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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">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
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echoid-s20050
"
xml:space
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">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
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echoid-s20053
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xml:space
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">cedant Pithij, nec glorietur Thebas. </
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<
s
xml:id
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echoid-s20054
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xml:space
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">cedant Nemei, nec glorietur
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Archintorus. </
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<
s
xml:id
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echoid-s20055
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xml:space
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">cedant Iſthmij, nec glorietur Palamon, nam Minerua omnes illos deos hæroesq́;</
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>
<
s
xml:id
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"
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
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xml:space
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">Sed nos ad inuenta, & </
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>
<
s
xml:id
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xml:space
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">rationes præclariſſimorum hominum eorum, qui bene uiuendi inſtituta, & </
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<
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echoid-s20059
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<
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doctrinarum præcepta posteris reliquere; </
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<
s
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xml:space
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">nam ſi in ſaltu, & </
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>
<
s
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xml:space
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">curſu agilitas requiritur, quid agilius, quid ue-
<
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<
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position
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note-514.01.300-01
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note-514.01.300-01a
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xml:space
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">10</
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locius animo erudito, & </
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<
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">in rerum contemplationeuerſato? </
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<
s
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echoid-s20063
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xml:space
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">qui terrena, & </
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<
s
xml:id
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xml:space
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">cœlestia quaſi uolando percurrat ?
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</
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<
s
xml:id
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echoid-s20065
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xml:space
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">Si in diſco, & </
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>
<
s
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">iaculo quis glorietur, quid aget mens eius, qui humana omnia impedimenta proiecerit, & </
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<
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uerterit ? </
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<
s
xml:id
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">Si lucta robur, & </
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<
s
xml:id
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echoid-s20069
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xml:space
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">uires quærit, quid ſapiens faciet, qui cum fortuna continenter luctando, uires
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eius infringit, & </
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>
<
s
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xml:space
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">uirtute ictus repellit, & </
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>
<
s
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xml:space
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">dexteritate inſultus deijcit, ac proſternit ? </
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>
<
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, & </
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>
<
s
xml:id
="
echoid-s20073
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xml:space
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">doctorum hominum, non publicum alimentum, non eorum
<
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aduentu murorum proiectio. </
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>
<
s
xml:id
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echoid-s20074
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xml:space
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">nullum enim par præmium uirtutis habetur in terris: </
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<
s
xml:id
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echoid-s20075
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xml:space
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">Sed cœlum, ſplendor, glo-
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ria, felicitas eos perpetuo manet.</
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<
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type
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<
head
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xml:space
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">Platonis inuentumde agro metiendo. Cap. I.</
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<
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>
, aut ager patibus lateribus, ſi erit quadratus, eumq́; </
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<
s
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">oportuetit iterum ex paribus
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lateribus duplicare, quia id genere numeri, ac multiplicationibus non inuenitur, ex de-
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ſcriptionibus linearum emendatis reperitur. </
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>
<
s
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xml:space
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">Eſt autem eius rei hæc demonſtratio.
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</
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<
s
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">Quadratus locus, qui erit longus, & </
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">latus pedes denos, efficit areæ pedes centum. </
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<
s
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">Si
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ergo opus fuerit eum duplicare, & </
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<
s
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xml:space
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">aream pedum ducentorum item ex paribus lateribus facere, quæ-
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rendum erit quàm magnum latus eius quadratifiat, ut ex eo ducenti pedes duplicationibus areæ re-
<
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ſpondeant. </
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>
<
s
xml:id
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xml:space
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">Idautem numero nemo poteſt inuenire; </
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<
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xml:space
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">nanque ſi 14. </
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<
s
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xml:space
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">conſtituentur, erunt multipli-
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catipedes 196. </
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<
s
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">ſi quindecim, pedes 125. </
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<
s
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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
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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-
<
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<
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note-514.01.300-03a
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">30</
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gonalis longitudinem, locus quadratus paribus lateribus deſcribatur. </
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<
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xml:space
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">Ita quam magna duo trigona,
<
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in minore quadrato quinquagenum pedum linea diagonica fuerint deſignata, eadem magnitudine, & </
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<
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<
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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.</
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</
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<
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<
s
xml:id
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xml:space
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">Quadratum menſuratur duorum laterum inter ſe multiplicatione facta. </
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<
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xml:space
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">Duplicatur quadratum ſumpta
<
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eius diagonia linea pro latere quadrati, quod duplex faciendum erit. </
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<
s
xml:id
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echoid-s20095
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xml:space
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">Diagonia hoc modo inuenitur, duo
<
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latera quadrati per ſe ſingula in ſe ipſa uertendo multiplica, ſummam collige ipſius multiplicationis, & </
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>
<
s
xml:id
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xml:space
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">eius
<
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ſummæ quadratam radicem quærito, tanta erit diagonia. </
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<
s
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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. </
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<
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xml:space
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">& </
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<
s
xml:id
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xml:space
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">iterum alterius lateris quinque in ſe du-
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cito reddentur 25. </
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<
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">hæc collecta cum prioribus 25. </
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<
s
xml:id
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echoid-s20101
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xml:space
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">ſummam efficient quinquaginta, quorum quadratara-
<
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<
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xlink:label
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note-514.01.300-04
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note-514.01.300-04a
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dix est ped. </
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<
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<
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xml:space
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">& </
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<
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xml:space
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">unius quartæ, eadem ratio in alijs rectangulis quadratis inuenitur, ut in oblongo quadrato
<
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e, f, g, h, latus, e, g, pedum octo, ducti in ſe efficiunt 64. </
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<
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">latus e, f, pedes ſex. </
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<
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">hi @ducti in ſe red-
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dunt 36. </
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<
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">qui cum 64. </
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<
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">collecti efficiunt centum, quorum radix quadrata ſunt decem, tanta igitur eſt dia-
<
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gonios, & </
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<
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xml:id
="
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">duplicis quadrati latus. </
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<
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">Exemplum ſchematis Vitr. </
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<
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">facile eſt. </
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<
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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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<
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xml:id
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">quod numeri ge-
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nerenullo efficitur, id grammicis rationibus abſoluitur. </
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<
s
xml:id
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xml:space
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">Vtiliſſima uero, & </
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<
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">huius reiratio in plurimis obſer-
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uationibus quotidiani uſus, ut experientibus erit manifeſtum.</
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<
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</
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">50</
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<
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xml:space
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">De norma Pythagoricum inuentum ex orthogonij trigoni
<
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deformatione. Cap. II.</
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<
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<
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Pythagoras normam ſine artificis fabricationibusinuentam oſtendit, & </
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<
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<
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gno labore fabri normam facientes uix ad uerum perducere poſſunt. </
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>
<
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xml:id
="
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xml:space
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">id rationibus, & </
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>
<
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<
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methodis emendatum, ex eius præceptis explicatur. </
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>
<
s
xml:id
="
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xml:space
="
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">Nanque ſi ſumantur regulæ tres, e
<
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quibus una ſit pedes tres, altera pedes quatuor, tertia pedes quinque, eæq́; </
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>
<
s
xml:id
="
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xml:space
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">regulæ inter
<
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ſe compoſitæ tangat alia aliam ſuis cacuminibus extremis, ſchema habentes trigoni, deformabunt nor
<
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mam emendatam. </
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>
<
s
xml:id
="
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xml:space
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">Ad eas autem regularum ſingularum longitudines, ſi ſingula quadrata paribus
<
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lateribus deſeribantur, quod erit pedum trium latus areæ, habebit pedes nouem, quod erit quatuor,
<
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ſexdecim, quod quinque erit, uigintiquinque. </
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>
<
s
xml:id
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xml:space
="
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">Ita quantum areæ pedum numerum duo quadrata, ex
<
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<
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position
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xlink:label
="
note-514.01.300-06
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xlink:href
="
note-514.01.300-06a
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">60</
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