Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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cunferentiam, angulus D, anguli I, duplus eſt; </
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<
s
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xml:space
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">erit quoque idem angulus D,
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<
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xlink:label
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xlink:href
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anguli CAH, duplus: </
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<
s
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xml:space
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">ac proinde angulus CAH, ſemiſsis erit anguli D, qui
<
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complementum eſt anguli DAC. </
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<
s
xml:id
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xml:space
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">Cum ergo CH, tangens ſit anguli CAH,
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ſitq́; </
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<
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xml:space
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">DA, recta rectæ DH, ex defin. </
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<
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xml:space
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">circuli, æqualis: </
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<
s
xml:id
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xml:space
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">liquido conſtat, ſecan-
<
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tem AD, arcus CE, æqualem eſſe tangenti CD, eiuſdem arcus, vnà cum CH,
<
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tangente ſemiſsis complementi arcus CE, ſeu anguli CAD. </
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>
<
s
xml:id
="
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xml:space
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">Quapropter Se-
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cans cuiuſuis arcus æqualis eſt tangenti eiuſdẽ, &</
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<
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xml:space
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">c. </
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<
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xml:space
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<
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<
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<
s
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">EX preximis duobus theorematibus mirificum nobis compendium ſuppeditatur ad
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<
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xlink:label
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xml:space
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">Compédl @
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mirificum
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pro cóſtru-
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ctione tabu
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læ tam tan
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gentium, q̃
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ſecantium.</
note
>
tabulam tam Tangentium, quàm Secantium conſtruendam. </
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>
<
s
xml:id
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xml:space
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">Nam ſiper ea, quæ pro-
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poſ. </
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<
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">18. </
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<
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">eiuſq́; </
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<
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xml:space
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">ſcholio præcepim{us}, tangentes omnium arcuum per ſingula minuta ex-
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tenſorum vſque ad ſemiſſem quadrantis, ſecantes vero omnium arcuum totius qua-
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drantis inquiramus; </
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>
<
s
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="
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xml:space
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">inueniemus earum beneficio per ſolam additionem tangentes
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aliorum arcuum, vſque ad arcum grad 67. </
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>
<
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xml:space
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">Min. </
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<
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">30 ſi nimirum tangentem, & </
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>
<
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tem cuiuſq; </
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<
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xml:space
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">arcus minoris ſemiſſe quadrantis, qui minuta numero paria contineat, in
<
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vnam ſummá colligamus: </
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>
<
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xml:id
="
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xml:space
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">propterea quòd tangens cuiuſuis arc{us} maioris ſemiſſe qua-
<
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<
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position
="
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xlink:label
="
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xlink:href
="
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xml:space
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">19. huius.</
note
>
drantis æqualis eſt tangenti, ac ſecanti arcus, qui duplus ſit exceſſus, quo datus arcus
<
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ſemiſſem quadrantis ſuperat; </
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>
<
s
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="
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xml:space
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>
<
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</
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<
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<
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">vt arcus Min. </
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<
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xml:space
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">2. </
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>
<
s
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xml:space
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">Min. </
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<
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xml:id
="
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xml:space
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">4. </
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>
<
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xml:space
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">Min. </
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<
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xml:space
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">6. </
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<
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">&</
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<
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">c. </
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<
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xml:space
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">Exempli cauſa. </
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<
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gra. </
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<
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">45. </
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<
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">Min. </
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>
<
s
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="
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xml:space
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">1 colligemus in vnam ſummam tangentem 5818. </
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>
<
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xml:space
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">& </
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>
<
s
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">ſecantẽ 10000002. </
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<
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">
<
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arcus Min. </
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>
<
s
xml:id
="
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xml:space
="
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">2 qui duplus eſt arcus Min. </
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>
<
s
xml:id
="
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"
xml:space
="
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">1. </
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>
<
s
xml:id
="
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xml:space
="
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">quo datus arcus grad. </
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>
<
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">45 Min. </
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<
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xml:space
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">1. </
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<
s
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">ſemißem quæ
<
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drantis, hoc eſt, arcũ grad. </
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<
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">45 ſuperat. </
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<
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xml:space
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">Numerus enim cõſlatus 10005820. </
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>
<
s
xml:id
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xml:space
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">dabit tã-
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gentẽ propoſiti arcus grad. </
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<
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xml:space
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<
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xml:id
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<
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xml:id
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xml:space
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">1. </
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>
<
s
xml:id
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xml:space
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<
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Min. </
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<
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<
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<
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<
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<
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<
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>
<
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<
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">1. </
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>
<
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<
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2. </
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<
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<
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xml:id
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xml:space
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">ſemiſſe cõplemẽti eiuſdẽ arcus, quod cõplectitur grad. </
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<
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<
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xml:id
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<
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<
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cu Min. </
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<
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<
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xml:space
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<
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<
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<
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<
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<
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mus, numerus 10005820. </
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<
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>
<
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gentem dicti arcus compoſiti ex arcu Min. </
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<
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<
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xml:space
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<
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xml:space
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</
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<
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<
s
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">EADEM ratione tangens cuiuſuis arcus mauris ſemiſſe quadrantis compone-
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tur ex tangẽte, & </
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>
<
s
xml:id
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xml:space
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">ſecante arcus, qui duplus ſit exceſſus, quo arcus ille ſemiſſem qua-
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drantis ſuperat. </
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>
<
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xml:id
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xml:space
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">Item ſi in vnam ſummã colligantur tangens, & </
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<
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xml:id
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">ſecans cuiuſuis ar-
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cus minoris ſemiſſe quadrátis, conſlabitur tàgens arcus cõpoſiti ex illo arcu, & </
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>
<
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ſe complementi eiuſdem. </
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<
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<
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xml:id
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">arcus grad. </
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>
<
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<
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xml:space
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">8. </
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>
<
s
xml:id
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xml:space
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">compoſita eſt
<
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ex tangente 3692500. </
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>
<
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xml:id
="
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xml:space
="
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">& </
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>
<
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="
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">ſecante 10659951. </
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>
<
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xml:id
="
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xml:space
="
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">arcus grad. </
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>
<
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xml:id
="
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xml:space
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">20 Min. </
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>
<
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xml:id
="
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"
xml:space
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">16. </
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>
<
s
xml:id
="
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"
xml:space
="
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">qui duplus eſt
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arcus grad. </
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>
<
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xml:id
="
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xml:space
="
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">10. </
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>
<
s
xml:id
="
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"
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="
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">Min. </
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>
<
s
xml:id
="
echoid-s8027
"
xml:space
="
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">8. </
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>
<
s
xml:id
="
echoid-s8028
"
xml:space
="
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">quo datus arcus grad. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">55 Min. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">8. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">quadrantis ſemiſſem ſuperat.
<
lb
/>
</
s
>
<
s
xml:id
="
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"
xml:space
="
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">Item ſi tangens 3692500. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">& </
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>
<
s
xml:id
="
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xml:space
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">ſecans 10659951. </
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>
<
s
xml:id
="
echoid-s8035
"
xml:space
="
preserve
">arcus grad. </
s
>
<
s
xml:id
="
echoid-s8036
"
xml:space
="
preserve
">20. </
s
>
<
s
xml:id
="
echoid-s8037
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s8038
"
xml:space
="
preserve
">16. </
s
>
<
s
xml:id
="
echoid-s8039
"
xml:space
="
preserve
">in vnam
<
lb
/>
ſummam colligantur, conſlabitur tangens 14352451. </
s
>
<
s
xml:id
="
echoid-s8040
"
xml:space
="
preserve
">arcus grad 55. </
s
>
<
s
xml:id
="
echoid-s8041
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s8042
"
xml:space
="
preserve
">8. </
s
>
<
s
xml:id
="
echoid-s8043
"
xml:space
="
preserve
">comſoſi-
<
lb
/>
ti ex illo arcu grad. </
s
>
<
s
xml:id
="
echoid-s8044
"
xml:space
="
preserve
">20. </
s
>
<
s
xml:id
="
echoid-s8045
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s8046
"
xml:space
="
preserve
">16. </
s
>
<
s
xml:id
="
echoid-s8047
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s8048
"
xml:space
="
preserve
">ſemiſſe complementi eiuſdem, nempe ex arcu grad. </
s
>
<
s
xml:id
="
echoid-s8049
"
xml:space
="
preserve
">
<
lb
/>
34. </
s
>
<
s
xml:id
="
echoid-s8050
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s8051
"
xml:space
="
preserve
">52. </
s
>
<
s
xml:id
="
echoid-s8052
"
xml:space
="
preserve
">cum complementũ arcus grad. </
s
>
<
s
xml:id
="
echoid-s8053
"
xml:space
="
preserve
">20. </
s
>
<
s
xml:id
="
echoid-s8054
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s8055
"
xml:space
="
preserve
">16. </
s
>
<
s
xml:id
="
echoid-s8056
"
xml:space
="
preserve
">cõprehendat grad. </
s
>
<
s
xml:id
="
echoid-s8057
"
xml:space
="
preserve
">69. </
s
>
<
s
xml:id
="
echoid-s8058
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s8059
"
xml:space
="
preserve
">44.</
s
>
<
s
xml:id
="
echoid-s8060
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s8061
"
xml:space
="
preserve
">
<
emph
style
="
sc
">ITAQVe</
emph
>
propoſito arcu quocunque, qui maior ſit quadrantis dimidio, ſi ex
<
lb
/>
eo detrahatur ſemiſsis quadrantis, id eſt, arcus grad. </
s
>
<
s
xml:id
="
echoid-s8062
"
xml:space
="
preserve
">45. </
s
>
<
s
xml:id
="
echoid-s8063
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s8064
"
xml:space
="
preserve
">reliqui arcus ſumatur
<
lb
/>
duplus, component tangens & </
s
>
<
s
xml:id
="
echoid-s8065
"
xml:space
="
preserve
">ſecans huius dupli arcus ſumpti tangentem propoſiti
<
lb
/>
illius arcus. </
s
>
<
s
xml:id
="
echoid-s8066
"
xml:space
="
preserve
">Vt ſi quæratur tangens arcus grad. </
s
>
<
s
xml:id
="
echoid-s8067
"
xml:space
="
preserve
">55. </
s
>
<
s
xml:id
="
echoid-s8068
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s8069
"
xml:space
="
preserve
">8. </
s
>
<
s
xml:id
="
echoid-s8070
"
xml:space
="
preserve
">detrahendi erunt grad.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s8071
"
xml:space
="
preserve
">45. </
s
>
<
s
xml:id
="
echoid-s8072
"
xml:space
="
preserve
">ex eo, & </
s
>
<
s
xml:id
="
echoid-s8073
"
xml:space
="
preserve
">reliqui arcus grad. </
s
>
<
s
xml:id
="
echoid-s8074
"
xml:space
="
preserve
">10. </
s
>
<
s
xml:id
="
echoid-s8075
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s8076
"
xml:space
="
preserve
">8. </
s
>
<
s
xml:id
="
echoid-s8077
"
xml:space
="
preserve
">ſumendus duplus arcus grad. </
s
>
<
s
xml:id
="
echoid-s8078
"
xml:space
="
preserve
">20. </
s
>
<
s
xml:id
="
echoid-s8079
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>