Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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Table of Notes
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<
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anguli.</
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<
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xml:space
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">11. DATIS omnibus lateribus trianguli non
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rectanguli, reperire omnes eius angulos.</
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<
s
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xml:space
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">DVCTA ad maximum latus perpẽdiculari ex angulo oppoſito, (vt per-
<
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xml:space
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">Propoſ. 11.
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triang. re-
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ctil.</
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pendicularis ſemper intra triangulum cadat) inueniãtur, per antecedens pro-
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blema, rectæ inter perpendicularem, & </
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<
s
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</
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<
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xml:space
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">Deinde fiat, vt minimum latus ad ſinum totum, ita minus ſegmentum baſis ad
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aliud, gigneturq́; </
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<
s
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">ſinus, cuius arcus complementum dabit angulum baſis mini-
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mo lateri adiacentem. </
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<
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xml:space
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">Rurſus fiat, vt medium latus ad ſinum totum, ita ma-
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ius ſegmentum baſis ad aliud, procreabiturq́; </
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<
s
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xml:space
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">ſinus, cuius arcus complemen-
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tum dabit angulum baſis medio lateri adiacentem. </
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<
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">Tertius vero angulus ma-
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ximo lateri oppoſitus conflabitur ex duobus arcubus duorum ſinuum inuen-
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torum: </
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<
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">Vel certe relinquetur poſt detractionem duorum angulorum inuen-
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torum ex duobus rectis.</
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<
s
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">SI triangulum ſit Iſoſceles, ducenda erit perpendicularis ad baſim, quam
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bifariam ſecabit. </
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<
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xml:space
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">Nam ſi tunc fiat, vt vnum æqualium laterum ad ſinum to-
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tum, ita dimidium baſis ad aliud, reperietur ſinus, cuius arcus complementum
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dabit vnum æqualium angulorum ſupra baſim, ac proinde & </
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<
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<
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tius ex his duobus elicietur.</
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<
s
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">IN æquilatero dabuntur anguli, etiam ſi latera non dentur, cum quilibet
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ſit tertia pars duorum rectorum, vel duæ tertiæ vnius recti.</
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<
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latus, cum
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eius angu-
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lis duobus.</
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<
head
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xml:space
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">12. DATIS duobus lateribus trianguli non
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rectanguli, cum angulo ab ipſis comprehen
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ſo, inuenire tertiũ latus, & reliquos angulos.</
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<
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<
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">SVBDVCTO angulo dato ex duobus rectis, vt aggregatum aliorum
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<
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xml:space
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">Propoſ. 12.
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triang. re-
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ctil.</
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duorum habeatur, inueniatur, per 6. </
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<
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<
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to, & </
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<
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">proportione laterum da torum eis oppoſitorum, (quæ eadem eſt, quæ
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inter ſinus eorum reperitur) vterque eorum. </
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>
<
s
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="
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xml:space
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">Deinde fiat, vt ſinus vtriusvis
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horum angulorum inuẽtorum ad ſinum anguli in principio dati, ita latus in-
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uento angulo, qui in aurea regula acceptus fuerit, oppoſitum ad aliud, inue-
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nieturq́; </
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<
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">tertium latus.</
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<
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<
s
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xml:space
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">QVOD ſi data duo latera ſint æqualia, ablato angulo dato ex duobus
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rectis, dabit ſemiſsis reſidui vtrumque angulorum æqualium: </
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<
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xml:space
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">Et ſi fiat, vt ſi-
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nus vnius illorum ad ſinum anguli dati, ita vnum laterum æqualium ad aliud,
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prodibit tertium latus.</
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</
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<
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duo angu-
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li, cum vno
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latere.</
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<
head
xml:id
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xml:space
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">13. DATIS duobus lateribus trianguli non
<
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rectanguli, cum angulo, qui vni eorum oppo
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nitur, inueſtigare reliquos angulos, & ter-
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tium latus: ſi modo, quando datus angulus
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eſt acutus, conſtet, num angulus alteri </
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