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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          <p style="it">
            <s xml:id="echoid-s1166" xml:space="preserve">
              <pb o="16" file="0036" n="36" rhead="GNOMONICES"/>
            eiuſdẽ arcus 30. </s>
            <s xml:id="echoid-s1167" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s1168" xml:space="preserve">ex demonſtratis à Ioanne Regiom. </s>
            <s xml:id="echoid-s1169" xml:space="preserve">& </s>
            <s xml:id="echoid-s1170" xml:space="preserve">Petro Nonio, vt dictum eſt, & </s>
            <s xml:id="echoid-s1171" xml:space="preserve">nos pro ver@
              <lb/>
            at que conceſſo ſumpſimus. </s>
            <s xml:id="echoid-s1172" xml:space="preserve">Igitur ſinus O φ, ęqualis eſt ſinui declinationis illius arcus Eclipticæ, qui 30.
              <lb/>
            </s>
            <s xml:id="echoid-s1173" xml:space="preserve">gradus complectitur, eſt arcui QX, ſimilis. </s>
            <s xml:id="echoid-s1174" xml:space="preserve">Quare arcus H γ, æqualis eſt arcui declinationis illius ar-
              <lb/>
            cus Eclipticæ 30. </s>
            <s xml:id="echoid-s1175" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s1176" xml:space="preserve">qui ar cui QX, 30. </s>
            <s xml:id="echoid-s1177" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s1178" xml:space="preserve">eſt ſimilis. </s>
            <s xml:id="echoid-s1179" xml:space="preserve">Eademq́, de cæteris arcubus zodiaci est ratio,
              <lb/>
            quod erat demonſtr andum.</s>
            <s xml:id="echoid-s1180" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1181" xml:space="preserve">INVENIRI quoque poſſunt declinationes omnium ſignorũ Eclipticæ hoc modo. </s>
            <s xml:id="echoid-s1182" xml:space="preserve">Circulus Ana-
              <lb/>
              <note position="left" xlink:label="note-0036-01" xlink:href="note-0036-01a" xml:space="preserve">Alia deſcriptio
                <lb/>
              pa@allelorã Ae-
                <lb/>
              quatoris per ſi-
                <lb/>
              gnorum prin-
                <lb/>
              cipia ductorum.</note>
            lemmatis A B C D, diuidatur in 12. </s>
            <s xml:id="echoid-s1183" xml:space="preserve">partes æquales, initio facto à puncto M, maximæ declinationis; </s>
            <s xml:id="echoid-s1184" xml:space="preserve">& </s>
            <s xml:id="echoid-s1185" xml:space="preserve">
              <lb/>
            quælibet duo puncta diuiſionum æqualiter à puncto M, remota, rectis lineis iungantur; </s>
            <s xml:id="echoid-s1186" xml:space="preserve">quales ſunt in
              <lb/>
            Analemmate lineæ punctis diſtinctæ, & </s>
            <s xml:id="echoid-s1187" xml:space="preserve">in punctis l, p, E, q, u, rectam M ρ, ſecantes; </s>
            <s xml:id="echoid-s1188" xml:space="preserve">quæ omnes paral-
              <lb/>
            lelæ inter ſe erunt, ex ſcholio propoſ. </s>
            <s xml:id="echoid-s1189" xml:space="preserve">27. </s>
            <s xml:id="echoid-s1190" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1191" xml:space="preserve">3. </s>
            <s xml:id="echoid-s1192" xml:space="preserve">Euclidis. </s>
            <s xml:id="echoid-s1193" xml:space="preserve">Hæ lineæ vbi rectam M ρ, ſecabunt, per ea
              <lb/>
              <note position="left" xlink:label="note-0036-02" xlink:href="note-0036-02a" xml:space="preserve">10</note>
              <figure xlink:label="fig-0036-01" xlink:href="fig-0036-01a" number="15">
                <image file="0036-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0036-01"/>
              </figure>
            puncta, qualia ſunt l, p, E, q, u, du-
              <lb/>
            cendæ erunt rectæ lineæ β λ, γ μ,
              <lb/>
            & </s>
            <s xml:id="echoid-s1194" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1195" xml:space="preserve">æquinoctiali lineæ H I, paral-
              <lb/>
            lelæ pro diametris parallelorũ per
              <lb/>
            ſignorum initia deſcriptorum; </s>
            <s xml:id="echoid-s1196" xml:space="preserve">ita
              <lb/>
            vt rurſus arcus H β, H γ, &</s>
            <s xml:id="echoid-s1197" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1198" xml:space="preserve">ſint
              <lb/>
            declinationes ſignorum Zodiaci.
              <lb/>
            </s>
            <s xml:id="echoid-s1199" xml:space="preserve">Quod vt demonſtremus, intelligen-
              <lb/>
            dus est circulus A B C D, eſſe
              <lb/>
            Ecliptica, cuius ſignorũ initia ſunt
              <lb/>
              <note position="left" xlink:label="note-0036-03" xlink:href="note-0036-03a" xml:space="preserve">20</note>
            in illis punctis diuiſionum 12. </s>
            <s xml:id="echoid-s1200" xml:space="preserve">ita
              <lb/>
            vt M, ρ, ſint principia ♋ & </s>
            <s xml:id="echoid-s1201" xml:space="preserve">
              <lb/>
            ♑. </s>
            <s xml:id="echoid-s1202" xml:space="preserve">Deindemanente hac Eclipti-
              <lb/>
            caimmobili, & </s>
            <s xml:id="echoid-s1203" xml:space="preserve">in coſitu, quem in
              <lb/>
            Sphæra habet, poſito principio
              <lb/>
            ♋ M, in Meridiano circulo ſu-
              <lb/>
            pra Horizontẽ, & </s>
            <s xml:id="echoid-s1204" xml:space="preserve">principio ♑,
              <lb/>
            ρ, in eodem ſub Horizonte, intelli-
              <lb/>
            gendus eſt idem circulus inſtar Co-
              <lb/>
            luri ſolſtitiorum circa diametrum
              <lb/>
              <note position="left" xlink:label="note-0036-04" xlink:href="note-0036-04a" xml:space="preserve">30</note>
            M ρ, conuerti, donec rectus ſit ad
              <lb/>
            Eclipticæ planum, & </s>
            <s xml:id="echoid-s1205" xml:space="preserve">punctum F,
              <lb/>
            directo ad polum arcticum, & </s>
            <s xml:id="echoid-s1206" xml:space="preserve">G,
              <lb/>
            ad antarcticum ſpectet, ita ut Ae-
              <lb/>
            quator ad hunc Colurum rectus per rectam H I, ductus, faciat in plano Eclipticæ communem ſectionem,
              <lb/>
              <note position="left" xlink:label="note-0036-05" xlink:href="note-0036-05a" xml:space="preserve">3. vndec.</note>
            rectam illam punctis not at am, quæ ipſam M ρ, ad angulos rectos ſecat in E, centro. </s>
            <s xml:id="echoid-s1207" xml:space="preserve">Cum enim tam pla-
              <lb/>
            num Eclipticæ, quàm Aequatoris ad Colurum ſit rectum, erit quoque communis illorum ſectio ad eundem
              <lb/>
              <note position="left" xlink:label="note-0036-06" xlink:href="note-0036-06a" xml:space="preserve">19. vndec.</note>
            recta, at que adeo & </s>
            <s xml:id="echoid-s1208" xml:space="preserve">ad rectam M ρ, in eodem Coluro exiſtentem. </s>
            <s xml:id="echoid-s1209" xml:space="preserve">Si igitur per punctum p, verbi gratia,
              <lb/>
            concipiamus tranſire planum Aequatori par allelum, faciet id in plano Eclipticæ rectam punctis diſtin-
              <lb/>
            ctam, & </s>
            <s xml:id="echoid-s1210" xml:space="preserve">per p, tranſeuntem, at que alteri rectæ per E, ductæ, punctis{q́ue} diſtinctæ par allelam; </s>
            <s xml:id="echoid-s1211" xml:space="preserve">propterea
              <lb/>
              <note position="left" xlink:label="note-0036-07" xlink:href="note-0036-07a" xml:space="preserve">16. vndec.</note>
              <note position="left" xlink:label="note-0036-08" xlink:href="note-0036-08a" xml:space="preserve">40</note>
            quòd hæ lineæ per E, & </s>
            <s xml:id="echoid-s1212" xml:space="preserve">p, ductæ ſint ſectiones planorum parallelorum, nempe Aequatoris, & </s>
            <s xml:id="echoid-s1213" xml:space="preserve">plani ipſi
              <lb/>
            paralleli, factæ à plano Eclipticæ. </s>
            <s xml:id="echoid-s1214" xml:space="preserve">In Sphera autem circulum efficiet ex propoſ. </s>
            <s xml:id="echoid-s1215" xml:space="preserve">1. </s>
            <s xml:id="echoid-s1216" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1217" xml:space="preserve">1. </s>
            <s xml:id="echoid-s1218" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s1219" xml:space="preserve">Aequa-
              <lb/>
            tori parallelum, cuius diameter per p, incedens parallela erit diametro Aequatoris H I; </s>
            <s xml:id="echoid-s1220" xml:space="preserve">propterea quòd
              <lb/>
              <note position="left" xlink:label="note-0036-09" xlink:href="note-0036-09a" xml:space="preserve">16. vndec.</note>
            H I, & </s>
            <s xml:id="echoid-s1221" xml:space="preserve">diameter huius circuli ſint ſectiones planorum parallelorum, nimirum Aequatoris, & </s>
            <s xml:id="echoid-s1222" xml:space="preserve">plani
              <lb/>
            ipſi æquidiſtantis, factæ à plano Coluri ſolſtitiorum. </s>
            <s xml:id="echoid-s1223" xml:space="preserve">Igitur recta γ ω, per p, ducta ipſi H I, parallela dia-
              <lb/>
            meter eſt illius paralleli, qui in Ecliptica per puncta terminantia rectam illam punctis not at am, & </s>
            <s xml:id="echoid-s1224" xml:space="preserve">per
              <lb/>
            p, ductam, tranſit, nempe per arcus 30. </s>
            <s xml:id="echoid-s1225" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s1226" xml:space="preserve">ab æquinoctialibus punctis computatos; </s>
            <s xml:id="echoid-s1227" xml:space="preserve">quæ quidem pun-
              <lb/>
            cta æquinoctialia terminantur àrecta illa punctis notata, & </s>
            <s xml:id="echoid-s1228" xml:space="preserve">per centrum E, ducta. </s>
            <s xml:id="echoid-s1229" xml:space="preserve">Quare cum arcus
              <lb/>
            Coluri ſolſtitiorum inter Aequatorem, & </s>
            <s xml:id="echoid-s1230" xml:space="preserve">parallelum circulum quemcunque interceptus metiatur decli-
              <lb/>
            nationem illius paralleli ab Aequatore, erit arcus H γ, declinatio paralleli, cuius diameter γ μ, qui{q́ue}
              <lb/>
              <note position="left" xlink:label="note-0036-10" xlink:href="note-0036-10a" xml:space="preserve">50</note>
            per ea puncta in Ecliptica incedit, quæ à recta punctis diſtincta, at que per punctum p, ducta terminan-
              <lb/>
            tur. </s>
            <s xml:id="echoid-s1231" xml:space="preserve">Eadem{q́ue} eſt ratio de cæteris. </s>
            <s xml:id="echoid-s1232" xml:space="preserve">Quòd ſi circulus A B C D, non ſolum in 12. </s>
            <s xml:id="echoid-s1233" xml:space="preserve">partes, ſed in ſingulos
              <lb/>
            etiam diſtribuatur gradus, eadem{q́ue} fiant, quæ prius, deſcribemus eodem artificio diametros parallelorum
              <lb/>
            per ſingulos gradus Eclipticæ incedentium.</s>
            <s xml:id="echoid-s1234" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1235" xml:space="preserve">DENIQVE, ſi declinationes ſignorum, vel quorumlibet punctorum Eclipticæ, inuentæ per doctri-
              <lb/>
              <note position="left" xlink:label="note-0036-11" xlink:href="note-0036-11a" xml:space="preserve">Alia adhue de-
                <lb/>
              ſcriptio paralle-
                <lb/>
              lorũ per puncta
                <lb/>
              Eclipticæ tran-
                <lb/>
              ſeuntium.</note>
            nam ſinuum, vt in coroll. </s>
            <s xml:id="echoid-s1236" xml:space="preserve">huius propoſ. </s>
            <s xml:id="echoid-s1237" xml:space="preserve">docuimus, ſupputentur ab Aequatoris diametro H I, ad vtram-
              <lb/>
            que partem in circulo Analemmatis, & </s>
            <s xml:id="echoid-s1238" xml:space="preserve">per fines ſupputationum ipſi H I, parallelæ agantur, erunt hæ
              <lb/>
            rurſus diametri parallelorum per initia ſignorum, vel per data puncta Eclipticæ, tranſeuntium, vt prius;
              <lb/>
            </s>
            <s xml:id="echoid-s1239" xml:space="preserve">quamuis vt in initio diximus, incerta eſt per hanc viam Analemmatis deſcriptio, propter declinationes,
              <lb/>
            quæ uix ſine errore in circulo A B C D, ſupputari poſſunt, cum in eo minuta, & </s>
            <s xml:id="echoid-s1240" xml:space="preserve">ſecunda graduum de-
              <lb/>
            ſignari nequeant.</s>
            <s xml:id="echoid-s1241" xml:space="preserve"/>
          </p>
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