Clavius, Christoph
,
Geometria practica
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GEOMETR. PRACT.
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ſi fiat, vt 71. </
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<
s
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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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<
s
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<
s
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<
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<
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Num. </
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<
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<
s
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<
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<
s
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">ſemidiametrum producetur area
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circuli {223/284}. </
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<
s
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<
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xlink:label
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quod eſt 1. </
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<
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">ad veram circuli aream, quę maior eſt, quam {223/284}. </
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<
s
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">minorem habebit
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proportionem, quam ad {223/284}. </
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<
s
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">Cum ergo ſit 1. </
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<
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<
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<
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<
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ex propoſ. </
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<
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<
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<
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natorem 284. </
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<
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<
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<
s
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</
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<
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<
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<
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<
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">ad aream veram
<
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circuli minorem proportionem, quam 284. </
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<
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xml:id
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<
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<
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ſtat ergo ſecunda etiam pars propoſitionis.</
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<
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head
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">PROPORTIO quadrati à circumferentia circuli cuiuſuis deſcripti
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ad circuli aream maior eſt, quam 892. </
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<
s
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">ad 71. </
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<
s
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88. </
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<
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</
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<
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enim circumferentia cuiuſuis circuli ad circumferentiam
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Num. 3.</
note
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terius circuli eſt, vt diameter ad diametrum: </
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<
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"> erit quoque quadratum circum- ferentiæ ad quadratum circumferentię, vt quadratum diametri, ad quadratum
<
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<
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diametri. </
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<
s
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"> Sed vt quadratrum diametri ad quadratum diametri, ita eſt
<
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ad circulum. </
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<
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">Igitur erit quadratum quo que circumferentię ad quadratum cir-
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cumferentię; </
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<
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">vt circulus ad circulum: </
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<
s
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">Et permutando quadratum circumfe-
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rentię, ad ſuum circulũ, vt quadratum alterius circumferentię ad ſuum circu-
<
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lum. </
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<
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">Poſita autem circumferentia alicuius circuli 1. </
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<
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">proportio quadrati circum-
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ferentię illius circuli ad circulum maior eſt, quam 892. </
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<
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<
s
xml:id
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88. </
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<
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<
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">Igitur & </
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<
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">proportio quadrati circumferentię cuiuslibet alterius circuli
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ad ipſum circulum maior erit, quam 892. </
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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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autem proportio quadrati ex circumferentia 1. </
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<
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circulum maior ſit, quam 892. </
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<
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">ad 71. </
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<
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xml:id
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<
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<
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bimus. </
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<
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<
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<
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xml:id
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">ita data circumferentia 1. </
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<
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xml:id
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">ad aliud, diameter
<
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procreatur {71/223}. </
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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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miſsis circumferentię ducta in {71/446}. </
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<
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">ſemiſſem diametri inuentę producat aream
<
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circuli {71/892}. </
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<
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">vera maiorem, vt Num. </
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<
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<
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<
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xml:id
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xml:space
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"> Igitur quadratum
<
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>
rentię 1. </
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<
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<
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xml:id
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xml:space
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">ad veram aream circuli, quę minor eſt, quam {71/892}. </
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>
<
s
xml:id
="
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xml:space
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">maiorem
<
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proportionem habebit, quam ad {71/892}. </
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<
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xml:id
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xml:space
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">Vt autem 1. </
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<
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<
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<
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</
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<
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">minutiarum, & </
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>
<
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xml:id
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">conuertendo, 892. </
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<
s
xml:id
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">ad 71. </
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<
s
xml:id
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xml:space
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">Igitur & </
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>
<
s
xml:id
="
echoid-s8678
"
xml:space
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">quadratum circumferentiæ
<
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1. </
s
>
<
s
xml:id
="
echoid-s8679
"
xml:space
="
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">ad veram circuli aream maiorem proportionem habebit, quam 892. </
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>
<
s
xml:id
="
echoid-s8680
"
xml:space
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">ad 71
<
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quod eſt propoſitum. </
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>
<
s
xml:id
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xml:space
="
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">Vera ergo eſt prior propoſitio nis pars.</
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>
<
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</
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<
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>
<
s
xml:id
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"
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<
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style
="
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">Rvrsvs</
emph
>
, quia ſi fiat, vt 22. </
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>
<
s
xml:id
="
echoid-s8684
"
xml:space
="
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">ad 7. </
s
>
<
s
xml:id
="
echoid-s8685
"
xml:space
="
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">ita data circumferentia 1. </
s
>
<
s
xml:id
="
echoid-s8686
"
xml:space
="
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">ad aliud, diame-
<
lb
/>
ter producitur {7/22}. </
s
>
<
s
xml:id
="
echoid-s8687
"
xml:space
="
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">minor quam vera: </
s
>
<
s
xml:id
="
echoid-s8688
"
xml:space
="
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">fit vt {1/2}. </
s
>
<
s
xml:id
="
echoid-s8689
"
xml:space
="
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">ſemiſsis circumferentię ducta in
<
lb
/>
{7/44}. </
s
>
<
s
xml:id
="
echoid-s8690
"
xml:space
="
preserve
">ſemiſſem diametri inuentæ producat aream circuli {7/88}. </
s
>
<
s
xml:id
="
echoid-s8691
"
xml:space
="
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">vera minorem, vt ex
<
lb
/>
iis, conſtat, quæ Num. </
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>
<
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="
echoid-s8692
"
xml:space
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">1. </
s
>
<
s
xml:id
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">diximus. </
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<
s
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="
echoid-s8694
"
xml:space
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"> Igitur quadratum circumferentię 1. </
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>
<
s
xml:id
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xml:space
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">quod
<
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="
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">8. quinti.</
note
>
1. </
s
>
<
s
xml:id
="
echoid-s8696
"
xml:space
="
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">ad aream veram circuli, quæ maior eſt, quam {7/88}. </
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>
<
s
xml:id
="
echoid-s8697
"
xml:space
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">minorem habebit proportio-
<
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nem, quam ad {7/88}. </
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>
<
s
xml:id
="
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"
xml:space
="
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">Vtautem 1. </
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>
<
s
xml:id
="
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"
xml:space
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">ad {7/88}. </
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>
<
s
xml:id
="
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"
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="
preserve
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