Vitruvius, De architectura libri decem, 1567

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          <div xml:id="echoid-div769" type="section" level="2" n="142">
            <p style="it">
              <s xml:id="echoid-s23027" xml:space="preserve">
                <pb o="303" file="514.01.335" n="335" rhead="NONVS."/>
              quidem ex duabus ſuper ficiebus oppoſitis per coni uerticem conficitur, & </s>
              <s xml:id="echoid-s23028" xml:space="preserve">utraque in infinitum producitur, ex
                <lb/>
              unius lineæ in utramque partem ductæ deſcriptione, quem admodum in diagrammate uidetur, ubi prima ſu-
                <lb/>
                <figure xlink:label="fig-514.01.335-01" xlink:href="fig-514.01.335-01a" number="134">
                  <variables xml:id="echoid-variables91" xml:space="preserve">a b c d f</variables>
                </figure>
              perficies a b c d. </s>
              <s xml:id="echoid-s23029" xml:space="preserve">oppoſita per uerticem e
                <lb/>
              f g. </s>
              <s xml:id="echoid-s23030" xml:space="preserve">lineæ in utramque partem ductæ c e. </s>
              <s xml:id="echoid-s23031" xml:space="preserve">& </s>
              <s xml:id="echoid-s23032" xml:space="preserve">
                <lb/>
              f d. </s>
              <s xml:id="echoid-s23033" xml:space="preserve">quas in infinitum abire imaginamur.</s>
              <s xml:id="echoid-s23034" xml:space="preserve">inte-
                <lb/>
              gram ergo hanc figurationem conicam ſuperfi-
                <lb/>
              ciem appellant. </s>
              <s xml:id="echoid-s23035" xml:space="preserve">in cono autem a e. </s>
              <s xml:id="echoid-s23036" xml:space="preserve">axis est.
                <lb/>
              </s>
              <s xml:id="echoid-s23037" xml:space="preserve">a. </s>
              <s xml:id="echoid-s23038" xml:space="preserve">uertex. </s>
              <s xml:id="echoid-s23039" xml:space="preserve">b d c. </s>
              <s xml:id="echoid-s23040" xml:space="preserve">baſis. </s>
              <s xml:id="echoid-s23041" xml:space="preserve">hæc imprimis ſunt
                <lb/>
              memoriæ commendanda, quoniam ad analem-
                <lb/>
                <note position="left" xlink:label="note-514.01.335-01" xlink:href="note-514.01.335-01a" xml:space="preserve">10</note>
              matum deſcriptionem maxime conferunt. </s>
              <s xml:id="echoid-s23042" xml:space="preserve">Co-
                <lb/>
              nica igitur ſuperficies, ſectiones plures habere
                <lb/>
              poteſt, quarum ratio nobis explicanda est. </s>
              <s xml:id="echoid-s23043" xml:space="preserve">pri-
                <lb/>
              mum ergo ſecari poteſt a uertice per axem, de=
                <lb/>
              inde modis alijs. </s>
              <s xml:id="echoid-s23044" xml:space="preserve">ſi a uertice per axem medium
                <lb/>
              ſecetur, & </s>
              <s xml:id="echoid-s23045" xml:space="preserve">ſectione uidebitur triangulus recti-
                <lb/>
              lineus. </s>
              <s xml:id="echoid-s23046" xml:space="preserve">ſi uero modis alijs diuidatur, aut tranſ-
                <lb/>
              uerſo ſegmento baſi parallelo, ſecabitur, aut
                <lb/>
              alio modo, ſi parallelo baſi ſegmento diuidetur,
                <lb/>
              circulus apparebit. </s>
              <s xml:id="echoid-s23047" xml:space="preserve">Quod ſi ſegmentum neque
                <lb/>
              per uerticem neque tranſuerſe fiet: </s>
              <s xml:id="echoid-s23048" xml:space="preserve">tum ſeg-
                <lb/>
                <note position="left" xlink:label="note-514.01.335-02" xlink:href="note-514.01.335-02a" xml:space="preserve">20</note>
              mentum lineam quandam inflexam oſtendet,
                <lb/>
              quæ a mathematicis ſectio conica nominatur.
                <lb/>
              </s>
              <s xml:id="echoid-s23049" xml:space="preserve">hæc ut modos, ita nomina quoque diuerſa ſor-
                <lb/>
              titur. </s>
              <s xml:id="echoid-s23050" xml:space="preserve">nam conus præter prædictas ſectiones potest ſegmento aut axi, aut lateri parallelo ſecari, ita ut aliquid
                <lb/>
              de baſi ſecetur. </s>
              <s xml:id="echoid-s23051" xml:space="preserve">Ex priori ſegmento linea fit, quæ hyperbole nominatur, ex posteriori uero parabole apparet: </s>
              <s xml:id="echoid-s23052" xml:space="preserve">
                <lb/>
              est & </s>
              <s xml:id="echoid-s23053" xml:space="preserve">ſegmenti aliud genus, quod tranſuerſa ſectione conum abſcindit, nihil de baſi tollit, & </s>
              <s xml:id="echoid-s23054" xml:space="preserve">baſi non eſt paral
                <lb/>
              lelum. </s>
              <s xml:id="echoid-s23055" xml:space="preserve">Ellipſim uocant eam ſectionem tanquam deficientem, ſicuti hyperbolem tanquam exuperantem, & </s>
              <s xml:id="echoid-s23056" xml:space="preserve">pa-
                <lb/>
              rabolem tanquam æquabilem ſectionem dicant. </s>
              <s xml:id="echoid-s23057" xml:space="preserve">Eſto ergo conus a b c d e. </s>
              <s xml:id="echoid-s23058" xml:space="preserve">ſegmentum lateri parallelum
                <lb/>
              f g h. </s>
              <s xml:id="echoid-s23059" xml:space="preserve">cuius ichnographia circulus b c d e. </s>
              <s xml:id="echoid-s23060" xml:space="preserve">in centro a. </s>
              <s xml:id="echoid-s23061" xml:space="preserve">ſectio apert a quæ hiperbole dicitur g f h. </s>
              <s xml:id="echoid-s23062" xml:space="preserve">
                <lb/>
                <note position="left" xlink:label="note-514.01.335-03" xlink:href="note-514.01.335-03a" xml:space="preserve">30</note>
              Quæres quomodo fiant, ita ex Durero declaratur. </s>
              <s xml:id="echoid-s23063" xml:space="preserve">Eſto ſegmentum f g h. </s>
              <s xml:id="echoid-s23064" xml:space="preserve">in duodenas partes diſtributum
                <lb/>
              ab f. </s>
              <s xml:id="echoid-s23065" xml:space="preserve">ad h. </s>
              <s xml:id="echoid-s23066" xml:space="preserve">partibus numeri apponantur. </s>
              <s xml:id="echoid-s23067" xml:space="preserve">1. </s>
              <s xml:id="echoid-s23068" xml:space="preserve">2. </s>
              <s xml:id="echoid-s23069" xml:space="preserve">3. </s>
              <s xml:id="echoid-s23070" xml:space="preserve">4. </s>
              <s xml:id="echoid-s23071" xml:space="preserve">uſque 11. </s>
              <s xml:id="echoid-s23072" xml:space="preserve">per partes autem illas ducantur li-
                <lb/>
              neæ tranſuerſæ baſi parallelæ, & </s>
              <s xml:id="echoid-s23073" xml:space="preserve">ab eiſdem partibus ubi numeri ſunt, ad rectos angulos cadant li-
                <lb/>
              neæ in baſim, ſic conus, cum ſuis partitionibus diſtinguetur, quæ omnes ad ichnographiam coni pertinebunt.
                <lb/>
              </s>
              <s xml:id="echoid-s23074" xml:space="preserve">hoc modo. </s>
              <s xml:id="echoid-s23075" xml:space="preserve">Esto circulus cuius dimetiens ſit linea coni b c d e. </s>
              <s xml:id="echoid-s23076" xml:space="preserve">ſit uero circulus b c d e. </s>
              <s xml:id="echoid-s23077" xml:space="preserve">ſub cono col-
                <lb/>
              locatus, cuius centrum ſit a. </s>
              <s xml:id="echoid-s23078" xml:space="preserve">in quod axis a cono cadat uſque ad e. </s>
              <s xml:id="echoid-s23079" xml:space="preserve">demum in circulum illum cadant om-
                <lb/>
              nes illæ lineæ a cono axi parallelæ, quæ lineæ in ichnographia ſuis numeris notentur, qui reſpondeant literis,
                <lb/>
              & </s>
              <s xml:id="echoid-s23080" xml:space="preserve">numeris in cono ſignatis g. </s>
              <s xml:id="echoid-s23081" xml:space="preserve">b. </s>
              <s xml:id="echoid-s23082" xml:space="preserve">f. </s>
              <s xml:id="echoid-s23083" xml:space="preserve">1. </s>
              <s xml:id="echoid-s23084" xml:space="preserve">2. </s>
              <s xml:id="echoid-s23085" xml:space="preserve">3. </s>
              <s xml:id="echoid-s23086" xml:space="preserve">4. </s>
              <s xml:id="echoid-s23087" xml:space="preserve">uſque ad 11. </s>
              <s xml:id="echoid-s23088" xml:space="preserve">has lineas ratione quadam ſecare opor-
                <lb/>
              tet, ut parabole efficiatur. </s>
              <s xml:id="echoid-s23089" xml:space="preserve">Sume a cono lineæ 11. </s>
              <s xml:id="echoid-s23090" xml:space="preserve">notatæ longitudinem. </s>
              <s xml:id="echoid-s23091" xml:space="preserve">lineæ inquam baſi coni paral-
                <lb/>
              lelæ: </s>
              <s xml:id="echoid-s23092" xml:space="preserve">& </s>
              <s xml:id="echoid-s23093" xml:space="preserve">in centro a uestigij ponatur circini pes unus,& </s>
              <s xml:id="echoid-s23094" xml:space="preserve">tantum circinationis duces, ut lineam in ueſtigio per
                <lb/>
              11. </s>
              <s xml:id="echoid-s23095" xml:space="preserve">notatam ſeces. </s>
              <s xml:id="echoid-s23096" xml:space="preserve">idem facies in lineis alijs a cono ad ueſtigium transferendis: </s>
              <s xml:id="echoid-s23097" xml:space="preserve">& </s>
              <s xml:id="echoid-s23098" xml:space="preserve">hoc modo parabole ue-
                <lb/>
                <note position="left" xlink:label="note-514.01.335-04" xlink:href="note-514.01.335-04a" xml:space="preserve">40</note>
              stigium deſcriptum erit. </s>
              <s xml:id="echoid-s23099" xml:space="preserve">Eueſtigio uero lineam eam duces hac ratione. </s>
              <s xml:id="echoid-s23100" xml:space="preserve">ſume a ues̃tigio lineæ g h. </s>
              <s xml:id="echoid-s23101" xml:space="preserve">longitu-
                <lb/>
              dinem, ex ea lineam ducas in quam mediam ad rectos angulos linea ſectionis f g. </s>
              <s xml:id="echoid-s23102" xml:space="preserve">in cono æqualis cadat, cu-
                <lb/>
              ius uertex ſit f. </s>
              <s xml:id="echoid-s23103" xml:space="preserve">diuidaturq; </s>
              <s xml:id="echoid-s23104" xml:space="preserve">ſecundum diuioſiones lineæ f g. </s>
              <s xml:id="echoid-s23105" xml:space="preserve">in cono diuiſæ, & </s>
              <s xml:id="echoid-s23106" xml:space="preserve">reſpondentibus numeris
                <lb/>
              ſignetur.</s>
              <s xml:id="echoid-s23107" xml:space="preserve">per puncta diuiſionis ducantur lineæ parallelæ lineæ g h. </s>
              <s xml:id="echoid-s23108" xml:space="preserve">ad eas lineas e ueſtigio transferes longitu-
                <lb/>
              dines linearum proportione reſpondentium, uerbi gratia: </s>
              <s xml:id="echoid-s23109" xml:space="preserve">ex linea ubi 11. </s>
              <s xml:id="echoid-s23110" xml:space="preserve">nota est in ueſtigio, transfertur
                <lb/>
              ad parabolem longitudo illa in lineam notatam ſimili nota 11. </s>
              <s xml:id="echoid-s23111" xml:space="preserve">ſic de reliquis. </s>
              <s xml:id="echoid-s23112" xml:space="preserve">inde uero extrema omnium
                <lb/>
              linearum, una linea conti nenti annectes, & </s>
              <s xml:id="echoid-s23113" xml:space="preserve">parabolem uidebis. </s>
              <s xml:id="echoid-s23114" xml:space="preserve">Ex hac ratione, & </s>
              <s xml:id="echoid-s23115" xml:space="preserve">ex diagrammate aliarum
                <lb/>
              ſectionum addiſces quomodo ducendæ ſint hyperbole, & </s>
              <s xml:id="echoid-s23116" xml:space="preserve">ellipſis. </s>
              <s xml:id="echoid-s23117" xml:space="preserve">Cæterum hæc dicta ſunt eo fine, ut ſcias
                <lb/>
              Solis effectus in mundo circa gnomonem. </s>
              <s xml:id="echoid-s23118" xml:space="preserve">Dico igitur, Solem quotidiana uerſatione radios in gnomonem im-
                <lb/>
                <note position="left" xlink:label="note-514.01.335-05" xlink:href="note-514.01.335-05a" xml:space="preserve">50</note>
              mittere: </s>
              <s xml:id="echoid-s23119" xml:space="preserve">ambitum Solis baſim coni: </s>
              <s xml:id="echoid-s23120" xml:space="preserve">gnomonis apicem coni μerticem imaginemur eſſe, radium uero a Sole e-
                <lb/>
              miſſum lineam dicemus illam, quæ circum circinationem mota conum deſignet. </s>
              <s xml:id="echoid-s23121" xml:space="preserve">Quod ſi in oppoſitam partem
                <lb/>
              proiectum radium intelligamus modo per uerticem coni uerſetur, conum eum facere dicemus alterum, ita
                <lb/>
              ut ſuperficiem conicam perfectam reddat; </s>
              <s xml:id="echoid-s23122" xml:space="preserve">nam ſuperficies una ea est a circulo Solis ad apicem gnomonis, al-
                <lb/>
              tera uero oppoſita ab apice gnomonis deorſum uerſus, quæ in infinitum abiret, niſi planum aliquod illi obijce-
                <lb/>
              retur. </s>
              <s xml:id="echoid-s23123" xml:space="preserve">Quoniam uero planum illud multis modis illi obijcitur, & </s>
              <s xml:id="echoid-s23124" xml:space="preserve">radios ſecat inferioris ſuperficiei, ideo pro-
                <lb/>
              prietates earum ſectionum conſider andæ ſunt,quoniam diuerſa faciunt linearum genera. </s>
              <s xml:id="echoid-s23125" xml:space="preserve">Planum autem uoco
                <lb/>
              tabulam, ſeu parietem, in quo deſcribuntur horologia. </s>
              <s xml:id="echoid-s23126" xml:space="preserve">Quod quidem planum interim finitori æque diſtat, in-
                <lb/>
              terim in finitorem ad rectos cadit angulos, cum in erectis parietibus deſcribuntur horaria, interim inclinatũ
                <lb/>
              eſt, tanquam domorum tecta, unde cum multis modis conicam ſuperficiem radijs & </s>
              <s xml:id="echoid-s23127" xml:space="preserve">gnom one factum ſecare
                <lb/>
              ſoleat, accidit ut umbra a gnomonis uertice in obiectum planum proiecta, faciat aliàs rectam, aliàs eircu-
                <lb/>
                <note position="left" xlink:label="note-514.01.335-06" xlink:href="note-514.01.335-06a" xml:space="preserve">60</note>
              </s>
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