Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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areus proxime minoris, vt fiat ſinus propositi arcus? </
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<
s
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xml:space
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pottionalẽ</
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pars proportionalis, quæ ſi addatur ſinui arcus proxime minoris, efficietur ſinus re-
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ctus arcus propoſiti. </
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<
s
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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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<
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ferentiam _2721_. </
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<
s
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">inter ſinum _3537469_. </
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<
s
xml:id
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echoid-s5835
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">arcus grad. </
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<
s
xml:id
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echoid-s5836
"
xml:space
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">_20_. </
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<
s
xml:id
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echoid-s5837
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xml:space
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">_M_in. </
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<
s
xml:id
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echoid-s5838
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xml:space
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">_43_. </
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<
s
xml:id
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xml:space
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">proxime minoris,
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& </
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<
s
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">ſinum _3540190_. </
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<
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xml:space
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">arcus grad. </
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<
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xml:space
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<
s
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xml:space
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<
s
xml:id
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echoid-s5844
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<
s
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<
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<
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<
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vequirunt differentiam _2721_. </
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<
s
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">addendam ſinui _3537469_. </
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<
s
xml:id
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echoid-s5850
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">arcus grad. </
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<
s
xml:id
="
echoid-s5851
"
xml:space
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<
s
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</
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<
s
xml:id
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xml:space
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<
s
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xml:space
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">arcus grad. </
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<
s
xml:id
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echoid-s5855
"
xml:space
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">_20_. </
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<
s
xml:id
="
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xml:space
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<
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echoid-s5857
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xml:space
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<
s
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echoid-s5858
"
xml:space
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">quantam differentiam poſtu-
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lant _20_. </
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<
s
xml:id
="
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xml:space
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">ſecunda addendam eidem ſinui _3537469_. </
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<
s
xml:id
="
echoid-s5860
"
xml:space
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">arcus grad. </
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<
s
xml:id
="
echoid-s5861
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xml:space
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">_20_. </
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<
s
xml:id
="
echoid-s5862
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xml:space
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">_M_in. </
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<
s
xml:id
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echoid-s5863
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xml:space
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<
s
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xml:space
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ſinus arcus grad. </
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<
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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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<
s
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xml:space
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portionalem _907_. </
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<
s
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">quæ addita ſinui _3537469_. </
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<
s
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">efficiet _3538376_. </
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<
s
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xml:space
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">ſinum arcus grad. </
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>
<
s
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">_20_. </
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<
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_M_in. </
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<
s
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xml:space
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>
<
s
xml:id
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echoid-s5877
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xml:space
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s
>
<
s
xml:id
="
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xml:space
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">_C_ommuniter tamen ab _A_ſtronomis negliguntur in hoc negotio _S_e-
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<
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xlink:label
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">Secũda cõl
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ter ĩttacta
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tione ſinuũ
<
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negligũ tut
<
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ab Aſtrone
<
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mis.</
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>
cunda, ſi pauciora ſunt, quàm _30._ </
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<
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xml:space
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">_S_i vero pl@ra, addunt proillis vnum minutum
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alijs _M_inutis. </
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<
s
xml:id
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<
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<
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dato arcugrad. </
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<
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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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xml:space
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">_20._ </
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<
s
xml:id
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xml:space
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">accipiunt ſinum arcus grad. </
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<
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<
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<
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xml:id
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<
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glectis illis _20_ ſec. </
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<
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<
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xml:id
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<
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xml:id
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<
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<
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">_48._ </
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<
s
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xml:space
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">ſumunt ſinum arcus grad.
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</
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<
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xml:id
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<
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xml:id
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<
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">_44._ </
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<
s
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">computatis illis _48._ </
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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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">arcus ſemicirculo maioris, non eſt quòd ſinus rectus
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<
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xlink:label
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note-181-03a
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">Semicircu-
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li, & arcꝰ ſe
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micirculo
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maioris, nõ
<
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eſt ſinus re
<
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ctus inqui-
<
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rendus; im-
<
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mo nullus
<
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eft eorũ ſi-
<
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nus rectus.</
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>
inueſtigetur, cùm nunquam in ſupputationibus _A_ſtronomicis buiuſmodi arcuum ſi-
<
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nus adbibeantur, quod ijs perſptcuum eſt, qui in triangulis rectilineis, ac ſphæri-
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cis, in quibus tota _S_inuum ſcientia verſatur, ſunt exercitati. </
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<
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xml:space
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">_I_mmo ſemicirculus
<
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nullum habet ſinum, vt ex vtraq; </
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<
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xml:space
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">defin. </
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<
s
xml:id
="
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xml:space
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">ſinus recti patet. </
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>
<
s
xml:id
="
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"
xml:space
="
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">quod etiam de arcu ma-
<
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iore dici poteſt, niſi quis in prima figura definitionum rectam _FK,_ ſinum rectum velit
<
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/>
appellare arcus _DBF_, ſecundum poſteriorem defin. </
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>
<
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xml:id
="
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">ſinus recti; </
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>
<
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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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">rectam _FH_, ſinum
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rectum arcus _
<
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style
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>
_. </
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<
s
xml:id
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xml:space
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">quod non videturproprie dici, cum huiuſmodi lineis prior defi-
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nitio ſinus recti nullo modo conuenire poſsit, vt ex eadem figura perſpicuum eſt.
<
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</
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<
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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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">Sinus com
<
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plemẽti ar-
<
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cus quadrã
<
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te minoris
<
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quomodo
<
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/>
i tabula re
<
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periatur.</
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>
</
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</
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<
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<
s
xml:id
="
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xml:space
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">_QVANDO_ autemdati arcus _Q_uadrante minoris ſinum complementi quæris, cape
<
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gradus illius in in feriori parte tabulæ, _M_inuta vero ad dexteram. </
s
>
<
s
xml:id
="
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xml:space
="
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">_I_n communi enim
<
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angulo continuò ſinum complementireperies, hoc eſt, ſinum rectum illius arcus, qui
<
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/>
dati arcus complementum eſt. </
s
>
<
s
xml:id
="
echoid-s5919
"
xml:space
="
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">_N_am ſinus ille rectus debetur arcui, cuius gradus in
<
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vertice tabulæ, & </
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>
<
s
xml:id
="
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"
xml:space
="
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">minuta in ſiniſtro latere collocantur, qui quidem dati arcus com-
<
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plementum eſt, vt ſupra diximus. </
s
>
<
s
xml:id
="
echoid-s5921
"
xml:space
="
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">_I_ta ſinum complementi arcus grad. </
s
>
<
s
xml:id
="
echoid-s5922
"
xml:space
="
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">_30_. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">ſupra
<
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grad. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">_30._ </
s
>
<
s
xml:id
="
echoid-s5925
"
xml:space
="
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">infimi lateris tabulæ è regione _M_inuti _0._ </
s
>
<
s
xml:id
="
echoid-s5926
"
xml:space
="
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">ad dextram collocati inuenies
<
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/>
_8660254_. </
s
>
<
s
xml:id
="
echoid-s5927
"
xml:space
="
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">qui quidem ſinus rectus eſt arcus grad. </
s
>
<
s
xml:id
="
echoid-s5928
"
xml:space
="
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">_59_. </
s
>
<
s
xml:id
="
echoid-s5929
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xml:space
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">_M_in. </
s
>
<
s
xml:id
="
echoid-s5930
"
xml:space
="
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">_60_. </
s
>
<
s
xml:id
="
echoid-s5931
"
xml:space
="
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">hoc eſt, arcus grad.
<
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/>
</
s
>
<
s
xml:id
="
echoid-s5932
"
xml:space
="
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">_60_. </
s
>
<
s
xml:id
="
echoid-s5933
"
xml:space
="
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">qui complementum eſt arcus grad. </
s
>
<
s
xml:id
="
echoid-s5934
"
xml:space
="
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">_30_. </
s
>
<
s
xml:id
="
echoid-s5935
"
xml:space
="
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">_I_tem ſinum complementi arcus grad. </
s
>
<
s
xml:id
="
echoid-s5936
"
xml:space
="
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">_30_. </
s
>
<
s
xml:id
="
echoid-s5937
"
xml:space
="
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">
<
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/>
_M_in. </
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>
<
s
xml:id
="
echoid-s5938
"
xml:space
="
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">_49_. </
s
>
<
s
xml:id
="
echoid-s5939
"
xml:space
="
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">reperies _8588110_. </
s
>
<
s
xml:id
="
echoid-s5940
"
xml:space
="
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">qui quidem sinus rectus eſt arcus grad. </
s
>
<
s
xml:id
="
echoid-s5941
"
xml:space
="
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">_59._ </
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>
<
s
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="
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"
xml:space
="
preserve
">_M_in. </
s
>
<
s
xml:id
="
echoid-s5943
"
xml:space
="
preserve
">_11._ </
s
>
<
s
xml:id
="
echoid-s5944
"
xml:space
="
preserve
">qui
<
lb
/>
complementum eſt arcus grad. </
s
>
<
s
xml:id
="
echoid-s5945
"
xml:space
="
preserve
">_30_. </
s
>
<
s
xml:id
="
echoid-s5946
"
xml:space
="
preserve
">_M_in. </
s
>
<
s
xml:id
="
echoid-s5947
"
xml:space
="
preserve
">_49_. </
s
>
<
s
xml:id
="
echoid-s5948
"
xml:space
="
preserve
">_S_i vero offeratur arcus _Q_uadrante
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-181-05
"
xlink:href
="
note-181-05a
"
xml:space
="
preserve
">Sinus cõple
<
lb
/>
mẽti cuiuſ
<
lb
/>
uis arcꝰ qua
<
lb
/>
drãte maio
<
lb
/>
ris, qua arte
<
lb
/>
deprehen -
<
lb
/>
datur.</
note
>
maior, ſed ſemicirculo minor, ita ſinum complementi ipſius reperies. </
s
>
<
s
xml:id
="
echoid-s5949
"
xml:space
="
preserve
">_D_etrabe ex eo
<
lb
/>
quadrantem, & </
s
>
<
s
xml:id
="
echoid-s5950
"
xml:space
="
preserve
">reſidui arcus ſinum rectum cape. </
s
>
<
s
xml:id
="
echoid-s5951
"
xml:space
="
preserve
">_C_um enim reliquus hic arcus ſit
<
lb
/>
complementum dati arcus, vt in definitionibus dictum eſt, erit eius ſinus rectus, ſinus
<
lb
/>
complementi dati arcus. </
s
>
<
s
xml:id
="
echoid-s5952
"
xml:space
="
preserve
">_V_t ſi oblatus ſit arcus grad. </
s
>
<
s
xml:id
="
echoid-s5953
"
xml:space
="
preserve
">_127_. </
s
>
<
s
xml:id
="
echoid-s5954
"
xml:space
="
preserve
">_M_in. </
s
>
<
s
xml:id
="
echoid-s5955
"
xml:space
="
preserve
">_30._ </
s
>
<
s
xml:id
="
echoid-s5956
"
xml:space
="
preserve
">_D_etrabe ex eo
<
lb
/>
quadrantem, hoc eſt, _90._ </
s
>
<
s
xml:id
="
echoid-s5957
"
xml:space
="
preserve
">gradus. </
s
>
<
s
xml:id
="
echoid-s5958
"
xml:space
="
preserve
">_S_inus namque rectus _6087614._ </
s
>
<
s
xml:id
="
echoid-s5959
"
xml:space
="
preserve
">reliqui arcus grad.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s5960
"
xml:space
="
preserve
">_37._ </
s
>
<
s
xml:id
="
echoid-s5961
"
xml:space
="
preserve
">_M_in. </
s
>
<
s
xml:id
="
echoid-s5962
"
xml:space
="
preserve
">_30._ </
s
>
<
s
xml:id
="
echoid-s5963
"
xml:space
="
preserve
">eſt ſinus complementi dati arcus grad. </
s
>
<
s
xml:id
="
echoid-s5964
"
xml:space
="
preserve
">_127._ </
s
>
<
s
xml:id
="
echoid-s5965
"
xml:space
="
preserve
">_M_in. </
s
>
<
s
xml:id
="
echoid-s5966
"
xml:space
="
preserve
">_30._ </
s
>
<
s
xml:id
="
echoid-s5967
"
xml:space
="
preserve
">cumille arcus ſit
<
lb
/>
buius complementum. </
s
>
<
s
xml:id
="
echoid-s5968
"
xml:space
="
preserve
">
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-181-06
"
xlink:href
="
note-181-06a
"
xml:space
="
preserve
">Sinꝰ cõple-
<
lb
/>
mẽti cuiuſ
<
lb
/>
uis arcꝰ ha
<
lb
/>
bẽtis Secũ-
<
lb
/>
da, p̃ter Mi
<
lb
/>
nuta, quo</
note
>
</
s
>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s5969
"
xml:space
="
preserve
">_QVOD_ ſi datus arcus præter gradus, ac _M_inuta habeat etiã _S_ecunda; </
s
>
<
s
xml:id
="
echoid-s5970
"
xml:space
="
preserve
">ſi quidem
<
lb
/>
_Q_uadrante minor ſit, inueſtigabis eius ſinum complementi per regulam proportio-
<
lb
/>
num, quemadmodum ſupra de ſinu recto diximus, niſi quòd hic differentia inuenta,
<
lb
/>
ſiue pars proportionalis ſubtrahenda eſt à ſinu arcus proxime minoris, _S_i vero </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>