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
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autem ſupputationis obſignetur notula F: </
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<
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<
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xml:space
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">à centro A, ad datum ſignum F, recta producatur li-
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nea A F. </
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<
s
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xml:space
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">Dato inſuper arcu B F, æqualis eidem conſtituatur in quadrante B E, ſitq; </
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<
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<
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xml:space
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gno F, ad ſignum G, recta ducatur linea F G. </
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<
s
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xml:space
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">Hæc enim à ſemidiametro A B, bifariam diuidetur,
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<
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xlink:label
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xml:space
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in ſigno quidem H: </
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<
s
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<
s
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">ad rectos angulos, per 3. </
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>
<
s
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xml:space
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">tertij elementorum Euclidis. </
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>
<
s
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xml:space
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">Erit itaq;
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</
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<
s
xml:id
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xml:space
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">recta linea F H, perpendicularis ſuper A B: </
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<
s
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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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">triangulum A F H, rectangulum. </
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>
<
s
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"
xml:space
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">Ergo circulus B C-
<
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D E, Meridianum, & </
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<
s
xml:id
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xml:space
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">B C, quadrantem eius ſeptentrionalem, A, vero centrum mundi repreſenta-
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<
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bit: </
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<
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xml:id
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xml:space
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">recta porro B D, Horizontem, & </
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>
<
s
xml:id
="
echoid-s10024
"
xml:space
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">C E, Verticalem circulum cum ipſo Meridiano ad rectos an
<
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gulos incidentem. </
s
>
<
s
xml:id
="
echoid-s10025
"
xml:space
="
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">Deinde paulo poſt ita rem proſequitur. </
s
>
<
s
xml:id
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"
xml:space
="
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">Data recta linea F H, æqualis eidem con
<
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ſtituatur in ſemidiametro A C, ſitq́, illa A I: </
s
>
<
s
xml:id
="
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xml:space
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">& </
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>
<
s
xml:id
="
echoid-s10028
"
xml:space
="
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">à ſigno H, ad ſignum I, recta linea ducatur H I, di-
<
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rimens rectam A F, in ſigno K. </
s
>
<
s
xml:id
="
echoid-s10029
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xml:space
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">Erit igitur triangulum A H I, ęqualeatque ſimile triangulo A F H:
<
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</
s
>
<
s
xml:id
="
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xml:space
="
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">quemadmodum ex 4. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">primi ipſius Euclidis fit manifeſtum. </
s
>
<
s
xml:id
="
echoid-s10032
"
xml:space
="
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">Hanc igitur deſcriptionem, generalem
<
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protypum Orontius appellat pro horizontalibus, Verticalibus{q́ue}, horologijs conſtruendis: </
s
>
<
s
xml:id
="
echoid-s10033
"
xml:space
="
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">ita vt ipſe trian
<
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gulo AHK, rtatur in horizontalibus horologijs fabricandis ad datam altitudinem poli B F, non ſecus,
<
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atq; </
s
>
<
s
xml:id
="
echoid-s10034
"
xml:space
="
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">nos in hac propoſitione vſi ſumus triangulo D H I, in portione Analemmatis contento pro eiſdẽ ho-
<
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rologijs componendis ad datam poli altitudinem C E. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Nam ſtatim in propoſ. </
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>
<
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xml:space
="
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">2. </
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>
<
s
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="
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xml:space
="
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">aſſumit in linea meridia-
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narectam ęqualem lateri A H, pro linea Horizontis, quemadmodum nos accepimus rectam æqualem la
<
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<
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="
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xml:space
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">30</
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>
tcri H I, in noſtro triangulo. </
s
>
<
s
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xml:space
="
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">Deinde pro linea Aequatoris ſumit aliam rectam æqualem lateri A K,
<
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quemadmodum nos ſumpſimus rectam æqualem rectæ D I, in noſtro triangulo. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Itaque vult in triangulo
<
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A H K, rectam A H, eſſe lineam Horizontis; </
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>
<
s
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="
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xml:space
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">H K, axem mundi; </
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>
<
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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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">A K, lineam Aequatoris, pro
<
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horizontalibus horologijs componendis. </
s
>
<
s
xml:id
="
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xml:space
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">Sic etiam in propoſ. </
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>
<
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xml:space
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">3. </
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>
<
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">eiuſdem lib. </
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>
<
s
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="
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xml:space
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">pro V erticalibus horologijs
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conſtruendis accipit in triangulo F H K, rectam F H, pro linea V erticalis circuli; </
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>
<
s
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xml:space
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">H K, pro axe mundi;
<
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</
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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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">F K, pro Aequatoris linea. </
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>
<
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xml:space
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">Qua in re ipſum eſſe mirum in modum hallucinatum, facile demonſtra-
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bimus hoc modo.</
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<
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</
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<
s
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">QVONIAM latera I A, A H, trianguli I A H, æqualia ſunt lateribus F H, H A, trianguli
<
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F H A, angulos{q́ue} continent æquales, vtpote rectos, erunt & </
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<
s
xml:id
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xml:space
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">baſes H I, A F, & </
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<
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xml:space
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">anguli A H I, H A F,
<
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<
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xml:space
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note
>
aquales. </
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<
s
xml:id
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xml:space
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">Quare quemadmodum A F, axis eſt reſpectu Horizontis A H, ita quoque H I, pro axc ſumi
<
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<
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potest reſpectu ciuſdem Horizontis A H, quandoquidem tam A F, quàm H I, cum A H, angulum alti-
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tudinis poli conſtituit. </
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<
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xml:space
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">Atque hucuſque inter nos & </
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>
<
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xml:space
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">Orontium nullum diſcrimen eſt: </
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<
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xml:space
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">Sed error ipſius cõ-
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ſiſtit in linea Aequat oris duntaxat, quam nulla ratione eſſe poſſe rectam A K, vt ipſe putat, in regione,
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cuius latitudo maior ſit, quàm grad. </
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<
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<
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">ita perſpicuum faciemus. </
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<
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xml:space
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maior, quàm grad. </
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<
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<
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">vt in eius figura. </
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<
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xml:space
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">Erit igitur angulus F A H, dimidio rectimaior; </
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<
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xml:space
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">ac proinde cum
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ei æqualis ſit oſtenſus angulus A H I, erunt duo anguli K A H, K H A, in triangulo A H K, ſimul re-
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cto maiores. </
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<
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<
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xml:space
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">Quare cum linea Aequatoris cum axe in omni
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<
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note
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climate rectos faciat angnlos, vt ex portione Analemmatis huius propoſ. </
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<
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in propoſ. </
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<
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<
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<
s
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">conſtat, quis adhuc dubitabit, rectam A K, quæ cum axe H K, angulum acutũ
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facit A K H, lineam Aequatoris eſſe non poſſe? </
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>
<
s
xml:id
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xml:space
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">Itaque vt in triangulo A H K, linea Aequatoris ha-
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<
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beatur, ducenda erit ex A, ad axem H K, perpendicularis A L, quæ neceſſario minor eſt quàm A K.
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</
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<
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Deinde ſit altitudo poli B F, minor, quàm grad. </
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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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">erit{q́ue} propterea
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angulus F A H, recto minor. </
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>
<
s
xml:id
="
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xml:space
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">Quare cum ei ęqualis ſit oſtenſus angulus A H I, erunt anguli H A F,
<
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<
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xml:space
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">32. primi.</
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A H I, ſimul vno recto minores; </
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>
<
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xml:space
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">ac proinde reliquus A K H, in triangulo A K H, rectum ſuperabit.
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</
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<
s
xml:id
="
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xml:space
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">Non igitur recta A K, eſſe poteſt linea Aequatoris, cum non faciat cum axe H I, angulos rectos: </
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>
<
s
xml:id
="
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xml:space
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cta A L, ad axem H I, perpendicularis lineam Aequatoris dabit. </
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>
<
s
xml:id
="
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xml:space
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">Solum in regione, vbi altitudo poli cõ-
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plectitur grad. </
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>
<
s
xml:id
="
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xml:space
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">45. </
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>
<
s
xml:id
="
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xml:space
="
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">recta A K, erit linea Aequatoris, quia ibi ſolum rectos angulos cum axe H I, conſti-
<
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tuit. </
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>
<
s
xml:id
="
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xml:space
="
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">Contineat enim altitudo poli B F, grad. </
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>
<
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xml:id
="
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xml:space
="
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">45. </
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>
<
s
xml:id
="
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xml:space
="
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">vt in tertia figura: </
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>
<
s
xml:id
="
echoid-s10087
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xml:space
="
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">erit{q́ue} propterea angulus F A H,
<
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ſemirectus. </
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>
<
s
xml:id
="
echoid-s10088
"
xml:space
="
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">Cum ergo ei æqualis oſtenſus ſit angulus A H I, erunt duo anguli H A K, A H K, ſimul vni
<
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recto ęquales: </
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>
<
s
xml:id
="
echoid-s10089
"
xml:space
="
preserve
">ac propterea reliquus angulus A K H, in triangulo A K H, rectus erit. </
s
>
<
s
xml:id
="
echoid-s10090
"
xml:space
="
preserve
">Igitur recta
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0176-10
"
xlink:href
="
note-0176-10a
"
xml:space
="
preserve
">32. primi.</
note
>
A K, fungetur munere lineę Aequatoris. </
s
>
<
s
xml:id
="
echoid-s10091
"
xml:space
="
preserve
">Manifeſtũ igitur eſt, Orontium pueriliter labi in linea </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>