Clavius, Christoph
,
Geometria practica
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101 - 110
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151 - 160
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41
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071
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71
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LIBER PRIMVS.
"/>
<
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<
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<
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style
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">Qvando</
emph
>
particula minor cum vno gradu repetita incidit in gradum ali-
<
lb
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quem præcisè, auferendi erunt ex gradibus percurſis tot gradus, quoties parti-
<
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/>
cula illa cum vno gradurepetita fuit. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Reliquus enim numerus erit Numerator
<
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/>
fractionis: </
s
>
<
s
xml:id
="
echoid-s1588
"
xml:space
="
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">Denominator autem erit, qui prius. </
s
>
<
s
xml:id
="
echoid-s1589
"
xml:space
="
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">Vtſi particula illa minor cum
<
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1. </
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>
<
s
xml:id
="
echoid-s1590
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xml:space
="
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">gradu repetita ſepties inciditin 10. </
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>
<
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xml:space
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">gradum; </
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>
<
s
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xml:space
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">demendi erunt 7. </
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>
<
s
xml:id
="
echoid-s1593
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xml:space
="
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">gradus repetiti.
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</
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>
<
s
xml:id
="
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xml:space
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">Atq; </
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>
<
s
xml:id
="
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"
xml:space
="
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">ita habebuntur iterum {3/7}. </
s
>
<
s
xml:id
="
echoid-s1596
"
xml:space
="
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">vnius gradus in data particula.</
s
>
<
s
xml:id
="
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"
xml:space
="
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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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">13. </
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<
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<
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style
="
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">Si</
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>
viciſsim ex quouis gradu auferre velimus particulam quotlibet mi-
<
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<
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position
="
right
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xlink:label
="
note-071-01
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xlink:href
="
note-071-01a
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xml:space
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">Quo pacto ex
<
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quouis gradu
<
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particula quot
<
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libet Minuto-
<
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/>
rum abſcin-
<
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/>
datur.</
note
>
nutorum, ita agendum erit. </
s
>
<
s
xml:id
="
echoid-s1600
"
xml:space
="
preserve
">In quadrante ſuperiore B C, accipiatur circino arcus
<
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/>
tot graduum, quot minuta deſiderantur; </
s
>
<
s
xml:id
="
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xml:space
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">atq; </
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>
<
s
xml:id
="
echoid-s1602
"
xml:space
="
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">(vt confuſionem vitemus) in ar-
<
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/>
cuminteruallo ſemidiametri quadrantis B C, deſcriptum transferatur. </
s
>
<
s
xml:id
="
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xml:space
="
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">Si enim
<
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hic arcus in 60. </
s
>
<
s
xml:id
="
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xml:space
="
preserve
">partes æquales ſecetur, (primum, videlicet in duas: </
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>
<
s
xml:id
="
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xml:space
="
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">deinde vna
<
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harũ iterum in duas: </
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>
<
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xml:id
="
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xml:space
="
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">Tertio vna harũ in tres; </
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>
<
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xml:id
="
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xml:space
="
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">ac poſtremo vna harũ in quinq;)
<
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/>
</
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">cõtinebit vna particula ſexageſima numerum minutorum propoſitũ. </
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>
<
s
xml:id
="
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xml:space
="
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">Verbigra-
<
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tia, ſi particula quæratur continens 50. </
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>
<
s
xml:id
="
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"
xml:space
="
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">min. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">accipiemus in arcu F G, adinterual-
<
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/>
lum ſemidiametri A C, deſcripto arcum F G, arcui C Z, graduum 50. </
s
>
<
s
xml:id
="
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xml:space
="
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">æqualem,
<
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/>
eumque in 60. </
s
>
<
s
xml:id
="
echoid-s1613
"
xml:space
="
preserve
">partes æquales ſecabimus, primum in duas in puncto K: </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Deinde
<
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/>
arcum F K, iterum in duas in puncto L; </
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>
<
s
xml:id
="
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xml:space
="
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">tertio arcum F L, in tres in punctis T, V. </
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>
<
s
xml:id
="
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xml:space
="
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">
<
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/>
ac tandem arcum F V, in quinque. </
s
>
<
s
xml:id
="
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xml:space
="
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">Vna namque harum 5. </
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>
<
s
xml:id
="
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"
xml:space
="
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">particularum compre-
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hendet 50. </
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>
<
s
xml:id
="
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xml:space
="
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">min. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">ac proinde ſi transferatur circino in quemlibet gradum Quadrã-
<
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tis B C, abſciſſa erunt 50. </
s
>
<
s
xml:id
="
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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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">ex eo gradu. </
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>
<
s
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="
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="
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">Hoc ita demonſtro. </
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>
<
s
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="
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xml:space
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">Quoniam eſt,
<
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vt arcus 60. </
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>
<
s
xml:id
="
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="
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">graduum ad 1. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">gradum, ita arcus C Z, vel F G, graduum 50. </
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>
<
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xml:id
="
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="
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">ad ſexa-
<
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geſimam partem eiuſdem arcus F G; </
s
>
<
s
xml:id
="
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xml:space
="
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">erit permutando, vt arcus 60. </
s
>
<
s
xml:id
="
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xml:space
="
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">graduum ad
<
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/>
arcum F G, graduum 50; </
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>
<
s
xml:id
="
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xml:space
="
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">ita 1. </
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>
<
s
xml:id
="
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xml:space
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">gradus ad ſexageſimam particulam arcus F G: </
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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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conuertendo, vt arcus F G, graduum 50. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">ad arcum graduum 60. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">ita particula ſe-
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xageſima arcus F G, ad 1. </
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<
s
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xml:space
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">gradum. </
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>
<
s
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="
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xml:space
="
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">Cum ergo arcus F G, contineat {50/60}, arcus 60. </
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<
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<
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graduum, continebit quoq; </
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>
<
s
xml:id
="
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xml:space
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">particula ſexageſima arcus F G, {50/60}. </
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>
<
s
xml:id
="
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xml:space
="
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">vnius gradus,
<
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hoc eſt, 50. </
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>
<
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xml:id
="
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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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">Quod eſt propoſitum.</
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</
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<
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<
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<
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style
="
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">Sed</
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>
hæcres incommodiſsima eſt in paruis Quadrantibus, præſertim ſi pau-
<
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ca Minuta, vtpote 1. </
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>
<
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<
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<
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">abſcindenda ſint. </
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>
<
s
xml:id
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xml:space
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">Quis enimin Quadrante exiguo
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arcum 1. </
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>
<
s
xml:id
="
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xml:space
="
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">gradus, vel 2. </
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>
<
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xml:id
="
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">vel 3. </
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>
<
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">in 60. </
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>
<
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xml:space
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">particulas diſtribuat? </
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>
<
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xml:id
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"
xml:space
="
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">Quamobrem commo-
<
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diusid, quod proponitur, efficiemus hacratione. </
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>
<
s
xml:id
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xml:space
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">Ex eo dem quadranteſupe-
<
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<
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="
hd-071-1
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xlink:href
="
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number
="
34
"/>
<
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="
hd-071-1
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xlink:href
="
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number
="
35
"/>
<
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xlink:label
="
hd-071-1
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xlink:href
="
hd-071-1a
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number
="
36
"/>
riore B C, arcus grad. </
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>
<
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">61. </
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>
<
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="
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xml:space
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">transferatur in arcum X Y, ad interuallum ſemidiame-
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tri A C. </
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>
<
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xml:space
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">deſcriptum, ab X, vſque ad Y. </
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>
<
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xml:id
="
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xml:space
="
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">Atque hic arcus X Y, in 6
<
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style
="
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">0</
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>
. </
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>
<
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xml:id
="
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xml:space
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">partes æquales
<
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ſecetur; </
s
>
<
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xml:id
="
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xml:space
="
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">Primum ſcilicet in 2. </
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<
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xml:space
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">deinde vtraq; </
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>
<
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xml:id
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"
xml:space
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">ſemiſsis in 3. </
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>
<
s
xml:id
="
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"
xml:space
="
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">Deinde prima pars in
<
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/>
<
handwritten
xlink:label
="
hd-071-1
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xlink:href
="
hd-071-1a
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number
="
34
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<
handwritten
xlink:label
="
hd-071-1
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xlink:href
="
hd-071-1a
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number
="
35
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<
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xlink:label
="
hd-071-1
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xlink:href
="
hd-071-1a
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number
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10. </
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>
<
s
xml:id
="
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xml:space
="
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">particulas æquales diuidatur, ita vt quælibet harum particularũ ſit {1/60}. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">arcus
<
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XY. </
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>
<
s
xml:id
="
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"
xml:space
="
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">Et quoniam vna harum particularum eſt ad arcum XY, vt 1. </
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>
<
s
xml:id
="
echoid-s1667
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xml:space
="
preserve
">gradus Qua-
<
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drantis B C, ad arcum 60. </
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>
<
s
xml:id
="
echoid-s1668
"
xml:space
="
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">graduum; </
s
>
<
s
xml:id
="
echoid-s1669
"
xml:space
="
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">cum vtrobique proportio ſit ſubſexagecu-
<
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pla; </
s
>
<
s
xml:id
="
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"
xml:space
="
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">erit permutando vna illarum particularum ad 1.</
s
>
<
s
xml:id
="
echoid-s1671
"
xml:space
="
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">
<
unsure
/>
grad. </
s
>
<
s
xml:id
="
echoid-s1672
"
xml:space
="
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">vt arcus XY, ad arcum
<
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/>
60. </
s
>
<
s
xml:id
="
echoid-s1673
"
xml:space
="
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">graduum. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Quocirca quemadmodum arcus X Y, arcum grad. </
s
>
<
s
xml:id
="
echoid-s1675
"
xml:space
="
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">60. </
s
>
<
s
xml:id
="
echoid-s1676
"
xml:space
="
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">continet
<
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ſemel, & </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">inſuper vnam eius partem ſexageſimam, id eſt, 1. </
s
>
<
s
xml:id
="
echoid-s1678
"
xml:space
="
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">ad grad. </
s
>
<
s
xml:id
="
echoid-s1679
"
xml:space
="
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">ex conſtru-
<
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/>
ctione; </
s
>
<
s
xml:id
="
echoid-s1680
"
xml:space
="
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">Ita quoq; </
s
>
<
s
xml:id
="
echoid-s1681
"
xml:space
="
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">vna illarum particularum comprehendet 1. </
s
>
<
s
xml:id
="
echoid-s1682
"
xml:space
="
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">gradum ſemel, & </
s
>
<
s
xml:id
="
echoid-s1683
"
xml:space
="
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">
<
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/>
inſuper vnam partem ſexageſimam vnius gradus, hoc eſt, 1. </
s
>
<
s
xml:id
="
echoid-s1684
"
xml:space
="
preserve
">Minutum. </
s
>
<
s
xml:id
="
echoid-s1685
"
xml:space
="
preserve
">Ex quo
<
lb
/>
fit, vt duæ particulæ complectantur 2. </
s
>
<
s
xml:id
="
echoid-s1686
"
xml:space
="
preserve
">grad. </
s
>
<
s
xml:id
="
echoid-s1687
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1688
"
xml:space
="
preserve
">inſuper 2. </
s
>
<
s
xml:id
="
echoid-s1689
"
xml:space
="
preserve
">Minuta. </
s
>
<
s
xml:id
="
echoid-s1690
"
xml:space
="
preserve
">Atvero 3. </
s
>
<
s
xml:id
="
echoid-s1691
"
xml:space
="
preserve
">par-
<
lb
/>
ticulæ contineant 3. </
s
>
<
s
xml:id
="
echoid-s1692
"
xml:space
="
preserve
">grad. </
s
>
<
s
xml:id
="
echoid-s1693
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1694
"
xml:space
="
preserve
">3. </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1697
"
xml:space
="
preserve
">ſic deinceps.</
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1699
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Itaqve</
emph
>
ſi in Quadrantem BC, transferatur vna particula ſexageſima arcus
<
lb
/>
<
handwritten
xlink:label
="
hd-071-1
"
xlink:href
="
hd-071-1a
"
number
="
34
"/>
<
handwritten
xlink:label
="
hd-071-1
"
xlink:href
="
hd-071-1a
"
number
="
35
"/>
<
handwritten
xlink:label
="
hd-071-1
"
xlink:href
="
hd-071-1a
"
number
="
36
"/>
XY, à puncto C, vel à quouis gradu, habebitur 1. </
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>
<
s
xml:id
="
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"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">in 2. </
s
>
<
s
xml:id
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"
xml:space
="
preserve
">gradu, vel quouis a-
<
lb
/>
lio. </
s
>
<
s
xml:id
="
echoid-s1703
"
xml:space
="
preserve
">Et ſi duæ particulæ transferantur, habebuntur in tertio gradu duo Minuta:</
s
>
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xml:id
="
echoid-s1704
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>