Apian, Petrus
,
Instrvmentvm Sinvvm, sev primi mobilis
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0015
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TABVLARVM SINVVM PER PET. APIANVM.
"/>
<
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<
s
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echoid-s467
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xml:space
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">SEd ut nõnihil degenerali huius inſtrumẽti uſu dicamus, retulerit plurimũ, imò neceſ
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ſariũ fuerit p̃mittere quædã, puta, ꝗd ſit Diameter, quid Chorda, quid etiã Sinus rect 9
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<
emph
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">Diameter</
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>
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<
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& </
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>
<
s
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echoid-s468
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xml:space
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">quid ſituerſus. </
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>
<
s
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xml:space
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">?</
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<
s
xml:id
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echoid-s470
"
xml:space
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">?Diameter ſiue dimetiẽs circuli, eſt linea recta ꝑ eius umbilicum
<
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trãſiens, illum´ in duo æqualia diuidens. </
s
>
<
s
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echoid-s471
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xml:space
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">?</
s
>
<
s
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echoid-s472
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xml:space
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">?Arcus eſt cuiuslibet circuli ſeu periferiæ
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<
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<
emph
style
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portio. </
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>
<
s
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echoid-s473
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">?</
s
>
<
s
xml:id
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echoid-s474
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xml:space
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">?Chorda eſt linea recta ſecãs circulũ in duas portiones inæquales. </
s
>
<
s
xml:id
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echoid-s475
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xml:space
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">?</
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>
<
s
xml:id
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echoid-s476
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xml:space
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">?Sinus
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<
emph
style
="
it
">Chorda.</
emph
>
</
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eſt linea recta, diametro circuli lõgitudine uel potẽtia cõmenſurabilis. </
s
>
<
s
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echoid-s477
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>
<
s
xml:id
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echoid-s478
"
xml:space
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">?Sinus totus
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<
emph
style
="
it
">Sinus.</
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>
</
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ſiue ꝑfectus eſt circuli ſemidiameter in aliquas ꝑtes diuiſa. </
s
>
<
s
xml:id
="
echoid-s479
"
xml:space
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">?</
s
>
<
s
xml:id
="
echoid-s480
"
xml:space
="
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">?Sinus diuiditur in Sinum
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<
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<
emph
style
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">Sinus totus</
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>
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<
emph
style
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">ſiue perfe-</
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>
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<
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style
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>
</
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rectũ ac uerſum. </
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>
<
s
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>
<
s
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xml:space
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">?Sinus rectus ſubdiuidit̃ in primũ & </
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>
<
s
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">ſecũdũ. </
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>
<
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s
>
<
s
xml:id
="
echoid-s485
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xml:space
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">?Sinus rectus pri-
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mus eſt medietas chordæ arcus dupli ad arcũ, cuius eſt ſinus, ſiue dimidiũ chordæ reſpe-
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/>
ctu totius arcus. </
s
>
<
s
xml:id
="
echoid-s486
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">?</
s
>
<
s
xml:id
="
echoid-s487
"
xml:space
="
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">?Sinus uerſus eſt portio diametri à ſinu recto ad periferiã cõprehen
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<
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xlink:label
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<
emph
style
="
it
">Sinus rect
<
emph
style
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">9</
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>
</
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>
<
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/>
<
emph
style
="
it
">dupliater</
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>
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<
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style
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">diuiditur.</
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>
</
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>
ſi, utpote ſagitta arcus. </
s
>
<
s
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s
>
<
s
xml:id
="
echoid-s489
"
xml:space
="
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">?Sinus rectus ſecũdus eſt reſiduũ cuiuslibet arc9 ſubtracti ex
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90. </
s
>
<
s
xml:id
="
echoid-s490
"
xml:space
="
preserve
">ſiue arcus ꝗ reſtat uſ ad cõplementũ quartæ circuli, is ſemper eſt æqualis ꝑti dime
<
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/>
tientis, quæ à cẽtro circuli ad ſinũ rectũ primũ terminatur. </
s
>
<
s
xml:id
="
echoid-s491
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">?</
s
>
<
s
xml:id
="
echoid-s492
"
xml:space
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">?Sector circuli eſt figura
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<
emph
style
="
it
">Sinus uerſ
<
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>
</
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<
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<
emph
style
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it
">quid.</
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>
</
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q̃ continetur à duabus lineis recte à centro ad circumferentiã ductis, necnon ab arcu qui
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<
emph
style
="
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">Sinus rect
<
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style
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>
</
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>
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<
emph
style
="
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">ſecundus.</
emph
>
</
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>
inter illos comprehẽditur. </
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>
<
s
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">Verum hic quo teiſtud celare nolo, ꝙ inſtrumentũ hoc
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oportet eſſe ſatis magnũ, omnino enim q̊ amplius fuerit, eò certius per illud operari pote
<
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<
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<
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="
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">Sector cir-</
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>
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<
emph
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">culi.</
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>
</
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ris. </
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>
<
s
xml:id
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echoid-s494
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xml:space
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">Quamuis ſi uoles, poteris q̊cũ alio numero ad hoc uti, alijs tamẽ cõmodiores ſunt
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numeri, qui unitatẽ habent cũ aliquot nullis 000 &</
s
>
<
s
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">c. </
s
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<
s
xml:id
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echoid-s496
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">quales ſunt 10. </
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<
s
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">100. </
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<
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">1000. </
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<
s
xml:id
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xml:space
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">10000.
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</
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>
<
s
xml:id
="
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">100000 &</
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>
<
s
xml:id
="
echoid-s501
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">c. </
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>
<
s
xml:id
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echoid-s502
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xml:space
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">ſiquidẽ per iſtos operatio nõ paulo redditur facilior in multiplicando pari
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ter & </
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>
<
s
xml:id
="
echoid-s503
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">diuidẽdo. </
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>
<
s
xml:id
="
echoid-s504
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xml:space
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">Diuiſa igitur linea A B in hũc modũ, porrò circinũ altero pede repone
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/>
in A, alte℞ uero extẽde ad ſingula illa pũcta, extẽdens hoc pacto circinũ uſ ad ſemicir
<
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/>
culũ A F B, omnibus deinde illis in eũ circulũ ſinuũ redactis, numeros adſcribe incipien
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/>
do in B ꝑ F uſ ad A, ea´ dicentur puncta ſinus uerſi, quamobrẽ & </
s
>
<
s
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="
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xml:space
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">ſemicirculus ille cir
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culus appellabitur ſinus uerſi. </
s
>
<
s
xml:id
="
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xml:space
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">Deinceps adductis iam punctis iſtis à linea A B uſ in cir
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<
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<
emph
style
="
it
">Vſus huius</
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>
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<
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="
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">ſemiarculi.</
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>
</
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>
culũ A F B, remoueri omnino aut deleri debet linea A B. </
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>
<
s
xml:id
="
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xml:space
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">uniuerſa aũt operatio illa ſatis
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patebit ex ſubiecta figura. </
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>
<
s
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="
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>
<
s
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">?Seꝗtur ita uſus huius ſemicirculi in hunc modum: </
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<
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<
figure
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xlink:href
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number
="
4
">
<
image
file
="
0015-01
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xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0015-01
"/>
</
figure
>
quando ſinũ uerſum ſcire cupis cuiuslibet arcus, filũ in centro A adfixũ
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repone ſuper illũ gradum, & </
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>
<
s
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">ſtatim ubicun filum iſtud ſemicirculum
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AFB attingit, ibi uidebis numerũ unà cũ punctis ſinus illius uerſi. </
s
>
<
s
xml:id
="
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">Vi
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ciſsim cum antea habes puncta ſinus uerſi, & </
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>
<
s
xml:id
="
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xml:space
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">hinc deſideras arcum eius
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cognoſcere, Age filum colloca ſuper illa puncta ſinus uerſi in ſemicir-
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culo AFB, & </
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>
<
s
xml:id
="
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xml:space
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">eo quo filum tanget circulũ AC, ſcilicet limbum exteri
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orem, ibi noris eſſe arcũ illorũ punctorũ ſinus uerſi propoſiti. </
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>
<
s
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="
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">Quod
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ſi & </
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>
<
s
xml:id
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xml:space
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">alte℞ ſemicirculũ AFC cupis in pũcta ſinus recti diuidere, ſemper
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tibi ꝓpone 10. </
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>
<
s
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="
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>
<
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">c. </
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<
s
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xml:space
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">ſecũdũ q̊d plura puncta habes in ſinu per-
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fecto, hoc eſt in tota ſemidiametro AB. </
s
>
<
s
xml:id
="
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xml:space
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">Vt ſi iã lineã AB in 100000.
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</
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>
<
s
xml:id
="
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"
xml:space
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">partes habes diuiſam (nõ ꝙ totidẽ pũcta poſsis in ea conſignare, q̊rũ quodlibet ſignificet
<
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/>
unũ, ſed hoc ſatis eſt, ſi unũquod punctũ deſignet 100. </
s
>
<
s
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="
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">aut 10. </
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<
s
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">aut 5.) </
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<
s
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xml:space
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">& </
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>
<
s
xml:id
="
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">porrò ſinũ re-
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ctum 100000. </
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>
<
s
xml:id
="
echoid-s526
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xml:space
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">punctorũ uis in circulũ AFC conſcribere, & </
s
>
<
s
xml:id
="
echoid-s527
"
xml:space
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">cõprehendere in 100. </
s
>
<
s
xml:id
="
echoid-s528
"
xml:space
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">pun-
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ctis, ita, ꝙ unaquæ diuiſio cõprehendit 1000. </
s
>
<
s
xml:id
="
echoid-s529
"
xml:space
="
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">tũc ſanè ſubtrahe 1000. </
s
>
<
s
xml:id
="
echoid-s530
"
xml:space
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">à toto ſinu qui in
<
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/>
hoc exemplo eſſe debet 100000. </
s
>
<
s
xml:id
="
echoid-s531
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s532
"
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">remanebũt 99000. </
s
>
<
s
xml:id
="
echoid-s533
"
xml:space
="
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">qui ſinus erit uerſus, cuius ſi arcũ
<
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ex ſupra dictis quæras, inuenies 88. </
s
>
<
s
xml:id
="
echoid-s534
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">gra. </
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>
<
s
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="
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">26. </
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>
<
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>
<
s
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="
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">ea ſubtrahe à 90. </
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>
<
s
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="
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xml:space
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">& </
s
>
<
s
xml:id
="
echoid-s539
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xml:space
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">reſidui erũt o. </
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>
<
s
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="
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">gr. </
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>
<
s
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="
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">34. </
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>
<
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="
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<
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/>
minut. </
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>
<
s
xml:id
="
echoid-s543
"
xml:space
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">Iam uero filũ repone ſuper o. </
s
>
<
s
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="
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">gra. </
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>
<
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="
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xml:space
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">& </
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<
s
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>
<
s
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="
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">mi. </
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>
<
s
xml:id
="
echoid-s548
"
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">numerãdo à Buerſus C, & </
s
>
<
s
xml:id
="
echoid-s549
"
xml:space
="
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">in eũ locũ
<
lb
/>
quo tanget circulũ AFC, adponito punctũ 1000. </
s
>
<
s
xml:id
="
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"
xml:space
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">puncta ſinus recti deſignans ex illis
<
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/>
100000. </
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>
<
s
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="
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">pũctis. </
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>
<
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="
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="
preserve
">Quod ſi aũt ſinus totus ſiue perfectus fuerit 10000. </
s
>
<
s
xml:id
="
echoid-s553
"
xml:space
="
preserve
">tũc punctũ illud ſi-
<
lb
/>
gnificat 100. </
s
>
<
s
xml:id
="
echoid-s554
"
xml:space
="
preserve
">rurſus ſi ſit ſinus perfectus 1000. </
s
>
<
s
xml:id
="
echoid-s555
"
xml:space
="
preserve
">punctũ hoc deſignabit 10. </
s
>
<
s
xml:id
="
echoid-s556
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s557
"
xml:space
="
preserve
">ſi fuerit ſinus
<
lb
/>
perfectus 100. </
s
>
<
s
xml:id
="
echoid-s558
"
xml:space
="
preserve
">punctũ iſtud ſignabit unũ tantũ. </
s
>
<
s
xml:id
="
echoid-s559
"
xml:space
="
preserve
">At eo modo operaberis cum ſingulis
<
lb
/>
numeris prædictis, qñ locũ eius in ſemicirculo AFC quæris & </
s
>
<
s
xml:id
="
echoid-s560
"
xml:space
="
preserve
">ſcire deſideras. </
s
>
<
s
xml:id
="
echoid-s561
"
xml:space
="
preserve
">Mihi au
<
lb
/>
tem conſultiſsimũ eſſe uidetur, ſi ſemicirculũ illũ diuidas in 100. </
s
>
<
s
xml:id
="
echoid-s562
"
xml:space
="
preserve
">partes, ſicut hic ſeꝗtur. </
s
>
<
s
xml:id
="
echoid-s563
"
xml:space
="
preserve
">
<
lb
/>
Principio ſemidiametrũ AB diuide in 100. </
s
>
<
s
xml:id
="
echoid-s564
"
xml:space
="
preserve
">partes æquales, adſcribe etiã numeros ſingu
<
lb
/>
larũ partiũ occulte ꝑ quinarios uel denarios retrorſum à B in A at ea pũcta erunt ſinus
<
lb
/>
uerſi, q̃ deinde, modo quo ſupra diximus, transfer cũ circino in ſemicirculũ AFB, adſcri
<
lb
/>
bendo numeros q̊ pari modo ſicut in ſemidiametro AB feciſti. </
s
>
<
s
xml:id
="
echoid-s565
"
xml:space
="
preserve
">Mox pũcta ſimul & </
s
>
<
s
xml:id
="
echoid-s566
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>
