Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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ducta recta AD, circulum tangat, recta autem CD, circulum ſecet, conueniens cum
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AD, in D, (conueniet enim neceſſario, propterea quòd duo anguli
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C, DCA,
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duobus rectis ſunt minores; </
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<
s
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xml:space
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">cum ille rectus ſit, hic autem
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recto minor, propter arcum
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B, quadrante minorem.)
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</
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<
s
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">dicetur AD, Tangens arcus
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B, at CD, Secans eiuſdẽ
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arcus. </
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<
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xml:space
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">Tangentem vocant nonnulli Adſcriptam, quòd
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ſcripta, &
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Hypotenu-
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ſa quid.</
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circulo quodãmodo adſcribatur; </
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">Secantem vero, Hypo-
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tenuſam, propterea quòd in triangulo rectãgulo ACD,
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(angulus enim
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, apud contactum rectus eſt) angulum
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rectum ſubtendit: </
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">Semidiametrum denique
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C, ſiue ſi-
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">18. tertij.</
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num totum, dicunt baſem eiuſdem trianguli.</
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autemin omni triangulo
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">Si in trian-
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gu’o rectan
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gulo alteru
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trum late-
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rum circa
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angulũ re-
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ctum pona
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tur ſinus to
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tus, erit al-
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terum latus
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circa angu-
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lum rectú
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tangens an
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gulĩ acutiſi
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bi oppoſiti,
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& latus re-
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cto angulo
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oppoſitum
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eiuſdem ſe
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cans.</
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rectangulo, ſilatus recto angulo oppoſitum ponatur ſinus
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totus, reliqua duo latera ſunt ſinus recti reliquorum angulorum acutorum, quibus
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opponuntur; </
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adiacentis, vt in definitionibus ſinuum traditum eſt: </
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<
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">ita quoque ſi alterutrum late-
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rum circa angulum rectum ſtatuatur ſinus totus, erit alterum latus circa angulum
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rectum Tangens anguli acuti ſibi oppoſiti, latus vero angulo recto oppoſitum Secans
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eiuſdem anguli. </
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">Vt in triangulo rectangulo ACD, latus CA, eſt ſinus totus, nempe
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ſemidiameter circuli AB: </
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">at
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D, tangens anguli C, vel arcus
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, & </
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<
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">CD, eiuſdem
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ſecans. </
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<
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">Eodem pacto, ſt DA, ſtatuatur ſinus totus, erit AC, tangens anguli D, & </
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DC, eiuſdem ſecans.</
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<
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">ETSI autem diximus, tangentem, & </
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minoris, tamen eadem tangens, & </
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ſemicirculum complet: </
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">adeo vt duo arcus ſemicirculum conficientes, vel duo anguli
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duobus rectis æquales, vnam eandemq; </
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modum & </
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">eundem ſinum rectum habent, vt in tractatione ſinuum tradidimus: </
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">Duo arcus
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ſem icircu-
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lú cóficiéte
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vel duo än
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guli duobꝰ
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rectis æqua
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les habent
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eandé tan-
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gentem &
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ſecantem.</
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vt ſi quæratur tangens & </
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">ſecans alicuius arcus quadrante maioris, ſumenda ſit tan
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gens, & </
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<
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<
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">Secantes omnium arcuum quadrantis
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reddantur cognitæ in partibus ſinus totius, ac proinde qua via tabula Tangentium,
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tabula item Secantium componenda ſit, ſequentibus propoſitionibus, quæ ad line{as}
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Tangentes, ac Secantes ſpectant, planum fiet.</
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<
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">Tangentes
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quomodo
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ſe habeant
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cũ ſinu to-
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to com pa-
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ratæ.</
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æqualis eſt: </
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<
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o
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quadrantis maior eſt ſinu toto: </
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">Et Tangens mino-
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ris arcus minor eſt. </
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<
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">Secans denique dimidij qua-
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drantis dupla eſt ſinus recti eiuſdem dimidij.</
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<
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">IN quadrante ABC, ſit arcus CD, ſemiſsis ipſius; </
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