Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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331 - 360
361 - 372
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ſinus verſus anguli A, ſiue arcus BL, ad KT, differentiam ſinuum verſorum
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BR, BQ, arcuum BC, BK; </
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<
s
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xml:space
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gula, ſed XA, AV, inter ſe non differant, quemadmodum neque KS, KT.</
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<
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te. </
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<
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<
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">reſecto quadrante AL, ex AC, producto
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item arcu BC, vt fiat quadrans BM, reliqua fiant, vt in ſuperioribus. </
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<
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ſtrabimus iam, vt in primo caſu,
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ita eſſe quadratum ſinus totius,
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nimirum rectangulum ſub DX,
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XA, ad rectangulum ſub AV,
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KY, ſinubus rectis arcuum AB,
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AC, vt eſt DZ, ſinus verſus an-
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guli A, ſeuarcus DL, ad KT,
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differentiam ſinuum verſorum
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BR, BQ, arcuum BC, Bk; </
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<
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ſi quòd triagulum XAV, trian
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gulo
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T, demonſtrandum eſt
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eſſe æquiangulum hac ratione. </
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ST, angulo oppoſito, & </
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interno YIX, æqualis eſt, erit in triangulis rectangulis
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T, IXY, & </
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liquus angulus
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T, reliquo angulo
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, hoc eſt, angulo oppoſito, & </
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no VAX, (cum parallelæ ſint AV, GH.) </
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<
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gulis
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T, XAV, anguli quoque reliqui
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ST, AXV, æquales erunt, ac
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proinde æquiangula erunt triangula
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T, XAV.</
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xml:space
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pleto circulo ABGF, & </
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circulis DEF,
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CN, ex polo A, ad interualla AL, AC, deſcribatur quoq;
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</
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<
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">ex polo B, ad interuallum quadrantis BC, circulus maximus GEH, atq; </
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frant, vt ſupra. </
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ergo eſt, ita eſſe quadratum ſinus
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totius, id eſt, rectágulum ſub DX,
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XA, ad rectangulum ſub AV,
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,
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ſinubus arcuum AB, AC, vt eſt
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DZ, ſinus verſus anguli A, arcuſ-
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ve DL, ad
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T, differentiam in-
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ter ſinus verſos BR, BQ, ar-
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cuum BC,
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. </
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ſtendemus, vtin primo caſu. </
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lum triangula
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T, XAV, pro-
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babũtur æquiangula eſſe, hoc mo
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do. </
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<
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T,
<
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. </
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<
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tur angulus reliquus
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T, reliquo angulo
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, hoceſt, angulo oppoſito, & </
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<
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interno VAX, (cum parallelę ſint AV, GH.) </
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<
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la triangula
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T, XAV, æquiangula erunt.</
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<
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<
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iores. </
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<
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<
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cubus AC, BC, fiant omnia alia, vt prius. </
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<
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mo caſu, ita eſſe quadratum ſinus totius, nempe rectangulum ſub DX,
<
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,
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ad rectangulum ſub AV,
<
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, ſinubus rectis arcuum AB, AC, vt eſt DZ, </
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