Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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HOROLOG. OSCILLATOR.
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gæ. </
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<
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xml:space
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">Quæritur jam, quo loco hoc virgæ imponendum, ut
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<
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<
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<
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.</
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uno ſcrupulo primo acceleretur horologii motus, ſpatio 24
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horarum. </
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<
s
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echoid-s3971
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xml:space
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">Item, ubi collocandum, ut duorum ſcrupulorum
<
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primorum ſit acceleratio; </
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<
s
xml:id
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echoid-s3972
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xml:space
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">item, ut trium, quatuor, atque
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ita porro.</
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<
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<
s
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echoid-s3974
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xml:space
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">Ductis viginti quatuor horis ſexagies, fiunt 1440, quot
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nempe ſcrupula prima una die continentur. </
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<
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echoid-s3975
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xml:space
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">Ex his unum
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aufer, quando unius ſcrupuli acceleratio quæritur: </
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<
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xml:space
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">ſuper-
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ſunt 1439. </
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<
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echoid-s3977
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xml:space
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">Ratio autem 1440 ad 1439 duplicata, proxime
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eſt ea quæ 1440 ad 1438. </
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<
s
xml:id
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echoid-s3978
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xml:space
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">Ergo, ſi penduli ſimplicis, ſe-
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cunda ſcrupula notantis, longitudo diviſa intelligatur in par-
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tes æquales 1440, earumque 1438 alii pendulo tribuantur,
<
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hoc præcedet alterum illud, in 24 horis, uno ſcrupulo pri-
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mo. </
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<
s
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echoid-s3979
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xml:space
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">Adeo ut hic p valeat partes 1438.</
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<
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</
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<
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<
s
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xml:space
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">Quia autem pendulum horologii, ex virga metallica & </
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<
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="
echoid-s3982
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<
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pondere appenſo compoſitum, iſochronum ponitur pendulo
<
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ſimplici partium 1440; </
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>
<
s
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="
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xml:space
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">invenienda primum eſt virgæ illius
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longitudo, ex æquatione ſuperius poſita. </
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<
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xml:id
="
echoid-s3984
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xml:space
="
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">Erat nempe
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{{1/3} a b + a c/{1/2} b + c} æquale longitudini penduli ſimplicis, quod iſochro-
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num compoſito ex virga habente longitudinem a, gravita-
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tem b, & </
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<
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xml:id
="
echoid-s3985
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xml:space
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">pondere affixo cujus gravitas c. </
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<
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xml:space
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">Ergo ſi longitu-
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do penduli ſimplicis iſochroni dicatur ſ. </
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>
<
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xml:space
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">Erit {{1/2} b ſ + c ſ/{1/3} b + c} = a.
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</
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<
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xml:space
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">poſitoque, ut hic, c = 50; </
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<
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xml:space
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">b = 1; </
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<
s
xml:id
="
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xml:space
="
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">ſ = 1440; </
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>
<
s
xml:id
="
echoid-s3991
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xml:space
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">fiet, a = 1444 {4/5},
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longitudo virgæ.</
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<
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xml:id
="
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xml:space
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</
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<
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<
s
xml:id
="
echoid-s3993
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xml:space
="
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">Jam, quia erat f = {1/2} p + vel @
<
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style
="
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">{1/4} p p + {1/2} a b p + a c p - {1/3} a a b - a a c/d</
emph
>
,
<
lb
/>
fiet f = {1/2} p + vel -
<
emph
style
="
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">{1/4} p p + 72962 p - 105061210</
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>
.
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</
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<
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echoid-s3994
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xml:space
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">Unde porro, ſi p ſit, uti diximus, partium 1438; </
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<
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xml:id
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xml:space
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">invenie-
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tur f = 1331 {1/2}, qualium nempe ſ, ſeu pendulum ſimplex,
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ſecunda ſcrupula oſcillationibus deſignans, continet 1440. </
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>
<
s
xml:id
="
echoid-s3996
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xml:space
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">Cu-
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jus longitudo ſi pedum trium ſtatuatur, quos horarios voca-
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vimus, habebit f uncias 33, & </
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>
<
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xml:space
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">3 unciarum uncias, quas
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lineas vocant. </
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>
<
s
xml:id
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xml:space
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">Vel, auferendo hanc longitudinem f à tota
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trium pedum longitudine, ſupererunt unciæ duæ, lineæ </
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