Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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DE CIRCULI MAGNIT. INVENTA.
"/>
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<
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xml:space
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preserve
">Inventorum terminorum differentia ſeſquitertia jungatur du-
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plæ ſubtenſæ & </
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<
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echoid-s1920
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xml:space
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">ſinui triplo, & </
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<
s
xml:id
="
echoid-s1921
"
xml:space
="
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">quam rationem habet ex his
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compoſita ad triplam ſeſquitertiam ſeu {10/3} utriuſque ſimul, ſi-
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nus, ſubtenſæque, eandem habeat ſubtenſæ ſupra ſinum exceſ-
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ſus ad aliam quandam; </
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>
<
s
xml:id
="
echoid-s1922
"
xml:space
="
preserve
">Hæc ad ſinum addita rectam conſtituet
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arcu minorem.</
s
>
<
s
xml:id
="
echoid-s1923
"
xml:space
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"/>
</
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<
s
xml:id
="
echoid-s1924
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xml:space
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">Minor terminus erat 104465 {2/3}. </
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<
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echoid-s1925
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xml:space
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">Major 104727. </
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<
s
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="
echoid-s1926
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xml:space
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">differentia
<
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horum eſt 261 {1/3}. </
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<
s
xml:id
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echoid-s1927
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xml:space
="
preserve
">Eſtque rurſus tribus numeris inveniendus
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quartus proportionalis. </
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<
s
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echoid-s1928
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xml:space
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">Primus eſt partium duplæ A B & </
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<
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="
echoid-s1929
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">
<
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triplæ A M & </
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<
s
xml:id
="
echoid-s1930
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xml:space
="
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">ſeſquitertiæ terminorum differentiæ, 460158
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vero major. </
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>
<
s
xml:id
="
echoid-s1931
"
xml:space
="
preserve
">Secundus {10/3} utriuſque ſimul A B, A M, 622008
<
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vero minor. </
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>
<
s
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="
echoid-s1932
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xml:space
="
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">Tertius denique exceſſus A B ſupra A M, 13397
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vero min. </
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<
s
xml:id
="
echoid-s1933
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xml:space
="
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">Quibus quartus proportionalis eſt 18109 vero min.
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</
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>
<
s
xml:id
="
echoid-s1934
"
xml:space
="
preserve
">Hic igitur additus numero partium A M 86602 {1/2} vero min. </
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>
<
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="
echoid-s1935
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xml:space
="
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">
<
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fiunt 104711 {1/2} minores arcu A B. </
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<
s
xml:id
="
echoid-s1936
"
xml:space
="
preserve
">Quare ſexcuplum earum,
<
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628269 minus erit circumferentiâ totâ. </
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>
<
s
xml:id
="
echoid-s1937
"
xml:space
="
preserve
">At quoniam 104727
<
lb
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majores inventæ ſunt arcu A B, earum ſexcuplum 628362
<
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circumferentiâ majus erit. </
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>
<
s
xml:id
="
echoid-s1938
"
xml:space
="
preserve
">Itaque circumferentiæ ad diame-
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trum ratio minor eſt quam 628362, major autem quam 628269
<
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ad 200000. </
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>
<
s
xml:id
="
echoid-s1939
"
xml:space
="
preserve
">Sive minor quam 314181, major autem quam
<
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314135 ad 100000. </
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>
<
s
xml:id
="
echoid-s1940
"
xml:space
="
preserve
">Unde conſtat minorem utique eſſe quam
<
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triplam ſeſquiſeptimam, & </
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>
<
s
xml:id
="
echoid-s1941
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xml:space
="
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">majorem quam 3 {10/@}. </
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>
<
s
xml:id
="
echoid-s1942
"
xml:space
="
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">Quin etiam
<
lb
/>
Longomontani error per hæc refutatur, qui ſcripſit peri-
<
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pheriam majorem eſſe partibus 314185 qualium rad. </
s
>
<
s
xml:id
="
echoid-s1943
"
xml:space
="
preserve
">
<
lb
/>
100000.</
s
>
<
s
xml:id
="
echoid-s1944
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1945
"
xml:space
="
preserve
">Eſto nunc arcus A B {1/@} circumferentiæ, & </
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>
<
s
xml:id
="
echoid-s1946
"
xml:space
="
preserve
">erit A M, ſe-
<
lb
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miſſis lateris quadrati circulo inſcripti, partium 7071068,
<
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non unâ minus, qualium radius D B 10000000. </
s
>
<
s
xml:id
="
echoid-s1947
"
xml:space
="
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">A B vero
<
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latus octanguli partium 7653668 non unâ majus. </
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>
<
s
xml:id
="
echoid-s1948
"
xml:space
="
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">Quibus da-
<
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tis ad ſimilitudinem præcedentium invenietur primus minor
<
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terminus longitudinis arcus A B 7847868. </
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>
<
s
xml:id
="
echoid-s1949
"
xml:space
="
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">Deinde major
<
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terminus 7854066. </
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>
<
s
xml:id
="
echoid-s1950
"
xml:space
="
preserve
">Et ex utroque rurſus terminus minor ac-
<
lb
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curatior 7853885. </
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>
<
s
xml:id
="
echoid-s1951
"
xml:space
="
preserve
">Unde conſtat peripheriæ ad diametrum
<
lb
/>
rationem minorem haberi quam 31416 {1/3}, majorem autem quam
<
lb
/>
31415 ad 10000.</
s
>
<
s
xml:id
="
echoid-s1952
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1953
"
xml:space
="
preserve
">Et quum terminus major 7854066 à vera arcus A B </
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