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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          <head xml:id="echoid-head13" xml:space="preserve">DE HOROLOGIIS IN VNIVERSVM,
            <lb/>
          eorumque neceſſitate, atque inuentione.</head>
          <p style="it">
            <s xml:id="echoid-s175" xml:space="preserve">HOROLOGIVM inſtrumentum eſſe, quo horæ deſignantur, deprehendun-
              <lb/>
              <note position="left" xlink:label="note-0022-01" xlink:href="note-0022-01a" xml:space="preserve">Horologium
                <lb/>
              quid.</note>
            turve
              <unsure/>
            , vocabulum ipſum indicat. </s>
            <s xml:id="echoid-s176" xml:space="preserve">Significat enim horologium, quaſi horarum ra
              <lb/>
            tionem, ita vt quicquid quodammodo horas indicat, horologium dici poſſit. </s>
            <s xml:id="echoid-s177" xml:space="preserve">Eſt
              <lb/>
              <note position="left" xlink:label="note-0022-02" xlink:href="note-0022-02a" xml:space="preserve">Hora quid.</note>
            autem hora vnum ex illis ſpatijs æqualibus, in quæ dies quælibet diuidi conſue-
              <lb/>
            uit. </s>
            <s xml:id="echoid-s178" xml:space="preserve">Quamuis enim apud veteres quatuor anni tempora, Ver, Æstas, Autum-
              <lb/>
              <note position="left" xlink:label="note-0022-03" xlink:href="note-0022-03a" xml:space="preserve">Vnde dict@ ſint
                <lb/>
              horæ.</note>
            nus, & </s>
            <s xml:id="echoid-s179" xml:space="preserve">Hyems, horæ dictæ ſint, {ἐπὸ} τοῦ ὁρίζ{ει}ν, vt Platoni placet in Cratylo, ꝙ
              <lb/>
              <note position="left" xlink:label="note-0022-04" xlink:href="note-0022-04a" xml:space="preserve">10</note>
            illas anni partes terminẽt, atq; </s>
            <s xml:id="echoid-s180" xml:space="preserve">definiant; </s>
            <s xml:id="echoid-s181" xml:space="preserve">hodie tamen æqualia illa diei ſpatia ho
              <lb/>
            ras nũcupamus, eo ꝙ, vt Macrobio placet lib. </s>
            <s xml:id="echoid-s182" xml:space="preserve">1. </s>
            <s xml:id="echoid-s183" xml:space="preserve">Saturnaliorũ, e{as} ſol, qui apud
              <lb/>
            Aegyptios Horus (ita enim Apollinẽ, qui idem eſt, qui ſol, appellabãt.) </s>
            <s xml:id="echoid-s184" xml:space="preserve">vocaba-
              <lb/>
            tur, ſuo curſu, motu{q́ue} efficiat. </s>
            <s xml:id="echoid-s185" xml:space="preserve">Alij tamen malunt, horas dici à nomine græco @@os, quod terminum, ſeu finẽ
              <lb/>
            ſignificat, propterea quod ſpatiũ illud continuũ temporis horis tanquam finibus diſtinguimus, ac termina-
              <lb/>
            mus. </s>
            <s xml:id="echoid-s186" xml:space="preserve">Deniq; </s>
            <s xml:id="echoid-s187" xml:space="preserve">horarum not atione inueſtig anda etiã ad ſordes ventum eſt, Non enim deſunt, qui arbitrẽtur,
              <lb/>
            æquales illas diei particul{as} hor{as} eſſe appellat{as} à verbo græco @pos, quod vrinã ſignificat. </s>
            <s xml:id="echoid-s188" xml:space="preserve">Aiunt enim
              <lb/>
            Hermetẽ Triſmegiſtum hor{as} primum obſeruaſſe, hoc eſt, diei ſpatia æqualia, ex vrina ſacri cuiuſdam ani-
              <lb/>
            malis apud Aegyptios, quod Serapi, id eſt, ſolierat dicatũ. </s>
            <s xml:id="echoid-s189" xml:space="preserve">Nam cum animaduertiſſet illud animal (rem
              <lb/>
            ſanè ridiculã, & </s>
            <s xml:id="echoid-s190" xml:space="preserve">AEgyptijs magis, quàm Triſmegiſto dignam) duodecies in die, toties{q́ue} in nocte tum lon-
              <lb/>
              <note position="left" xlink:label="note-0022-05" xlink:href="note-0022-05a" xml:space="preserve">20</note>
            ga, tum breui, vrinam emittere, æqualibus ſemper interuallis, conſent ancum eſſe rationi put auit, diem no-
              <lb/>
            ctem{q́ue} in totidem æqualia ſpatia diſtingui, quæ horæ ab vrina illi{us} animalis nuncuparentur. </s>
            <s xml:id="echoid-s191" xml:space="preserve">Hinc for-
              <lb/>
            taſſis factum eſt, vt tota ferme antiquit{as} duodecim horis diem quemcunque, noctem{q́ue} diuiſerit. </s>
            <s xml:id="echoid-s192" xml:space="preserve">Qua de
              <lb/>
            re paulo poſt plura dicem{us}.</s>
            <s xml:id="echoid-s193" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Neceſſitas ho-
            <lb/>
          rologiorum.</note>
          <p style="it">
            <s xml:id="echoid-s194" xml:space="preserve">DE neceſſitate vero horologiorum non eſt, quod multa verba faciam. </s>
            <s xml:id="echoid-s195" xml:space="preserve">Neminem ſiquidem latere arbi-
              <lb/>
            tror, quam miſerum, & </s>
            <s xml:id="echoid-s196" xml:space="preserve">infelix foret genus humanum, ſi hor arum diſtinctionem nullam haberet. </s>
            <s xml:id="echoid-s197" xml:space="preserve">Videm{us}
              <lb/>
            enim plerunq; </s>
            <s xml:id="echoid-s198" xml:space="preserve">eos, (quod & </s>
            <s xml:id="echoid-s199" xml:space="preserve">in ſeipſo quiuis experitur) qui quota ſit hora neſciunt, ſimiliter vt eos, qui
              <lb/>
            qua in regione verſentur, ignorant, quaſi ſtupore quodam animi affectos eſſe, & </s>
            <s xml:id="echoid-s200" xml:space="preserve">meo quidem iudicio non
              <lb/>
            immerito. </s>
            <s xml:id="echoid-s201" xml:space="preserve">Nam horarum diſcrimine ſinguli ſuos labores, ſua{q́ue} otia metiuntur, & </s>
            <s xml:id="echoid-s202" xml:space="preserve">certa ſibi tempora
              <lb/>
            in ſuis occupationibus omnibus præfiniunt. </s>
            <s xml:id="echoid-s203" xml:space="preserve">Immo vero cum vita hominum magna ex parte cõmertijs con-
              <lb/>
              <note position="left" xlink:label="note-0022-07" xlink:href="note-0022-07a" xml:space="preserve">30</note>
            ſumatur fere, at q; </s>
            <s xml:id="echoid-s204" xml:space="preserve">conuentibus, ægre profecto carere poſſemus vſu horologiorum, quandoquidem ipſorum
              <lb/>
            beneficio cert{as} nobis horas, certa{q́ue} temporum ſpatia præſtituim{us}, quibus ad res nostras per agend{as}
              <lb/>
            commodè, ſine vlla rei familiaris, aut aliarum rerum iactura, conuenire poſſimus. </s>
            <s xml:id="echoid-s205" xml:space="preserve">Teſtantur hoc ipſum om
              <lb/>
            nes propemodum benè inſtitutæ respublicæ, quæ in vrbib{us} at q; </s>
            <s xml:id="echoid-s206" xml:space="preserve">oppidis paſſim publicis, priuatis{q́ue} ſumpti
              <lb/>
            bus varia horologiorum genera tum ſolaria, tum alia fabricant, eorum{q́ue} cuſtodes ac moderatores annuis
              <lb/>
            ſtipendijs alunt: </s>
            <s xml:id="echoid-s207" xml:space="preserve">quod nulla ſanè ratione facerent, niſi horum vſum ſummè ciuitatibus neceſſarium iudica-
              <lb/>
            rent. </s>
            <s xml:id="echoid-s208" xml:space="preserve">Teſtantur quoq; </s>
            <s xml:id="echoid-s209" xml:space="preserve">id ipſum omnes propemodum agricolæ, ac ſolitarij homines, qui cum horologia non
              <lb/>
            habeant, neq; </s>
            <s xml:id="echoid-s210" xml:space="preserve">vero eis ſine magno incommodo poſſint carere, annituntur, quacunque id ratione poſſint,
              <lb/>
            hoc incommodum ſubleuare. </s>
            <s xml:id="echoid-s211" xml:space="preserve">Hinc enim videmus eos plerunq; </s>
            <s xml:id="echoid-s212" xml:space="preserve">vmbram ſuorum corporum metiri, vel alia,
              <lb/>
            at q; </s>
            <s xml:id="echoid-s213" xml:space="preserve">alia radijs ſolaribus ſignafigere, vel deniq; </s>
            <s xml:id="echoid-s214" xml:space="preserve">in ipſo cælo certa motus ſolis interdiu, noctu aliorum ſy-
              <lb/>
              <note position="left" xlink:label="note-0022-08" xlink:href="note-0022-08a" xml:space="preserve">40</note>
            derum interualla notare, vt hiſce ſaltem obſeruationibus quoquo modo, licet non omni ex parte accuratè,
              <lb/>
            & </s>
            <s xml:id="echoid-s215" xml:space="preserve">ad vnguem, hor arum diſcrimina, ſpatia{q́ue} deprehendere, ac dimetiri queant.</s>
            <s xml:id="echoid-s216" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s217" xml:space="preserve">CVM igitur horarum cognitio tam vtilis ſit, atq; </s>
            <s xml:id="echoid-s218" xml:space="preserve">adeo neceſſaria omnibus rebuspub. </s>
            <s xml:id="echoid-s219" xml:space="preserve">ſummo ſemper
              <lb/>
            studio maiores noſtri varia, & </s>
            <s xml:id="echoid-s220" xml:space="preserve">ingenioſa inſtrumenta, (quæ horologia appellam{us}) quibus hor arum in-
              <lb/>
            terualla dignoſceremus, excogit arunt; </s>
            <s xml:id="echoid-s221" xml:space="preserve">quæ quidem omnia ad duo genera reuocari poſſunt. </s>
            <s xml:id="echoid-s222" xml:space="preserve">Quædam inter-
              <lb/>
              <note position="left" xlink:label="note-0022-09" xlink:href="note-0022-09a" xml:space="preserve">Horologiorum
                <lb/>
              uaria genera.</note>
            diu ex ſola vmbra ſolis, noctu vel ex Lunæ vmbra, vel ex inſpectione aliorum ſyderum, hor{as} indicant,
              <lb/>
            de quibus infra plura ſcribemus. </s>
            <s xml:id="echoid-s223" xml:space="preserve">Quædam verò inſtrumento aliquo mechanico, & </s>
            <s xml:id="echoid-s224" xml:space="preserve">varijs motibus oſtendũt
              <lb/>
            hor{as}, quæ multiplicia ſunt. </s>
            <s xml:id="echoid-s225" xml:space="preserve">Cum enim priora illa horologia tempore nubilo null{as} prorſus monſtrarent
              <lb/>
            hor{as}, oportuit illos aliam viam, qua hor{as} not arent, inuenire. </s>
            <s xml:id="echoid-s226" xml:space="preserve">Hinc effectum eſt, vt quidam hydrauli-
              <lb/>
            cis horologijs vſi ſint, in quibus beneficio motus aquæ horæ exquiruntur: </s>
            <s xml:id="echoid-s227" xml:space="preserve">qua in re mirum in modum lau-
              <lb/>
              <note position="left" xlink:label="note-0022-10" xlink:href="note-0022-10a" xml:space="preserve">50</note>
            dat{us} fuit Cteſibius Alexandrin{us}. </s>
            <s xml:id="echoid-s228" xml:space="preserve">Hic enim, vt Vitruuius lib. </s>
            <s xml:id="echoid-s229" xml:space="preserve">9. </s>
            <s xml:id="echoid-s230" xml:space="preserve">refert, ingenio mir abili cõſtituit (Vtor
              <lb/>
            verbis Vitruuij) cauũ ex auro perfectum, aut ex gemma terebrata, ea enim nec teruntur percuſſu aquæ,
              <lb/>
            nec ſordes recipiunt, vt obturentur. </s>
            <s xml:id="echoid-s231" xml:space="preserve">Namq; </s>
            <s xml:id="echoid-s232" xml:space="preserve">æqualiter per id cauum influens aqua ſubleuabat ſcapbum
              <lb/>
            inuerſum, in quo collocata regula, verſatilia tympana denticulis æqualibus ſunt perfecta: </s>
            <s xml:id="echoid-s233" xml:space="preserve">qui denticuli
              <lb/>
            alius aliũ impellentes, verſationes modicas faciunt, & </s>
            <s xml:id="echoid-s234" xml:space="preserve">motiones, & </s>
            <s xml:id="echoid-s235" xml:space="preserve">cætera huiuſmodi, vnde diei partes,
              <lb/>
            id eſt, horæ cognoſci poterant, & </s>
            <s xml:id="echoid-s236" xml:space="preserve">dijudicari. </s>
            <s xml:id="echoid-s237" xml:space="preserve">Plinius vero ad finem lib. </s>
            <s xml:id="echoid-s238" xml:space="preserve">7. </s>
            <s xml:id="echoid-s239" xml:space="preserve">ſcribit, Scipionem Naſicam pri-
              <lb/>
            mum aqua diuiſiſſe hor{as} æquè noctium, ac dierum, anno Vrbis 595. </s>
            <s xml:id="echoid-s240" xml:space="preserve">Non nulli aut em ponebant vaſa quæ
              <lb/>
            dam ænea aquis plena, & </s>
            <s xml:id="echoid-s241" xml:space="preserve">ſubtiliter perforata. </s>
            <s xml:id="echoid-s242" xml:space="preserve">quantum enim aquarum in aliud vas @ecidiſſet, cum ad
              <lb/>
            inſcripta inſpexiſſent ſigna, quid temporis elapſum eſſet, intelligebant. </s>
            <s xml:id="echoid-s243" xml:space="preserve">Talia horologia à perforati vaſis
              <lb/>
            ſimilitudine clepſydr{as} appellabant, quòd furarentur quodammodo aquam, & </s>
            <s xml:id="echoid-s244" xml:space="preserve">guttat im infundendo per
              <lb/>
            anguſtum for amen de vaſe in v{as} emitterẽt. </s>
            <s xml:id="echoid-s245" xml:space="preserve">Vnde ſæpe legimus, oratoribus tres, aut quatuor </s>
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