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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nor quàm E F. </
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<
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<
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E F. </
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<
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ctæ A C, quæ minor eſt ostenſa, quàm D F, ſubtendatur{q́ue} recta D I, quæ minor quoque
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erit, quàm D F. </
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<
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am rectangulum ſub E N, N F, ad rectam E F, applicatum, deficiens{q́ue} quadrato ex N F,
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quàm rectangulum ſub F O, O E, ad eandem rectam E F, applicatum, deficiens{q́ue} qua-
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drato ex O E, æquale eße quadrato ex A C, hoc eſt, quartæ parti rectanguli ſub E F, E I.
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</
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<
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<
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0054-01
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tur figura, vt vides. </
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<
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xml:space
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gramma D H, G L, L F, circa eandem diame-
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trum exiſtentia, ſimilia ſunt, eſt{q́ue} D H, quadra-
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tum, erunt quoque G L, L F, quadrata. </
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<
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xml:space
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quadratum D H, æquale est quadratis ex F I,
<
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<
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D I, hoc eſt, quadrato ex A C, vna cum quadra-
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to G L; </
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<
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xml:space
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">(Eſt enim angul{us} D I F, rect{us}, & </
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<
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<
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F I, D I, æquales fuerunt rectis A C, D N, vel
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K L.) </
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<
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">erit gnomon K N H, quadrato ex A C, æqualis. </
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<
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<
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lis quoque ſit rectangulo E L, (Nam cum E K, ipſi K F, hoc eſt, ipſi N H, æquale ſit; </
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<
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<
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">36. primi.</
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to communi D L, fit totum E L, toti gnomoni K N H, æquale) erit quoque rectangulum
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E L, contentum ſub E N, N F; </
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<
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xml:space
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">(quòd recta N F, rectæ N L, æqualis ſit, ob quadratum
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L F.) </
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<
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">æquale quadrato ex A C. </
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<
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xml:space
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">Applicatum eſt ergo ad E F, diametrum tranſuerſam
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rectangulum ſub E N, N F, æquale quartæ parti rectanguli ſub E F, E I, deficiens{q́ue} qua-
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drato rectæ N F. </
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<
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xml:space
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">Eodem modo demonſtrabitur rectangulum ſub F O, O E, applicatum ad
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E F, deficiens{q́ue} quadrato ex E O, æquale eße quartæ parti rectanguli ſub E F, E I. </
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<
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eſt propoſitum.</
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</
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<
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Ellipſis in pla-
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no.</
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<
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">HIS præmiſſis ſit E F, axis tranſuerſus Ellipſis E F, & </
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<
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</
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Applicetur per 2. </
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<
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">lemma, ad E F, ex vtraque parte rectangulum tam ſub F O, O E, quàm ſub E N,
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N F, quartæ parti rectanguli ſub E F, E I, æquale, quorum illud quidem deficiat quadrato ex E O, hoc
<
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vero, quadrato ex F N. </
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<
s
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xml:space
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">Et diuiſa N O, bifariam in A, ſumantur inter A, & </
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<
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cunque B, C, D. </
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<
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<
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cus ſemutuo ſecantes hinc inde in G. </
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<
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<
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cus deſcribantur, quos in puncto H, ſecent alij quatuor arcus ex eiſdem punctis ad interuallum F B, de-
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ſcripti. </
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<
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xml:space
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<
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in I; </
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<
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">& </
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<
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<
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qui ex O, & </
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<
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xml:space
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">N, deſcribendi ſunt, deſcribantur ex O, vltra punctum A, & </
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<
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ctum A; </
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<
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<
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<
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puncta E, G, H, I, F, Ellipſis erit deſcribenda. </
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<
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quàm rectæ N H, O H, id est, E B, F B, &</
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<
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<
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per puncta E, G, H, I, F; </
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<
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">quandoquidem, vt vult propoſitio 52. </
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<
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<
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N, O, ad vnum idem{q́ue} Ellipſis punctum inclinatæ æquales ſunt axi E F. </
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<
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tranſit per punctum I, tranſeat, ſifieri poteſt, per K, ſecans rectam N I, in K, vel vltra, vel citra I,
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iungatur{q́ue}, recta O K. </
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<
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">Quoniam igitur Ellipſis prædicta tranſit per K, erunt rectæ N K, O K, ſimul æqua-
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les axi E F, ex propoſ. </
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<
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<
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æquales ſunt. </
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<
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<
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<
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<
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cto K, vltra I, erunt rectæ I K, K O, maiores recta I O; </
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<
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xml:space
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<
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maiores, quàm N I, O I: </
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<
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<
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ta ergo communi K N, erunt N I, O I, maiores, quàm N k, O K) Quod est abſurdum. </
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<
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Ellipſis per aliud punctum, quàm per I, tranſibit. </
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<
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m{q́ue} modo demonſtrabimus eandem per reliqua
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puncta H, G, &</
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<
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<
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<
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<
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<
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">PERSPICVVM etiam eſt, hanc deſcriptionem non conuenire conis ſcalenis, niſi cum triangula
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<
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xlink:label
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Parabola qua-
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liſ
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unque in
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plano deſcriba-
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tur.</
note
>
per axem ad baſes conorum recta ſunt. </
s
>
<
s
xml:id
="
echoid-s2376
"
xml:space
="
preserve
">Tunc enim ſolum diameter ellipſis ad angulos rectos ſecat ordi-
<
lb
/>
natim applicatas, vt ex propoſ. </
s
>
<
s
xml:id
="
echoid-s2377
"
xml:space
="
preserve
">7. </
s
>
<
s
xml:id
="
echoid-s2378
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s2379
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s2380
"
xml:space
="
preserve
">Apoll. </
s
>
<
s
xml:id
="
echoid-s2381
"
xml:space
="
preserve
">conſtat, atque adeo axis eſt.</
s
>
<
s
xml:id
="
echoid-s2382
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s2383
"
xml:space
="
preserve
">QVOD ſi vt cunque Parabolã aliquam, Hyperbolã, vel etiã duas oppoſitas, aut Ellipſim deſcribere
<
unsure
/>
<
lb
/>
velimus, nulla habita ratione conorũ, à quibus oriuntur, accipiemus pro parabola axem cuiuſcunque ma-
<
lb
/>
gnitudinis E H, vt in ſuperiori parabola, & </
s
>
<
s
xml:id
="
echoid-s2384
"
xml:space
="
preserve
">in eo quotcunque partes æquales vt libet, et per puncta termi
<
lb
/>
nantia primam partem, & </
s
>
<
s
xml:id
="
echoid-s2385
"
xml:space
="
preserve
">ſequẽtes tres, & </
s
>
<
s
xml:id
="
echoid-s2386
"
xml:space
="
preserve
">ſequentes quinque, & </
s
>
<
s
xml:id
="
echoid-s2387
"
xml:space
="
preserve
">ſeque
<
unsure
/>
ntes ſeptem, &</
s
>
<
s
xml:id
="
echoid-s2388
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s2389
"
xml:space
="
preserve
">ducemus lineas
<
lb
/>
inter ſe parallelas; </
s
>
<
s
xml:id
="
echoid-s2390
"
xml:space
="
preserve
">ſumpta autem ex prima, quantacunque linea vtrinque A D, accipiemus eius </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>