Vitruvius
,
De architectura libri decem
,
1567
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514.01.300
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300
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LIBER
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<
s
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xml:space
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">Quis igitur cum excellentibus illis uiris athletas uel fortiſſimos, & </
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<
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xml:space
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">gladiatores comparabit ? </
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<
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xml:space
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">qui eos
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cum ijs conferet, qui memorabili beneficio præſente uictoria ſibi aliquas gentes deuinxerit? </
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>
<
s
xml:id
="
echoid-s20050
"
xml:space
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preserve
">Merito igitur
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cum Vitruuio adiudicabimus diuinos honores his, qui pulchra, & </
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>
<
s
xml:id
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echoid-s20051
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xml:space
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">honeſta inuenta reliquere, potius quàm
<
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Græcis illis, qui robore corpore floruere, & </
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>
<
s
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="
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"
xml:space
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">præſentes uires in certaminibus Dijs dedicatis oſtendere, cedant
<
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Olympij uictorès, nec glorietur Iuppiter. </
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<
s
xml:id
="
echoid-s20053
"
xml:space
="
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">cedant Pithij, nec glorietur Thebas. </
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>
<
s
xml:id
="
echoid-s20054
"
xml:space
="
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">cedant Nemei, nec glorietur
<
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Archintorus. </
s
>
<
s
xml:id
="
echoid-s20055
"
xml:space
="
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">cedant Iſthmij, nec glorietur Palamon, nam Minerua omnes illos deos hæroesq́;</
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>
<
s
xml:id
="
echoid-s20056
"
xml:space
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">. in quorum ho-
<
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norem ludi eiuſmodi celebrati ſunt, gloria antecellit, cum rerum inuentores cum illis certatoribus compara-
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/>
tos uiderit. </
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>
<
s
xml:id
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xml:space
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">Sed nos ad inuenta, & </
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>
<
s
xml:id
="
echoid-s20058
"
xml:space
="
preserve
">rationes præclariſſimorum hominum eorum, qui bene uiuendi inſtituta, & </
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>
<
s
xml:id
="
echoid-s20059
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xml:space
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">
<
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/>
doctrinarum præcepta posteris reliquere; </
s
>
<
s
xml:id
="
echoid-s20060
"
xml:space
="
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">nam ſi in ſaltu, & </
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>
<
s
xml:id
="
echoid-s20061
"
xml:space
="
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">curſu agilitas requiritur, quid agilius, quid ue-
<
lb
/>
<
note
position
="
left
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xlink:label
="
note-514.01.300-01
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xlink:href
="
note-514.01.300-01a
"
xml:space
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">10</
note
>
locius animo erudito, & </
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>
<
s
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xml:space
="
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">in rerum contemplationeuerſato? </
s
>
<
s
xml:id
="
echoid-s20063
"
xml:space
="
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">qui terrena, & </
s
>
<
s
xml:id
="
echoid-s20064
"
xml:space
="
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">cœlestia quaſi uolando percurrat ?
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/>
</
s
>
<
s
xml:id
="
echoid-s20065
"
xml:space
="
preserve
">Si in diſco, & </
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>
<
s
xml:id
="
echoid-s20066
"
xml:space
="
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">iaculo quis glorietur, quid aget mens eius, qui humana omnia impedimenta proiecerit, & </
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>
<
s
xml:id
="
echoid-s20067
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xml:space
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">ſub-
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/>
uerterit ? </
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>
<
s
xml:id
="
echoid-s20068
"
xml:space
="
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">Si lucta robur, & </
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>
<
s
xml:id
="
echoid-s20069
"
xml:space
="
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">uires quærit, quid ſapiens faciet, qui cum fortuna continenter luctando, uires
<
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/>
eius infringit, & </
s
>
<
s
xml:id
="
echoid-s20070
"
xml:space
="
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">uirtute ictus repellit, & </
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>
<
s
xml:id
="
echoid-s20071
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xml:space
="
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">dexteritate inſultus deijcit, ac proſternit ? </
s
>
<
s
xml:id
="
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xml:space
="
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">Non oleaster, non po-
<
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/>
ma, non pinus, non apium præmia ſunt bonorum, & </
s
>
<
s
xml:id
="
echoid-s20073
"
xml:space
="
preserve
">doctorum hominum, non publicum alimentum, non eorum
<
lb
/>
aduentu murorum proiectio. </
s
>
<
s
xml:id
="
echoid-s20074
"
xml:space
="
preserve
">nullum enim par præmium uirtutis habetur in terris: </
s
>
<
s
xml:id
="
echoid-s20075
"
xml:space
="
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">Sed cœlum, ſplendor, glo-
<
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ria, felicitas eos perpetuo manet.</
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>
<
s
xml:id
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xml:space
="
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"/>
</
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</
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<
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type
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2
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<
head
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xml:space
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">Platonis inuentumde agro metiendo. Cap. I.</
head
>
<
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position
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left
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xml:space
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">20</
note
>
<
p
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<
s
xml:id
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<
emph
style
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emph
>
, aut ager patibus lateribus, ſi erit quadratus, eumq́; </
s
>
<
s
xml:id
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xml:space
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">oportuetit iterum ex paribus
<
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/>
lateribus duplicare, quia id genere numeri, ac multiplicationibus non inuenitur, ex de-
<
lb
/>
ſcriptionibus linearum emendatis reperitur. </
s
>
<
s
xml:id
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echoid-s20079
"
xml:space
="
preserve
">Eſt autem eius rei hæc demonſtratio.
<
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/>
</
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>
<
s
xml:id
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xml:space
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">Quadratus locus, qui erit longus, & </
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>
<
s
xml:id
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xml:space
="
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">latus pedes denos, efficit areæ pedes centum. </
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>
<
s
xml:id
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xml:space
="
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">Si
<
lb
/>
ergo opus fuerit eum duplicare, & </
s
>
<
s
xml:id
="
echoid-s20083
"
xml:space
="
preserve
">aream pedum ducentorum item ex paribus lateribus facere, quæ-
<
lb
/>
rendum erit quàm magnum latus eius quadratifiat, ut ex eo ducenti pedes duplicationibus areæ re-
<
lb
/>
ſpondeant. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Idautem numero nemo poteſt inuenire; </
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>
<
s
xml:id
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"
xml:space
="
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">nanque ſi 14. </
s
>
<
s
xml:id
="
echoid-s20086
"
xml:space
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">conſtituentur, erunt multipli-
<
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/>
catipedes 196. </
s
>
<
s
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xml:space
="
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">ſi quindecim, pedes 125. </
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>
<
s
xml:id
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echoid-s20088
"
xml:space
="
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">Ergo quoniam id non explicatur numero in eo quadra-
<
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/>
to longo, & </
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>
<
s
xml:id
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echoid-s20089
"
xml:space
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">lato pedes decem, quæ fuerit, linea ab angulo ad angulum diagonios perducatur, uti
<
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/>
diuidatur in duo trigona æqua magnitudine, ſingula areæ pedum quinquagenum, ad eius lineæ dia-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-514.01.300-03
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xlink:href
="
note-514.01.300-03a
"
xml:space
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">30</
note
>
gonalis longitudinem, locus quadratus paribus lateribus deſcribatur. </
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>
<
s
xml:id
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echoid-s20090
"
xml:space
="
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">Ita quam magna duo trigona,
<
lb
/>
in minore quadrato quinquagenum pedum linea diagonica fuerint deſignata, eadem magnitudine, & </
s
>
<
s
xml:id
="
echoid-s20091
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xml:space
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">
<
lb
/>
codem pedum numero, quaturo in maiore erunt effecta, Hac ratione duplicatio grammicis ratio-
<
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/>
nibus a Platone, uti eſt ſchema ſubſcriptum, fuit explicata.</
s
>
<
s
xml:id
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</
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<
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<
s
xml:id
="
echoid-s20093
"
xml:space
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">Quadratum menſuratur duorum laterum inter ſe multiplicatione facta. </
s
>
<
s
xml:id
="
echoid-s20094
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xml:space
="
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">Duplicatur quadratum ſumpta
<
lb
/>
eius diagonia linea pro latere quadrati, quod duplex faciendum erit. </
s
>
<
s
xml:id
="
echoid-s20095
"
xml:space
="
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">Diagonia hoc modo inuenitur, duo
<
lb
/>
latera quadrati per ſe ſingula in ſe ipſa uertendo multiplica, ſummam collige ipſius multiplicationis, & </
s
>
<
s
xml:id
="
echoid-s20096
"
xml:space
="
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">eius
<
lb
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ſummæ quadratam radicem quærito, tanta erit diagonia. </
s
>
<
s
xml:id
="
echoid-s20097
"
xml:space
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">Sit quadratum a, b, c, d, in ſingulis lateri-
<
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/>
bus pedes quinque, duc unius lateris puinque in ſe reddentur 25. </
s
>
<
s
xml:id
="
echoid-s20098
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xml:space
="
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">& </
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>
<
s
xml:id
="
echoid-s20099
"
xml:space
="
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">iterum alterius lateris quinque in ſe du-
<
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cito reddentur 25. </
s
>
<
s
xml:id
="
echoid-s20100
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xml:space
="
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">hæc collecta cum prioribus 25. </
s
>
<
s
xml:id
="
echoid-s20101
"
xml:space
="
preserve
">ſummam efficient quinquaginta, quorum quadratara-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-514.01.300-04
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xlink:href
="
note-514.01.300-04a
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xml:space
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">40</
note
>
dix est ped. </
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<
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xml:id
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">7. </
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<
s
xml:id
="
echoid-s20103
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xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s20104
"
xml:space
="
preserve
">unius quartæ, eadem ratio in alijs rectangulis quadratis inuenitur, ut in oblongo quadrato
<
lb
/>
e, f, g, h, latus, e, g, pedum octo, ducti in ſe efficiunt 64. </
s
>
<
s
xml:id
="
echoid-s20105
"
xml:space
="
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">latus e, f, pedes ſex. </
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>
<
s
xml:id
="
echoid-s20106
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xml:space
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">hi @ducti in ſe red-
<
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dunt 36. </
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<
s
xml:id
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echoid-s20107
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xml:space
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">qui cum 64. </
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>
<
s
xml:id
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echoid-s20108
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xml:space
="
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">collecti efficiunt centum, quorum radix quadrata ſunt decem, tanta igitur eſt dia-
<
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/>
gonios, & </
s
>
<
s
xml:id
="
echoid-s20109
"
xml:space
="
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">duplicis quadrati latus. </
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>
<
s
xml:id
="
echoid-s20110
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xml:space
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">Exemplum ſchematis Vitr. </
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>
<
s
xml:id
="
echoid-s20111
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xml:space
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">facile eſt. </
s
>
<
s
xml:id
="
echoid-s20112
"
xml:space
="
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">nam quadratum, a, c, h, d, du-
<
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plum eſt quadrato a, d, quoniam eius latus fit ex diagonali a, d, minoris quadrati, & </
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>
<
s
xml:id
="
echoid-s20113
"
xml:space
="
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">quod numeri ge-
<
lb
/>
nerenullo efficitur, id grammicis rationibus abſoluitur. </
s
>
<
s
xml:id
="
echoid-s20114
"
xml:space
="
preserve
">Vtiliſſima uero, & </
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>
<
s
xml:id
="
echoid-s20115
"
xml:space
="
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">huius reiratio in plurimis obſer-
<
lb
/>
uationibus quotidiani uſus, ut experientibus erit manifeſtum.</
s
>
<
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xml:id
="
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</
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</
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<
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type
="
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level
="
2
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n
="
133
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<
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position
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xml:space
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">50</
note
>
<
head
xml:id
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"
style
="
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"
xml:space
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">De norma Pythagoricum inuentum ex orthogonij trigoni
<
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/>
deformatione. Cap. II.</
head
>
<
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<
s
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<
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style
="
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">ITem</
emph
>
Pythagoras normam ſine artificis fabricationibusinuentam oſtendit, & </
s
>
<
s
xml:id
="
echoid-s20118
"
xml:space
="
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">quàm ma-
<
lb
/>
gno labore fabri normam facientes uix ad uerum perducere poſſunt. </
s
>
<
s
xml:id
="
echoid-s20119
"
xml:space
="
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">id rationibus, & </
s
>
<
s
xml:id
="
echoid-s20120
"
xml:space
="
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">
<
lb
/>
methodis emendatum, ex eius præceptis explicatur. </
s
>
<
s
xml:id
="
echoid-s20121
"
xml:space
="
preserve
">Nanque ſi ſumantur regulæ tres, e
<
lb
/>
quibus una ſit pedes tres, altera pedes quatuor, tertia pedes quinque, eæq́; </
s
>
<
s
xml:id
="
echoid-s20122
"
xml:space
="
preserve
">regulæ inter
<
lb
/>
ſe compoſitæ tangat alia aliam ſuis cacuminibus extremis, ſchema habentes trigoni, deformabunt nor
<
lb
/>
mam emendatam. </
s
>
<
s
xml:id
="
echoid-s20123
"
xml:space
="
preserve
">Ad eas autem regularum ſingularum longitudines, ſi ſingula quadrata paribus
<
lb
/>
lateribus deſeribantur, quod erit pedum trium latus areæ, habebit pedes nouem, quod erit quatuor,
<
lb
/>
ſexdecim, quod quinque erit, uigintiquinque. </
s
>
<
s
xml:id
="
echoid-s20124
"
xml:space
="
preserve
">Ita quantum areæ pedum numerum duo quadrata, ex
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-514.01.300-06
"
xlink:href
="
note-514.01.300-06a
"
xml:space
="
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">60</
note
>
</
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</
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