ particula inter duas, quæ rectum continent datum angulum, equalis ſit da-
<
lb
/>
tæ lineæ quod hoc modo facies. </
s
>
<
s
xml:id
="
echoid-s21125
"
xml:space
="
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">Eſto data linea a b. </
s
>
<
s
xml:id
="
echoid-s21126
"
xml:space
="
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">ex parte b, infinita, ſupra quam datus an--
<
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/>
<
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="
left
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xlink:label
="
note-514.01.310-02
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xlink:href
="
note-514.01.310-02a
"
xml:space
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">20</
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>
gulus b a g. </
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<
s
xml:id
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xml:space
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">nota extra ſit c. </
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>
<
s
xml:id
="
echoid-s21128
"
xml:space
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">recta autem data ſic d. </
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>
<
s
xml:id
="
echoid-s21129
"
xml:space
="
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">ab c, ad a b. </
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>
<
s
xml:id
="
echoid-s21130
"
xml:space
="
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">ducatur perpendicula-
<
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/>
ris c e. </
s
>
<
s
xml:id
="
echoid-s21131
"
xml:space
="
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">cui addatur e f. </
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>
<
s
xml:id
="
echoid-s21132
"
xml:space
="
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">æ qualis ipſi d. </
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>
<
s
xml:id
="
echoid-s21133
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s21134
"
xml:space
="
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">ex organo a polo c. </
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>
<
s
xml:id
="
echoid-s21135
"
xml:space
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">& </
s
>
<
s
xml:id
="
echoid-s21136
"
xml:space
="
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">interuallo e f, ad regulam a
<
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/>
b deſcribatur linea flexa conchoides prima. </
s
>
<
s
xml:id
="
echoid-s21137
"
xml:space
="
preserve
">Ergo ex ſecunda proprietate a g, primæ conchoidis produ-
<
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/>
cta eoincidet cum conchoidi f g. </
s
>
<
s
xml:id
="
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"
xml:space
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">coincidet ergo in g, & </
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>
<
s
xml:id
="
echoid-s21139
"
xml:space
="
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">linea c g, producta, ſecabit a b. </
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>
<
s
xml:id
="
echoid-s21140
"
xml:space
="
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">in h. </
s
>
<
s
xml:id
="
echoid-s21141
"
xml:space
="
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">aio li-
<
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/>
neam g h. </
s
>
<
s
xml:id
="
echoid-s21142
"
xml:space
="
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">eſſe æqualem ipſi d. </
s
>
<
s
xml:id
="
echoid-s21143
"
xml:space
="
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">quod inde patet, quoniam ex conchoidis primæ diffinitione, g h, eſt æ-
<
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/>
qualis ipſi e f, ſed ex præ ſumpto e f eſt æ qualis ipſi d. </
s
>
<
s
xml:id
="
echoid-s21144
"
xml:space
="
preserve
">ergo ex communi ſententia quæ æ qualia tertio,
<
lb
/>
æ qualia inuicem dicuntur, recta g h, eſt æ qualis ipſi d. </
s
>
<
s
xml:id
="
echoid-s21145
"
xml:space
="
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">propoſitum ergo habemus. </
s
>
<
s
xml:id
="
echoid-s21146
"
xml:space
="
preserve
">Ex Nicomede igitur duæ
<
lb
/>
mediæ comparabiles hoc modo inuenientur. </
s
>
<
s
xml:id
="
echoid-s21147
"
xml:space
="
preserve
">Sint duæ rectæ a b, & </
s
>
<
s
xml:id
="
echoid-s21148
"
xml:space
="
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">b c, ad angulos rectos poſitæ, inter
<
lb
/>
quas comparabiles duas medias inuenire oporteat: </
s
>
<
s
xml:id
="
echoid-s21149
"
xml:space
="
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">perficiatur parallelogrammum a b c d. </
s
>
<
s
xml:id
="
echoid-s21150
"
xml:space
="
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">ſecetur utra-
<
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/>
que in duas partes, c d, quidem in e. </
s
>
<
s
xml:id
="
echoid-s21151
"
xml:space
="
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">d a. </
s
>
<
s
xml:id
="
echoid-s21152
"
xml:space
="
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">uero in f. </
s
>
<
s
xml:id
="
echoid-s21153
"
xml:space
="
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">coniungaturq́; </
s
>
<
s
xml:id
="
echoid-s21154
"
xml:space
="
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">b e, &</
s
>
<
s
xml:id
="
echoid-s21155
"
xml:space
="
preserve
">tranſeat uſque ad a d.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s21156
"
xml:space
="
preserve
">
<
note
position
="
left
"
xlink:label
="
note-514.01.310-03
"
xlink:href
="
note-514.01.310-03a
"
xml:space
="
preserve
">30</
note
>
productam in punctum g. </
s
>
<
s
xml:id
="
echoid-s21157
"
xml:space
="
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">ſed in linea a d. </
s
>
<
s
xml:id
="
echoid-s21158
"
xml:space
="
preserve
">cadat ad rectos angulos linea f h. </
s
>
<
s
xml:id
="
echoid-s21159
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s21160
"
xml:space
="
preserve
">producatur a h. </
s
>
<
s
xml:id
="
echoid-s21161
"
xml:space
="
preserve
">quæ
<
lb
/>
ſit & </
s
>
<
s
xml:id
="
echoid-s21162
"
xml:space
="
preserve
">qualis ipſi c e. </
s
>
<
s
xml:id
="
echoid-s21163
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s21164
"
xml:space
="
preserve
">iungatur g h. </
s
>
<
s
xml:id
="
echoid-s21165
"
xml:space
="
preserve
">cui æque diſtet, a i. </
s
>
<
s
xml:id
="
echoid-s21166
"
xml:space
="
preserve
">ita ut angulus k a i, ſit æqualis angulo
<
lb
/>
f g h. </
s
>
<
s
xml:id
="
echoid-s21167
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s21168
"
xml:space
="
preserve
">expræcedenti aſſumpto ducatur recta g i k. </
s
>
<
s
xml:id
="
echoid-s21169
"
xml:space
="
preserve
">quæ ſecet a i.</
s
>
<
s
xml:id
="
echoid-s21170
"
xml:space
="
preserve
">in i. </
s
>
<
s
xml:id
="
echoid-s21171
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s21172
"
xml:space
="
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">d a. </
s
>
<
s
xml:id
="
echoid-s21173
"
xml:space
="
preserve
">in parte a. </
s
>
<
s
xml:id
="
echoid-s21174
"
xml:space
="
preserve
">pro-
<
lb
/>
ducta ſupra k. </
s
>
<
s
xml:id
="
echoid-s21175
"
xml:space
="
preserve
">ita ut. </
s
>
<
s
xml:id
="
echoid-s21176
"
xml:space
="
preserve
">i k. </
s
>
<
s
xml:id
="
echoid-s21177
"
xml:space
="
preserve
">ſit æqualis ipſi. </
s
>
<
s
xml:id
="
echoid-s21178
"
xml:space
="
preserve
">a h. </
s
>
<
s
xml:id
="
echoid-s21179
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s21180
"
xml:space
="
preserve
">iuncta k b, producatur in l, donec cadat in d c.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s21181
"
xml:space
="
preserve
">productum. </
s
>
<
s
xml:id
="
echoid-s21182
"
xml:space
="
preserve
">Dico iam quod ſicut ſe habet a b. </
s
>
<
s
xml:id
="
echoid-s21183
"
xml:space
="
preserve
">ad a k. </
s
>
<
s
xml:id
="
echoid-s21184
"
xml:space
="
preserve
">ita a k. </
s
>
<
s
xml:id
="
echoid-s21185
"
xml:space
="
preserve
">ad l c. </
s
>
<
s
xml:id
="
echoid-s21186
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s21187
"
xml:space
="
preserve
">l c. </
s
>
<
s
xml:id
="
echoid-s21188
"
xml:space
="
preserve
">ad c b. </
s
>
<
s
xml:id
="
echoid-s21189
"
xml:space
="
preserve
">quoniam
<
lb
/>
c d. </
s
>
<
s
xml:id
="
echoid-s21190
"
xml:space
="
preserve
">est in duas partes diuiſa in e. </
s
>
<
s
xml:id
="
echoid-s21191
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s21192
"
xml:space
="
preserve
">huic apponitur k a. </
s
>
<
s
xml:id
="
echoid-s21193
"
xml:space
="
preserve
">ergo ex eadem ſexta ſecundi elementorum,
<
lb
/>
quod eſt ſub d k a. </
s
>
<
s
xml:id
="
echoid-s21194
"
xml:space
="
preserve
">cum eo, quod fit ex a f æquale est illi, quod fit ex f k. </
s
>
<
s
xml:id
="
echoid-s21195
"
xml:space
="
preserve
">Apponatur commune, quod
<
lb
/>
eſtinter f h. </
s
>
<
s
xml:id
="
echoid-s21196
"
xml:space
="
preserve
">ergo quod est ſub d k a cum eo, quod fit ex a f & </
s
>
<
s
xml:id
="
echoid-s21197
"
xml:space
="
preserve
">ex f h. </
s
>
<
s
xml:id
="
echoid-s21198
"
xml:space
="
preserve
">hoc eſt cum eo, quod fit ex
<
lb
/>
a g. </
s
>
<
s
xml:id
="
echoid-s21199
"
xml:space
="
preserve
">æquale est illi, quod fit ex k f. </
s
>
<
s
xml:id
="
echoid-s21200
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s21201
"
xml:space
="
preserve
">ex f h. </
s
>
<
s
xml:id
="
echoid-s21202
"
xml:space
="
preserve
">ideſt illi, quod fit ex k h. </
s
>
<
s
xml:id
="
echoid-s21203
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s21204
"
xml:space
="
preserve
">quoniam ſicuti ſe habet
<
lb
/>
l c, ad c d. </
s
>
<
s
xml:id
="
echoid-s21205
"
xml:space
="
preserve
">ita ſe habet d a. </
s
>
<
s
xml:id
="
echoid-s21206
"
xml:space
="
preserve
">ad a k. </
s
>
<
s
xml:id
="
echoid-s21207
"
xml:space
="
preserve
">ſed c e. </
s
>
<
s
xml:id
="
echoid-s21208
"
xml:space
="
preserve
">eſt dimidium ipſius c d. </
s
>
<
s
xml:id
="
echoid-s21209
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s21210
"
xml:space
="
preserve
">a g. </
s
>
<
s
xml:id
="
echoid-s21211
"
xml:space
="
preserve
">est dupla ipſi d a. </
s
>
<
s
xml:id
="
echoid-s21212
"
xml:space
="
preserve
">
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-514.01.310-04
"
xlink:href
="
note-514.01.310-04a
"
xml:space
="
preserve
">40</
note
>
quoniam ex quarta ſexti elementorum ut ſe habet a b. </
s
>
<
s
xml:id
="
echoid-s21213
"
xml:space
="
preserve
">ad d e. </
s
>
<
s
xml:id
="
echoid-s21214
"
xml:space
="
preserve
">ita ſe habet g a. </
s
>
<
s
xml:id
="
echoid-s21215
"
xml:space
="
preserve
">ad a d. </
s
>
<
s
xml:id
="
echoid-s21216
"
xml:space
="
preserve
">ex ſuppoſi-
<
lb
/>
tis b a, eſt dupla ipſi d e. </
s
>
<
s
xml:id
="
echoid-s21217
"
xml:space
="
preserve
">ergo g a. </
s
>
<
s
xml:id
="
echoid-s21218
"
xml:space
="
preserve
">est dupla ipſi a d. </
s
>
<
s
xml:id
="
echoid-s21219
"
xml:space
="
preserve
">ſequetur ergo, ut ſicuti l c. </
s
>
<
s
xml:id
="
echoid-s21220
"
xml:space
="
preserve
">ſe habet ad c e.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s21221
"
xml:space
="
preserve
">ita g a. </
s
>
<
s
xml:id
="
echoid-s21222
"
xml:space
="
preserve
">ad a k. </
s
>
<
s
xml:id
="
echoid-s21223
"
xml:space
="
preserve
">exæquali & </
s
>
<
s
xml:id
="
echoid-s21224
"
xml:space
="
preserve
">permutata proportione,ex uigeſima tertia quinti elementorum. </
s
>
<
s
xml:id
="
echoid-s21225
"
xml:space
="
preserve
">ſed ut g a. </
s
>
<
s
xml:id
="
echoid-s21226
"
xml:space
="
preserve
">
<
lb
/>
ad a k. </
s
>
<
s
xml:id
="
echoid-s21227
"
xml:space
="
preserve
">ita h i. </
s
>
<
s
xml:id
="
echoid-s21228
"
xml:space
="
preserve
">ad i k. </
s
>
<
s
xml:id
="
echoid-s21229
"
xml:space
="
preserve
">exſecunda ſexti elementorum. </
s
>
<
s
xml:id
="
echoid-s21230
"
xml:space
="
preserve
">quoniam ex ſubiectis g h. </
s
>
<
s
xml:id
="
echoid-s21231
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s21232
"
xml:space
="
preserve
">a i. </
s
>
<
s
xml:id
="
echoid-s21233
"
xml:space
="
preserve
">ſunt æ qui-
<
lb
/>
distantes, & </
s
>
<
s
xml:id
="
echoid-s21234
"
xml:space
="
preserve
">ex decima octaua quinti elementorum componendo ſequitur, quod ſicut ſe habet l e ad c e,
<
lb
/>
ita ſe habeat h k. </
s
>
<
s
xml:id
="
echoid-s21235
"
xml:space
="
preserve
">ad k i. </
s
>
<
s
xml:id
="
echoid-s21236
"
xml:space
="
preserve
">ſed poſita eſt i k. </
s
>
<
s
xml:id
="
echoid-s21237
"
xml:space
="
preserve
">æ qualis c e. </
s
>
<
s
xml:id
="
echoid-s21238
"
xml:space
="
preserve
">quoniam i k. </
s
>
<
s
xml:id
="
echoid-s21239
"
xml:space
="
preserve
">eſt æqualis ipſi a h. </
s
>
<
s
xml:id
="
echoid-s21240
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s21241
"
xml:space
="
preserve
">a h. </
s
>
<
s
xml:id
="
echoid-s21242
"
xml:space
="
preserve
">ipſi
<
lb
/>
c e. </
s
>
<
s
xml:id
="
echoid-s21243
"
xml:space
="
preserve
">ergo e l. </
s
>
<
s
xml:id
="
echoid-s21244
"
xml:space
="
preserve
">eſt æqualis ipſi h k. </
s
>
<
s
xml:id
="
echoid-s21245
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s21246
"
xml:space
="
preserve
">conſequenter æquale est illud, quod fit e x l e, illi quod fit, ex h
<
lb
/>
k. </
s
>
<
s
xml:id
="
echoid-s21247
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s21248
"
xml:space
="
preserve
">quod fit ex l e, æquale eſt illi, quod fit ſub d l c. </
s
>
<
s
xml:id
="
echoid-s21249
"
xml:space
="
preserve
">cum eo quod fit ex c e, per ſextam ſecundi ele-
<
lb
/>
mentorum. </
s
>
<
s
xml:id
="
echoid-s21250
"
xml:space
="
preserve
">Eiautem quod est ex h k. </
s
>
<
s
xml:id
="
echoid-s21251
"
xml:space
="
preserve
">demonſtratum est æquale eſſe id, quod fit ſub d k a. </
s
>
<
s
xml:id
="
echoid-s21252
"
xml:space
="
preserve
">cum eo, quod
<
lb
/>
ex a h. </
s
>
<
s
xml:id
="
echoid-s21253
"
xml:space
="
preserve
">Quorumid, quod eſt ex c e, æquale eſt ei, quod ex a h. </
s
>
<
s
xml:id
="
echoid-s21254
"
xml:space
="
preserve
">Aequalis nanque poſitaes̃t a h. </
s
>
<
s
xml:id
="
echoid-s21255
"
xml:space
="
preserve
">ipſi
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-514.01.310-05
"
xlink:href
="
note-514.01.310-05a
"
xml:space
="
preserve
">50</
note
>
c e. </
s
>
<
s
xml:id
="
echoid-s21256
"
xml:space
="
preserve
">Sed ex communi ſententia, ſi ab æqualibus auferantur æqualia, æqualia ſunt reliqua, igitur quod fit ſub
<
lb
/>
d l c, æquale eſt ei, quod fit ſub d k a atuqui per decimam quartam ſexti æqualium, & </
s
>
<
s
xml:id
="
echoid-s21257
"
xml:space
="
preserve
">æquiangulorum pa-
<
lb
/>
rallelogrammorum latera mutua ſe proportione conſequuntur. </
s
>
<
s
xml:id
="
echoid-s21258
"
xml:space
="
preserve
">ergo ut ipſa l d. </
s
>
<
s
xml:id
="
echoid-s21259
"
xml:space
="
preserve
">ad d k. </
s
>
<
s
xml:id
="
echoid-s21260
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s21261
"
xml:space
="
preserve
">k a. </
s
>
<
s
xml:id
="
echoid-s21262
"
xml:space
="
preserve
">ad c l.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s21263
"
xml:space
="
preserve
">verũ ut d l. </
s
>
<
s
xml:id
="
echoid-s21264
"
xml:space
="
preserve
">ad d k. </
s
>
<
s
xml:id
="
echoid-s21265
"
xml:space
="
preserve
">et a b ad a k & </
s
>
<
s
xml:id
="
echoid-s21266
"
xml:space
="
preserve
">l c. </
s
>
<
s
xml:id
="
echoid-s21267
"
xml:space
="
preserve
">ad c b. </
s
>
<
s
xml:id
="
echoid-s21268
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s21269
"
xml:space
="
preserve
">l c. </
s
>
<
s
xml:id
="
echoid-s21270
"
xml:space
="
preserve
">ad c b. </
s
>
<
s
xml:id
="
echoid-s21271
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s21272
"
xml:space
="
preserve
">a b, ad a k. </
s
>
<
s
xml:id
="
echoid-s21273
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s21274
"
xml:space
="
preserve
">a k. </
s
>
<
s
xml:id
="
echoid-s21275
"
xml:space
="
preserve
">ad a k. </
s
>
<
s
xml:id
="
echoid-s21276
"
xml:space
="
preserve
">ad l c.</
s
>
<
s
xml:id
="
echoid-s21277
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s21278
"
xml:space
="
preserve
">ipſa l c, ad c b. </
s
>
<
s
xml:id
="
echoid-s21279
"
xml:space
="
preserve
">
<
lb
/>
Duabus igitur datis rectis lineis a b. </
s
>
<
s
xml:id
="
echoid-s21280
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s21281
"
xml:space
="
preserve
">b c. </
s
>
<
s
xml:id
="
echoid-s21282
"
xml:space
="
preserve
">mediæ duæ inuentæ ſunt comparabiles, & </
s
>
<
s
xml:id
="
echoid-s21283
"
xml:space
="
preserve
">reſpondentes a k. </
s
>
<
s
xml:id
="
echoid-s21284
"
xml:space
="
preserve
">
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s21285
"
xml:space
="
preserve
">l c. </
s
>
<
s
xml:id
="
echoid-s21286
"
xml:space
="
preserve
">quod facere propoſitum fuit. </
s
>
<
s
xml:id
="
echoid-s21287
"
xml:space
="
preserve
">Cæ terum modi alij ſunt antiquor um inueniendi duas medias compara-
<
lb
/>
biles, quos ne moleſtus ſim, omittam, præſertim cum eos in commentarijs Archimedis uidere poſſis, & </
s
>
<
s
xml:id
="
echoid-s21288
"
xml:space
="
preserve
">a Ver
<
lb
/>
Hero diligenter explicati ſint. </
s
>
<
s
xml:id
="
echoid-s21289
"
xml:space
="
preserve
">nam Philoponus, Dion Bizantius, Diocles, Pappus in mechanicis, Porus, & </
s
>
<
s
xml:id
="
echoid-s21290
"
xml:space
="
preserve
">
<
lb
/>
Menechmus de ijs multa. </
s
>
<
s
xml:id
="
echoid-s21291
"
xml:space
="
preserve
">dixere. </
s
>
<
s
xml:id
="
echoid-s21292
"
xml:space
="
preserve
">V eniam igitur ad id, quod quinto libro pollicitus ſum, & </
s
>
<
s
xml:id
="
echoid-s21293
"
xml:space
="
preserve
">modum ponam,
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-514.01.310-06
"
xlink:href
="
note-514.01.310-06a
"
xml:space
="
preserve
">60</
note
>
</
s
>
</
p
>
</
div
>
</
div
>
</
text
>
</
echo
>