Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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operationis ratio perſpicua eſt ex prima figura in expoſitione definitionũ poſita. </
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enim ſinus verſus _AH,_ ex ſinu toto _
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_, ſublatus relinquit _HE_, vel _
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K_, ſinum comple
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menti arcus _AF_, qui dicto ſinui verſo _AH_, debetur. </
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<
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xml:space
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">_I_tem ex ſinu verſo _HC_, ſubdu-
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ctus ſinus totus _
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C_, relinquit _
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H_, vel _
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_, ſinum rectum arcus _
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B_, qui quadranti
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_BC_, adiectus componit arcum _
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C_, dicto ſinui verſo _HC_, reſpondentem.</
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<
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xml:space
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">_EX_ eadem tabula ſinuum rectorum indagabimus quoq; </
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<
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<
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">arcus chordam;
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">Chorda cu-
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iuſq; arcꝰ;
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& cõtra, ar-
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cus chordæ
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cuiuſq; qua
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rõne ex ta-
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bula ſinuũ
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eliciatur.</
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& </
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">contra datæ cuiusq; </
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xml:space
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">_N_am ſi dimidij arcus propoſiti ſi-
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num rectũ accipiamus, eumq; </
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<
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<
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datæ chordæ dimidium, tanquàm sinum rectum ſumamus, eiuſq́; </
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<
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bit hic arcus duplicatus arcum datæ chordæ reſpondentem. </
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<
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prima, quã in definitionum explicatione deſcripsimus, manifeſtum eſt. </
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H_,
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ſinus rectus arcus _
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,_ vel _
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C_, eſt ſemißis chordæ _
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G_, arcus _
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AG_, vel _
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CG_, &</
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<
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<
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<
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RVM_ quia tabulam ſinuum non ſemper in promptu habemus, non iniucun-
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dum ſtudioſis fore ſum arbitratus, ſi breuiter hoc loco doceam, antequam ad alia
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progrediar, qua ratione ſinubus _G_eometrice, ſine auxilio numerorum, vti poßimus in
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theorematibus, atq; </
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<
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ſolo circini beneficio omnia illa conſequamur, quæ longis multiplicationibus, diuiſioni
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busq́; </
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<
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">numerorum in ſinuum tabula contentorũ inquiri ſolẽt. </
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tim conſultum erit, qui vel magnã moleſtiam in numerorũ ſupputationibus ſentiũt,
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vel non admodum in ijs ſeſe exercuerunt. </
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<
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vno aut altero exemplo exponemus. </
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cuiuſuis puncti _E_clipticæ, vt grad. </
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. </
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CD_, vnà cum
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">Quo pacto
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ſinubus vtẽ
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dũ ſit Geo-
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metricè ſi-
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ne tabu la
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finuum.</
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duabus diame-
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="
185-01
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/185-01
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tris _AC, BD_,
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ſeſe in centro
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_
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_, ad angulos
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rectos ſecanti-
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bus. </
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_tquoniã,
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vt in coroll.
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</
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_1._ </
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monices oſten-
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dimus, ea eſt
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proportio ſi-
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nus totius ad
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ſinum maximæ declinationis, quæ ſinus illius arcus, quo datum punctum à viciniori
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puncto æquinoctij diſtat, ad ſinum declinationis eiuſdem puncti; </
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mæ declinationis _
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_, (quod quidem facile fiet, ſi adſit quadrãs æneus, aut ligneus ac-
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curate in _90_. </
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<
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">gradus diuiſus, de quo in initio noſtræ _G_nomonices ſcripſimus. </
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<
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enim quadrãte non eſſet operæ pretium velle ſinubus vti ſine numeris.) </
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">& </
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_50._ </
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. </
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">ex _
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, G_, ad _
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_,
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perpendiculares demittantur _
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I, GH_; </
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<
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">quod facile fiet, ſi arcubus _DF,
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,_ ſuman-
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tur arcus _DK, DL_, æquales: </
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<
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, L,_ & </
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, K_, iungentes erunt ad
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_
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">De</
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_, perpendiculares, cum per ſcholium in definitionibus poſitum ſecentur in _H,_
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_I_, bifariam, ac propterea ad angulos rectos: </
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<
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_runt autem _FI,
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H_, ſinus re-
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<
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">3. tertij.</
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cti arcuum _
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,
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._ </
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<
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I_, ſinui ma-
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ximæ declinationis, & </
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