Theodosius <Bithynius>; Clavius, Christoph - Theodosii Tripolitae Sphaericorum libri tres

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191179

PRAETEREA, cum latus trianguli æquilateri in circulo deſcripti ſit
1112. tertij-
dec. potentia triplum ſemidiametri eiuſdem circuli, efficitur, vt quadratum ſe-
midiametri triplicatum det quadratum lateris triãguli 300000000000000. cu-
ius radix quadrata idem latus exhibebit partium 17320508.

SIT inſuper AB, ſemidiameter circuli cuiuſuis, qua diuiſa ſecundum ex-
2230.ſexti. tremam ac mediam rationem

141[Figure 141] in C, vt maius ſegmentum ſit
BC; producta autem AB, &
abſciſſa BD, quæ maiori ſeg-
mento BC, ſit æqualis; erit
quoq; AD, in B, diuiſa ſecundum extremam ac mediam rationem, maiusq́;
335. terrijdec.
coroll. 15.6
Schol. 9. 13 ſegmentum erit AB: quod cum ſit latus hexagoni in circulo, cuius ſemidia-
meter AB; erit BD, latus decagoni in eodem circulo. Quod hac ratione
notum efficietur. Secta AB, bifariam in E, erit quadratum rectæ DE, com-
poſitæ ex minori ſegmento DB, & dimidio BE, maioris ſegmenti BA, quin-
443. tertijdec. tuplum quadrati rectæ BE, quæ cognita eſt, cum ſit ſemiſsis ſemidiametri
AB, ac proinde partium 5000000. Quare ſi quadratum rectæ BE, quincupli-
cetur, fiet quadratum rectæ DE, 125000000000000. cuius radix quadrata
dabit rectam DE, partium 11180340. ex qua ſi dematur recta BE, partium
5000000. reliquum erit BD, latus decagoni partium 6180340.

POSTREMO, quoniam pentagoni latus poteſt & latus hexagoni, &
5510. tertij-
dec. latus decagoni; ſi quadratum lateris hexagoni 100000000000000. & quadra-
tum lateris decagoni 38196602515600. ſimul componantur, fiet quadratum
lateris pentagoni 138196602515600. cuius radix quadrata dabit latus pen-
tagoni partium 11755705. Atq; ita latera trianguli æquilateri, quadrati, pen
tagoni, hexagoni, & decagoni nota facta ſunt in partibus diametri circuli, in
quo deſcribuntur. Ex data igitur circuli diametro quotlibet particularum,
latera trianguli æquilateri, quadrati, & c. inueſtigauimus. Quod erat fa-
ciendum.

PROBL. 5. PROP. 13.

66Qua ratio-
ne ex dua-
buschordis
cognitis in
ueſtigetur
chorda dif-
ferentiæ,
qua arcus
chordarũ
datarũ in-
ter ſe diffe
runt.

EX datis chordis duorum arcuũ inæqualium
chordam arcus, quo maior arcus minorem ſupe-
rat, inquirere.

IN ſemicirculo ABCD, ſint datæ chordæ AB, AC, & BC, ſit chorda
arcus BC, quo maior arcus AC, minorem AB, ſuperat: oporteatq́; inqui-
rere chordã BC. Ductis rectis BD, CD; quoniam
773. huius.

142[Figure 142] chordæ AB, AC, ponuntur notæ, notæ quoque
erunt chordæ BD, CD. Rectangulum ergo ſub
datis rectis AB, CD, comprehenſum, notum erit:
Itemrectangulum ſub datis rectis AC, BD. Eſt
autem rectangulum ſub rectis, AC, BD, æquale
8811.huius. duobus rectangulis ſub AB, CD, & ſub BC, AD.
Ablato ergo rectangulo noto ſub AB, CD, ex
rectangulo ſub AC, BD, notum ſiet reliquum rectangulum ſub BC, AD.

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