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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49
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LIBER PRIMVS.
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<
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style
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<
s
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echoid-s1986
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xml:space
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">HAEC ratio deſcribendæ conicæ ſectionis, vna cum demonſtratione, non differt ab ea, quam Fede-
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ricus Commandinus adducit in libro de horologiorum deſcriptione, niſi quòd ipſe de cono recto ſolum lo-
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quitur, nos autem problema omni cono tam recto, quàm ſcaleno accommodauimus, & </
s
>
<
s
xml:id
="
echoid-s1987
"
xml:space
="
preserve
">praxes, quæ ad
<
lb
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deſcriptionem ſectionum conorum rectorum requiruntur, ſimul complexi ſumus. </
s
>
<
s
xml:id
="
echoid-s1988
"
xml:space
="
preserve
">Præcipit enim ipſe, vt
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ſumantur in primis figuris, in diametro D E, quotcunque puncta K, L, atque per ipſa baſi B C, paralle-
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læ agantur. </
s
>
<
s
xml:id
="
echoid-s1989
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xml:space
="
preserve
">Sed facilius eſt in cono recto, beneficio circini in vtroque latere A B, A C, puncta ſumere F,
<
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G, H, I. </
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>
<
s
xml:id
="
echoid-s1990
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xml:space
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preserve
">Rectæ enim hæc puncta connectentes parallelæ ſunt, vt oſtendimus. </
s
>
<
s
xml:id
="
echoid-s1991
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xml:space
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preserve
">Deinde iubet in primis figu-
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ris, inter K F, k H, & </
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>
<
s
xml:id
="
echoid-s1992
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xml:space
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">L G, L I, inuenire medias proportionales: </
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>
<
s
xml:id
="
echoid-s1993
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xml:space
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preserve
">quod quidem nos præstitimus ſemi-
<
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<
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xlink:label
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note-0049-01
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xlink:href
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xml:space
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">10</
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circulis deſcriptis in ſecundis figuris. </
s
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<
s
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echoid-s1994
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xml:space
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">Poſtremo, diuiſa diametro D E, in plano ſeorſum, nimirum in
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tertijs figuris, vt diuiſa eſt in cono primarum figurarum, iubet ex punctis diuiſionum in tertijs figuris
<
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perpendiculares vtrinque educere ad diametrum: </
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>
<
s
xml:id
="
echoid-s1995
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xml:space
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">quod & </
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<
s
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xml:space
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">nos in tertijs figuris fecimus praxi perfacili
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& </
s
>
<
s
xml:id
="
echoid-s1997
"
xml:space
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preserve
">breui, præſertim vbi multa eſſent puncta. </
s
>
<
s
xml:id
="
echoid-s1998
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xml:space
="
preserve
">In has perpendiculares transfert medias proportionales
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inuentas, vt nos, & </
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>
<
s
xml:id
="
echoid-s1999
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xml:space
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">per extrema puncta mediarum proportionalium translatarum ducit ſectionem coni-
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cam, quemadmodum & </
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>
<
s
xml:id
="
echoid-s2000
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xml:space
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">à nobis factum eſt.</
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<
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</
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<
s
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xml:space
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">FRANCISCVS Maurolycus abbas libro tertio de lineis horarijs vtitur alijs deſcriptionibus
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particularibus trium conicarum ſectionum: </
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<
s
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echoid-s2003
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xml:space
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">ſed ratio deſcriptionis à nobis tradita ſimplicior est, & </
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<
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xml:space
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">fa-
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cilior, conuenit{q́ue} in omnes ſectiones, vt conſtat. </
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>
<
s
xml:id
="
echoid-s2005
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xml:space
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preserve
">Nihil autem diximus de conica illa ſectione deſcriben-
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da, quæ circulus eſt, quia perfacilis eſt eius deſcriptio, cognita diametro.</
s
>
<
s
xml:id
="
echoid-s2006
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="
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</
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xml:space
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">20</
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<
s
xml:id
="
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xml:space
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">PLACET autem hoc loco tradere aliam rationem non iniucundam, & </
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<
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echoid-s2008
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xml:space
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">fortaſſis ea, quam expli-
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cauimus, faciliorem, deſcribendi parabolam, duas hyperbolas oppoſitas, & </
s
>
<
s
xml:id
="
echoid-s2009
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xml:space
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">Ellipſim, quarum axes dati
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ſint, quæ quidem ratio (quod vehementer miror) à nemine hactenus, quod ſciam, obſeruata eſt. </
s
>
<
s
xml:id
="
echoid-s2010
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xml:space
="
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">Hanc au-
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tem conis rectis duntaxat accommodabimus, propterea quòd ijs ſolum in horologiorum deſcriptionibus
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vſuri ſumus. </
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>
<
s
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echoid-s2011
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xml:space
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">Pro Parabola igitur præmittendum eſt huiuſmodi lemma conueniens tam cono recto
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quàm Scaleno.</
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<
s
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</
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</
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<
head
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xml:space
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">LEMMA.</
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<
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<
s
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">DATO cono & </
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s
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">diametro parabolæ, inuenire latus rectum parabolæ.</
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<
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ris recti Parabo
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les, cuius diam@
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ter in cono da-
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ta ſit.</
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<
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0049-01
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<
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<
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xml:space
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">SIT datus conus A B C, in quo triangulum per axem A B C: </
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<
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">ſecetur autem conus
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plano faciente parabolam E F G, iuxta ea, quæ ab Apollonio demonstrata ſunt propoſ. </
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<
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</
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<
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">lib. </
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<
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">1. </
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<
s
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xml:space
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">ita vt eius axis E H, æquidiſtans ſit lateri A C, trianguli per axem. </
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<
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xml:space
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">Huius igitur
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paraboles rectum latus inueniemus hoc modo. </
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<
s
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xml:space
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">Fiat vt alterum latus trianguli per axem,
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nempe A B, ad baſim B C, ita B C, ad A I. </
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<
s
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xml:space
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">Deinde vt alterum latus A C, ad A I, inuen-
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<
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xml:space
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tam, ita A E, ad E K. </
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<
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xml:space
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">Dico E K, eſſe rectum latus paraboles E F G, hoc eſt, illam eſſere-
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<
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xlink:label
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xml:space
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">12. ſexti.</
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ctam, iuxta quam poſſunt or dinatim applicatæ ad diametrum E H. </
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<
s
xml:id
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echoid-s2026
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xml:space
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">Sit enim rectangulũ
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C B, contentum ſub lateribus trianguli per axem A B, A C; </
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<
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xml:id
="
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xml:space
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">& </
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<
s
xml:id
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echoid-s2028
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xml:space
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">ad A B, applicetur rectan-
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gulum B I, contentum ſub A B, A I, quod æquale erit quadrato baſis B C, propterea quòd
<
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<
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xlink:label
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xlink:href
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xml:space
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">17. ſexti.</
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tres rectæ A B, B C, A I, continuè proportionales ſunt, ex conſt
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ructione; </
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<
s
xml:id
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xml:space
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">erit{q́ue} C A I,
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vna linea recta, quòd duo anguli ad A, recti ſint. </
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<
s
xml:id
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xml:space
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">Quoniam igitur eſt, vt C A, ad A I,
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<
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xlink:label
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">14. primi.</
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ita A E, ad E K, per conſtructionem; </
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<
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xml:space
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">& </
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<
s
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">conuertendo, vt A I, ad A C, ita E K, ad A E;
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</
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<
s
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xml:space
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">Vt autem A I, ad A C, ita eſt rectangulum B I, hoc eſt, quadr atum baſis B C, ad rectan-
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<
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