Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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">IN triangulo ABC, cuius angulus C, rectus, dat@
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ſint primum duo arcus AC, CB, circa angulum rectum
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C. </
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">Dico dari quoque tertium arcum AB, cum duobus an-
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gulis A,
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. </
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">Quoniam enim eſt, vt ſinus complementi ar-
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">43. huius.</
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cus
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, ad ſinum complementi arcus AC, ita ſinus com-
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plementi arcus CB, ad ſinum totum; </
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>
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">erit conuertendo, vt
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ſinus totus ad ſinum complementi arcus CB, ita ſinus com
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plementi arcus AC, ad ſinum complementi arcus AB.</
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<
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">QV AMOBREM, datis duobus arcubus rectum angulum ambien
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">Praxis, quã
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do dantut
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duo arcus
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circa angu
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lũ rectum.</
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tibus, ſi fiat, vt ſinus totus ad ſinum complementi vtriuſlibet arcuum
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datorum, ita ſinus complementi alterius arcus dati ad aliud, producetur
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ſinus complementi arcus recto angulo oppoſiti, qui quæritur. </
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<
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tem arcu, quirecto angulo opponitur, cum vtrouis arcu cir ca rectum an-
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gulum, inuenietur angulus ci oppoſitus, vt in probtemate 1. </
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">VTRVM vero quæſitus arcus AB, quadrante minor ſit, aut maior, docebunt
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">35. huius.</
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duo arcus dati, Si enim vter que fuerit minor, aut maior quadrante, erit arcus AB,
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quadrante minor: </
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">alter maior, erit arcus AB,
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quadrante maior.</
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circa angulum rectum, vt cum AC. </
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<
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">Dico rurſum dari reliquum arcum CB, cum
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duobus angulis A, B. </
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<
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xml:space
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">Nam cum ſit, vt ſinus complementi arcus
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">Ab</
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, ad ſinum com-
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<
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plementi arcus AC, ita ſinus complementi arcus
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, ad ſinum totum; </
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<
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tendo, vt ſinus complementi arcus AC, ad ſinum complementi arcus
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, ita ſinus
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totus ad ſinum complementi arcus
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.</
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<
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">QV APROPTER, dato arcu, qui recto angulo opponitur, cum
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">Praxis, quã
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do datur
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arcus recto
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angulo op-
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poſitus, cũ
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alterutro
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circa angu
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lũ rectum.</
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alterutro arcuum circa angulum rectum, ſi ſiat, vt ſinus complementi ar-
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cus dati circa angulum rectum ad ſinum complementi arcus angulo recto
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oppoſiti, ita ſinus totus ad aliud, inuenietur ſinus complementi alterius
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arcus circa angulum rectum, qui quæritur. </
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<
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cir ca rectum angulum, cum arcu, quirecto angulo opponitur, reperietur
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angulus illi arcui oppoſitus, vt in problemate 1. </
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tum est.</
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<
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">AN vero tertius arcus CB, quæſitus ſit quadrante minor, aut maior, intellige-
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mus ex duobus arcubus datis. </
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<
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, angulo recto oppoſitus fuerit
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quadrante minor, ſi quidem & </
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CB, quadrante minor; </
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<
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">CB, maior qua-
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<
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drante. </
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, fuerit quadrante maior, ſi quidem & </
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<
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C, ſit quadrante
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maior, erit CB, quadrante minor; </
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<
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quadrante maior.</
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<
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demonſtra
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tur de triã-
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gulo ſphæ.</
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