Clavius, Christoph, Gnomonices libri octo, in quibus non solum horologiorum solariu[m], sed aliarum quo[quam] rerum, quae ex gnomonis umbra cognosci possunt, descriptiones geometricè demonstrantur

Table of contents

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[21.] SCHOLIVM.
Page: 41 (21)
[22.] THEOREMA 3. PROPOSITIO 4.
Page: 41 (21)
[23.] COROLLARIVM.
Page: 41 (21)
[24.] THEQREMA 4. PROPOSITIQ 5.
Page: 42 (22)
[25.] COROLLARIVM.
Page: 42 (22)
[26.] THEOREMA 5. PROPOSITIO 6.
Page: 43 (23)
[27.] SCHOLIVM.
Page: 44 (24)
[28.] COROLLARIVM.
Page: 44 (24)
[29.] THEOREMA 6. PROPOSITIO 7.
Page: 44 (24)
[30.] COROLLARIVM.
Page: 45 (25)
[31.] PROBLEMA 2. PROPOSITIO 8.
Page: 46 (26)
[32.] SCHOLIVM.
Page: 49 (29)
[33.] LEMMA.
Page: 49 (29)
[34.] LEMMA PRIMVM.
Page: 51 (31)
[35.] LEMMA II.
Page: 51 (31)
[36.] LEMMA PRIMVM.
Page: 53 (33)
[37.] LEMMA II.
Page: 53 (33)
[38.] THEOREMA 7. PROPOSITIO 9.
Page: 57 (37)
[39.] SCHOLIVM.
Page: 58 (38)
[40.] THEOREMA 8. PROPOSITIQ 10.
Page: 59 (39)
[41.] COROLLARIVM.
Page: 60 (40)
[42.] SCHOLIVM.
Page: 60 (40)
[43.] THEOREMA 9. PROPOSITIO 11.
Page: 62 (42)
[44.] SCHOLIVM.
Page: 63 (43)
[45.] COROLLARIVM PRIMVM.
Page: 63 (43)
[46.] COROLLARIVM II.
Page: 63 (43)
[47.] THEOREMA 10. PROPOSITIO 12.
Page: 63 (43)
[48.] COROLLARIVM.
Page: 64 (44)
[49.] THEOREMA 11. PROPOSITIO 13.
Page: 64 (44)
[50.] THEOREMA 12. PROPOSITIO 14.
Page: 65 (45)
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        <div xml:id="echoid-div29" type="section" level="1" n="14">
          <p style="it">
            <s xml:id="echoid-s626" xml:space="preserve">
              <pb o="8" file="0028" n="28" rhead="GNOMONICES"/>
            deſcripta ſint. </s>
            <s xml:id="echoid-s627" xml:space="preserve">Dionyſiou
              <unsure/>
            or{us} inuentor fuit, vt aiunt, coni, ſeu horologij figurę conicę. </s>
            <s xml:id="echoid-s628" xml:space="preserve">Atq; </s>
            <s xml:id="echoid-s629" xml:space="preserve">ita alij alias
              <lb/>
            form{as} horologiorũ excogitaſſe memorantur à Vitruuio. </s>
            <s xml:id="echoid-s630" xml:space="preserve">Horologiorũ autem vſum ſerius Romę cœpiſſe,
              <lb/>
            auctor eſt Plinius lib. </s>
            <s xml:id="echoid-s631" xml:space="preserve">7. </s>
            <s xml:id="echoid-s632" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s633" xml:space="preserve">60. </s>
            <s xml:id="echoid-s634" xml:space="preserve">Primum enim duodecim, inquit, tabulis ort{us} tantum, & </s>
            <s xml:id="echoid-s635" xml:space="preserve">occaſus nomi-
              <lb/>
            nantur, poſt aliquot annos adiectus eſt & </s>
            <s xml:id="echoid-s636" xml:space="preserve">Meridies, Accenſo conſulum id pronuntiante, vſq; </s>
            <s xml:id="echoid-s637" xml:space="preserve">ad primum
              <lb/>
            punicum bellum. </s>
            <s xml:id="echoid-s638" xml:space="preserve">Deinde ſolare horologium, imperfectum tamen, ſecundum rostra in columna poſitum eſſe
              <lb/>
            à M. </s>
            <s xml:id="echoid-s639" xml:space="preserve">Valerio Meſſala conſule, tradit M. </s>
            <s xml:id="echoid-s640" xml:space="preserve">Varro, Catina capta in Sicilia anno vrbis 477. </s>
            <s xml:id="echoid-s641" xml:space="preserve">quo quidem vſi
              <lb/>
            ſunt annis vndecentum, donec Q. </s>
            <s xml:id="echoid-s642" xml:space="preserve">Marti{us} Philipp{us}, qui cum L. </s>
            <s xml:id="echoid-s643" xml:space="preserve">Paulo fuit cenſor, diligenti{us} or dinatũ
              <lb/>
            iuxta poſuit, id{q́ue} mun{us} inter cenſoria opera gratiſſimè acceptum eſt. </s>
            <s xml:id="echoid-s644" xml:space="preserve">Scipio autem Naſica Collega Lęna-
              <lb/>
            tis prim{us} aqua diuiſit hor{as} ęquè noctium, ac dierum. </s>
            <s xml:id="echoid-s645" xml:space="preserve">Id{q́ue} horologium ſub tecto dicauit anno vrbis 595.
              <lb/>
            </s>
            <s xml:id="echoid-s646" xml:space="preserve">hęc ferè Plinius.</s>
            <s xml:id="echoid-s647" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s648" xml:space="preserve">SCRIPTOREM porrò qui de Gnomonica, ſeu horologiorum ratione egerit, non reperio antiquio-
              <lb/>
              <note position="left" xlink:label="note-0028-01" xlink:href="note-0028-01a" xml:space="preserve">Scriptores ho
                <lb/>
              rologiorum.</note>
              <note position="left" xlink:label="note-0028-02" xlink:href="note-0028-02a" xml:space="preserve">10</note>
            rem Vitruuio, qui libro 9. </s>
            <s xml:id="echoid-s649" xml:space="preserve">pauca quædam diſſerit de Analemmatis conſtructione, per quod qua ratione ho
              <lb/>
            rologia cõficiend
              <unsure/>
            a ſint, potius innuit, quàm docet. </s>
            <s xml:id="echoid-s650" xml:space="preserve">Ptolemęus autem libellum acutiſſimum edidit de Ana-
              <lb/>
            lemmate, in quem Federic{us} Commandinus doctiſſimos commentarios conſcripſit vna cum libro de horo-
              <lb/>
            logiorum deſcriptione, cuius omnes demonſtrationes ex Analemmate Ptolemęi petuntur, ex quo libro
              <lb/>
            Daniel Barbarus in commentarijs in lib. </s>
            <s xml:id="echoid-s651" xml:space="preserve">9. </s>
            <s xml:id="echoid-s652" xml:space="preserve">Vitruuij omnia decerpſit, quę de horologiorum deſcriptione
              <lb/>
            tradit. </s>
            <s xml:id="echoid-s653" xml:space="preserve">Analemma autem Ptolemęi vna cum libro Federici Commandini de horologiorum deſcriptione
              <lb/>
            longè clari{us}, hreui{us}{q́ue} proponemus, Deo iuuante, lib. </s>
            <s xml:id="echoid-s654" xml:space="preserve">6. </s>
            <s xml:id="echoid-s655" xml:space="preserve">huius operis. </s>
            <s xml:id="echoid-s656" xml:space="preserve">Albategnius quoq; </s>
            <s xml:id="echoid-s657" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s658" xml:space="preserve">56. </s>
            <s xml:id="echoid-s659" xml:space="preserve">in li-
              <lb/>
            bro de ſcientia stellarum breuiſſimè docet, qua ratione horologium horarum inęqualium ad quamcunq;
              <lb/>
            </s>
            <s xml:id="echoid-s660" xml:space="preserve">latitudinem poſſit conſtrui. </s>
            <s xml:id="echoid-s661" xml:space="preserve">Inter recentiores, qui hanc Matheſeos partem illustrarunt, numer ari poteſt
              <lb/>
            Petrus Noni{us} Luſitanus celebris Mathematicus, qui in libello de Erratis Orontij demonstrat, qua ra-
              <lb/>
              <note position="left" xlink:label="note-0028-03" xlink:href="note-0028-03a" xml:space="preserve">20</note>
            tione horizontalia, & </s>
            <s xml:id="echoid-s662" xml:space="preserve">Verticalia horologia tantum, alijs omiſſis, deſcribantur; </s>
            <s xml:id="echoid-s663" xml:space="preserve">Federic{us} Commandin{us},
              <lb/>
            qui, vt dixim{us}, commentarios in Analemma Ptolemęi, & </s>
            <s xml:id="echoid-s664" xml:space="preserve">libellum de horologiorum deſcriptione in lu-
              <lb/>
            cem edidit; </s>
            <s xml:id="echoid-s665" xml:space="preserve">Oronti{us} Finę{us}; </s>
            <s xml:id="echoid-s666" xml:space="preserve">Ioannes Conrad{us} Vlmer{us} German{us}; </s>
            <s xml:id="echoid-s667" xml:space="preserve">Ioannes Baptiſta Vimercatus ordi-
              <lb/>
            nis Carthuſianorum lingua Italica; </s>
            <s xml:id="echoid-s668" xml:space="preserve">Andreas Schonerus Norimbergenſis; </s>
            <s xml:id="echoid-s669" xml:space="preserve">Ioãnes Paduanius Veronenſis;
              <lb/>
            </s>
            <s xml:id="echoid-s670" xml:space="preserve">Petr{us} Roderic{us} Hiſpan{us} ſermone Hiſpanico; </s>
            <s xml:id="echoid-s671" xml:space="preserve">Franciſcus Maurolyc{us} Abb{as} Sicul{us}, qui tres ſubti-
              <lb/>
            liſſimos libros de lineis horarijs conſcripſit; </s>
            <s xml:id="echoid-s672" xml:space="preserve">Ioannes Baptiſta Benedict{us}, qui nouiſſimè librum compoſuit
              <lb/>
            de Gnomonum, vmbrarum{q́ue} ſolarium vſu, in quo plurima continentur ſcitu digniſſima.</s>
            <s xml:id="echoid-s673" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s674" xml:space="preserve">IGITVR vt & </s>
            <s xml:id="echoid-s675" xml:space="preserve">nos aliquam huic tam pręſtanti ſcientiæ Gnomonices lucem afferam{us}, exordiemur
              <lb/>
            à conſtructione Analemmatis, quod mirabile ſanè veterum inuentum eſt, & </s>
            <s xml:id="echoid-s676" xml:space="preserve">baſis, ac fundamentum om-
              <lb/>
            nium ferè, quę demonſtr aturi ſum{us} in hoc opere. </s>
            <s xml:id="echoid-s677" xml:space="preserve">Eſt autẽ Analemma figura quædam circularis circa cen-
              <lb/>
              <note position="left" xlink:label="note-0028-04" xlink:href="note-0028-04a" xml:space="preserve">Analemma
                <lb/>
              quì
                <unsure/>
              d ſit.</note>
              <note position="left" xlink:label="note-0028-05" xlink:href="note-0028-05a" xml:space="preserve">30</note>
            trum Meridiani, vel cuiusuis alteri{us} circuli maximi per polos mundi tranſeuntis, & </s>
            <s xml:id="echoid-s678" xml:space="preserve">in ei{us} plano deſcri
              <lb/>
            pta, communes ſectiones præcipuorum cir culorum ſphęrę (quales ſunt Aequator, eius{q́ue} paralleli, Eclipti
              <lb/>
            ca, Horizon, atq; </s>
            <s xml:id="echoid-s679" xml:space="preserve">Verticalis) ac Meridiani, vel illi{us} maximi circuli per mundi polos ducti, continens. </s>
            <s xml:id="echoid-s680" xml:space="preserve">Quę
              <lb/>
            quidem deſcriptio ex ſequenti prima propoſitione clariſſimè intelligetur. </s>
            <s xml:id="echoid-s681" xml:space="preserve">Dixerunt autem veteres huiuſ-
              <lb/>
            modi figuram Analemma, quaſi reſumptionem, quoniam antequam diametros aliorum cir culorum deſcri-
              <lb/>
            berent, deſignationes quaſdam vmbr arum ſu@ebant, & </s>
            <s xml:id="echoid-s682" xml:space="preserve">reſumebant, vt in cir culo Analemmatis diame-
              <lb/>
            tros aliorum cir culorum in proprio ſitu collocarent, vt ex ijs colligitur, quę Vitruui{us}, eiuſ{q́ue} interpres
              <lb/>
            Daniel Barbar{us} docent lib. </s>
            <s xml:id="echoid-s683" xml:space="preserve">9. </s>
            <s xml:id="echoid-s684" xml:space="preserve">Vnde factũ eſt, vt Vitruui{us} eo loco Analemma ita deſcriberet. </s>
            <s xml:id="echoid-s685" xml:space="preserve">Analem-
              <lb/>
              <note position="left" xlink:label="note-0028-06" xlink:href="note-0028-06a" xml:space="preserve">Analemma
                <lb/>
              quo modo de-
                <lb/>
              ſcribatur à Vi-
                <lb/>
              truuio.</note>
            ma eſt ratio conquiſita ſolis curſu, & </s>
            <s xml:id="echoid-s686" xml:space="preserve">vmbrę creſcentis à Brumę obſeruatione inuenta, è qua per rationes
              <lb/>
            architectonic{as}, cir cini{q́ue} deſcriptiones eſt inuentus cęli effectus in mundo. </s>
            <s xml:id="echoid-s687" xml:space="preserve">Quia videlicet à ſolis, & </s>
            <s xml:id="echoid-s688" xml:space="preserve">vm-
              <lb/>
              <note position="left" xlink:label="note-0028-07" xlink:href="note-0028-07a" xml:space="preserve">40</note>
            brę à Gnomone proiectę curſu incipientes à bruma, hoc eſt, à ſolſtitio hyberno, antiqui, vt ex Vitruuio col
              <lb/>
            ligitur, in Analemmate not ahant diametros par allelorum ſolis ſecundum propri{as} diſtanti{as} inter ſeſe,
              <lb/>
            ex quo deinde Analemmate inuentus eſt effect{us} cœli in mundo, nemperatio ſolarium horologiorũ ad quã-
              <lb/>
            cunque poli altitudinem, quantitates dierum & </s>
            <s xml:id="echoid-s689" xml:space="preserve">noctium, ort{us} & </s>
            <s xml:id="echoid-s690" xml:space="preserve">occaſus ſolis, & </s>
            <s xml:id="echoid-s691" xml:space="preserve">alia penè innumer abi-
              <lb/>
            lia, quę omnia recenſere non eſt huius loci. </s>
            <s xml:id="echoid-s692" xml:space="preserve">Sed noſtra deſcriptio magis accommodata eſt ad vſum, quem
              <lb/>
            Analemma nobis pręſtat, vt ex ijs, quę ſequuntur, fiet perſpicuum. </s>
            <s xml:id="echoid-s693" xml:space="preserve">Quare ad Analemma deſcribendum
              <lb/>
            & </s>
            <s xml:id="echoid-s694" xml:space="preserve">ad alia theoremata, problemata{q́ue} explicanda iam aggrediamur; </s>
            <s xml:id="echoid-s695" xml:space="preserve">Sitamen prius conſtructionem qua-
              <lb/>
            drantis cuiuſdam pręmittamus, qui mirificum vſum non ſolum in horologiorum deſcriptione, verum etiã
              <lb/>
            in aſtrolabij, aliorum{q́ue} inſtrumentorum tum ad Aſtronomiam, tum ad Geometriam ſpectantium, conſtru-
              <lb/>
            ctione nobis prębet, & </s>
            <s xml:id="echoid-s696" xml:space="preserve">opus ipſum quodam modo facilius reddit, & </s>
            <s xml:id="echoid-s697" xml:space="preserve">breui{us}. </s>
            <s xml:id="echoid-s698" xml:space="preserve">Id quod experientia ipſa
              <lb/>
              <note position="left" xlink:label="note-0028-08" xlink:href="note-0028-08a" xml:space="preserve">50</note>
            quilibet vel facile diſcet.</s>
            <s xml:id="echoid-s699" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s700" xml:space="preserve">CONTINEANT igitur duę rectę AB, AC, intabella quapiam ęnea, vel lignea ductę angulũ
              <lb/>
              <note position="left" xlink:label="note-0028-09" xlink:href="note-0028-09a" xml:space="preserve">Conſtructio
                <lb/>
              quadrantis plu-
                <lb/>
              rimas vtilitates
                <lb/>
              habentis in ho-
                <lb/>
              rologiorum de-
                <lb/>
              ſeriptionibus,
                <lb/>
              & in alijs inſtru
                <lb/>
              mentis Mathe-
                <lb/>
              maticis conſtru
                <lb/>
              endis.</note>
            rectum in A, puncto, ex quo, vt centro, quadrans circuli deſcribatur BC, atque hic in gradus 90. </s>
            <s xml:id="echoid-s701" xml:space="preserve">diuida-
              <lb/>
            tur, initio facto à puncto B. </s>
            <s xml:id="echoid-s702" xml:space="preserve">Deinde ex centro A, ad ſingulos gradus rectę lineę emittantur, ac tandem
              <lb/>
            ex A, quotuis alij quadrantes minores deſcribantur inter rect{as} AB, AC, comprehenſi. </s>
            <s xml:id="echoid-s703" xml:space="preserve">Deſcriptus igi-
              <lb/>
            tur erit hac ratione quadrans, qui quant{as} in rebus mathematicis habeat vtilitates, vix dici poteſt. </s>
            <s xml:id="echoid-s704" xml:space="preserve">Nã
              <lb/>
            dicto citi{us} ea omnia nobis pręſtat, quæ per multas alioquin cir culorum diuiſiones non ſine magno labore,
              <lb/>
            atque molestia nobis eſſent inquirenda. </s>
            <s xml:id="echoid-s705" xml:space="preserve">Cui{us} rei vnum, aut alterum exemplum in medium hic adducam.
              <lb/>
            </s>
            <s xml:id="echoid-s706" xml:space="preserve">Nam vberrimi ei{us} fructus ex ijs, quę in toto hoc opere dicturi ſumus, paſſim colligentur. </s>
            <s xml:id="echoid-s707" xml:space="preserve">Sit exempligra
              <lb/>
              <note position="left" xlink:label="note-0028-10" xlink:href="note-0028-10a" xml:space="preserve">Vſus deſcri-
                <lb/>
              pti quadrantis.</note>
            tia in figura quapiam, in qua circulus H I, ex centro G, & </s>
            <s xml:id="echoid-s708" xml:space="preserve">ad interuallum ſemidiametri G H, </s>
          </p>
        </div>
      </text>
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