Clavius, Christoph
,
Gnomonices libri octo, in quibus non solum horologiorum solariu[m], sed aliarum quo[quam] rerum, quae ex gnomonis umbra cognosci possunt, descriptiones geometricè demonstrantur
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GNOMONICES
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ex coroll. </
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<
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<
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<
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</
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<
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xml:space
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">ablato communi arcu M Q, erit P M, arcus æqualis arcui Q N, inclinationem plani ad Horizon-
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tem metienti. </
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<
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<
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0124-01
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<
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triangulis, vel per propoſitionem 13. </
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<
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<
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<
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<
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<
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ſphæricorum, ſit vt ſinus arcus P M, qui inclinationi plani ad Horizontem æqualis eſt, ad ſinum
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anguli H, inclinationis Meridiani ipſius plani inclinati ad Meridianum Horizontis, ita ſinus arcus
<
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H M, complementi altitudinis poli ſupra Horizontem, ad ſinum anguli P, hoc eſt, ad ſinum ar-
<
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cus I Q; </
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>
<
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xml:space
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">Si fiat, vt ſinus inclinationis ad Horizontem, ad ſinum inclinationis Meridiani ipſius pla
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ni inclinati ad Meridianum Horizontis, per propoſ. </
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<
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xml:space
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">pręcedentem inuentę, ita ſinus complementi
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altitudinis poli ſupra Horizontem ad aliud, habebitur ſinus arcus primi I Q, quæſiti.</
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<
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</
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<
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<
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xml:space
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">RVRSVS ducto arcu circuli maximi per puncta G, P, erunt duo arcus G P, G M, trianguli
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<
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xlink:label
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xml:space
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">Arcus plani in-
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clinati inter ma
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ximum circulũ
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per eius polos,
<
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& per polos Ho
<
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@zontis ductũ,
<
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& Meridianum
<
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Horizontis in-
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tercep us, quo
<
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artificio explo-
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retur.</
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ſphærici G M P, noti; </
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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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<
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P, polus ſit circuli E F, arcus vero G M, notus eſt, quia interijcitur inter planum inclinatum, & </
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<
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<
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verticem M, ac proinde, per coroll. </
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<
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<
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<
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Meridiani inter planum inclinatum, & </
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<
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<
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xml:space
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<
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enim circulus O N, ductus per polos P, M, circulorum E F, E B F, ſecat arcus E F, E B F, per pro-
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poſ. </
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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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<
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quadrans, atque adeò quadranti k C, ęqualis. </
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<
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xml:space
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">ablato ergo communi arcu k N, relinquetur arcus
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E k, declinationis plani E F, à Verticali, arcui N C, ęqualis, atque adeo arcus N C, notus erit. </
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<
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& </
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<
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<
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">reliquus ex duobus rectis G M P, notus erit. </
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<
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xml:space
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<
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eſt in triangulo ſphęrico G P M, per propoſ. </
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<
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<
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<
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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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xml:space
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<
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xml:space
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<
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xml:space
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<
s
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xml:space
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">noſtrorum triangulorum ſphæricorum, vt ſinus arcus
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G P, nempe ſinus totus, ad ſinum anguli G M P, nempe ad ſinum declinationis plani à Verticali,
<
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/>
(habent enim arcus N C, C O, angulorum N M C, C M O, vel G M P, cũ ſemicirculum cõficiant,
<
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eundem ſinum) ita ſinus arcus G M, Meridiani, qui inter planum, & </
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<
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ſinum anguli G P M, hoc eſt, ad ſinum arcus G Q; </
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<
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ſinus arcus Meridiani inter planum, & </
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<
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xml:space
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di G Q, qui quæritur.</
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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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xml:space
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<
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xml:space
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">Exemplum.</
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tio Meridiani B D, ipſius plani inclinati E F, ad Meridianum Horizontis A C, grad. </
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<
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<
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xml:space
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fiat vt 78854. </
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<
s
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xml:space
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<
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xml:space
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">ſinũ totum, nempe ad ſinum incli-
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nationis Meridianorũ, ita 74314. </
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>
<
s
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="
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xml:space
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">ſinus complementi altitudinis poli ſupra Horizontẽ ad aliud,
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inuenietur hic ferè ſinus 94242. </
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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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<
s
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xml:space
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nati, & </
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>
<
s
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xml:space
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">circulum maximum interijcitur, qui inclinationem plani ad Horizontem metitur.</
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>
<
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</
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<
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<
s
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">RVRSVS ſi fiat, vt 100000. </
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>
<
s
xml:id
="
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xml:space
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">ſinus totus ad 50000. </
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>
<
s
xml:id
="
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xml:space
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">ſinum declinationis plani à Verticali (po-
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<
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="
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nimus enim idem planum, de quo proximè egimus, declinare à Verticali à Septentrione in ortũ,
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grad. </
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>
<
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">30. </
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>
<
s
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xml:space
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">ita vt inclinatio cadat in partem auſtralem) ita 66913. </
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>
<
s
xml:id
="
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xml:space
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">ſinus arcus Meridiani inter pla-
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num, & </
s
>
<
s
xml:id
="
echoid-s6213
"
xml:space
="
preserve
">verticem intercepti (qui quidem arcus complectitur grad. </
s
>
<
s
xml:id
="
echoid-s6214
"
xml:space
="
preserve
">42. </
s
>
<
s
xml:id
="
echoid-s6215
"
xml:space
="
preserve
">Nam arcus inter planum,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s6216
"
xml:space
="
preserve
">Horizontem continet, per propoſ. </
s
>
<
s
xml:id
="
echoid-s6217
"
xml:space
="
preserve
">28. </
s
>
<
s
xml:id
="
echoid-s6218
"
xml:space
="
preserve
">huius lib. </
s
>
<
s
xml:id
="
echoid-s6219
"
xml:space
="
preserve
">grad. </
s
>
<
s
xml:id
="
echoid-s6220
"
xml:space
="
preserve
">48. </
s
>
<
s
xml:id
="
echoid-s6221
"
xml:space
="
preserve
">ſub Horizonte ad partes boreales, qui
<
lb
/>
ablatus ex quadrante relinquit arcum inter planum inclinatum, & </
s
>
<
s
xml:id
="
echoid-s6222
"
xml:space
="
preserve
">verticem ad partes auſtrales
<
lb
/>
grad. </
s
>
<
s
xml:id
="
echoid-s6223
"
xml:space
="
preserve
">42. </
s
>
<
s
xml:id
="
echoid-s6224
"
xml:space
="
preserve
">ex coroll. </
s
>
<
s
xml:id
="
echoid-s6225
"
xml:space
="
preserve
">propoſ. </
s
>
<
s
xml:id
="
echoid-s6226
"
xml:space
="
preserve
">28. </
s
>
<
s
xml:id
="
echoid-s6227
"
xml:space
="
preserve
">huius lib.) </
s
>
<
s
xml:id
="
echoid-s6228
"
xml:space
="
preserve
">ad aliud, reperietur hic propemodum ſinus 33456. </
s
>
<
s
xml:id
="
echoid-s6229
"
xml:space
="
preserve
">cui
<
lb
/>
reſpondet arcus ferme grad. </
s
>
<
s
xml:id
="
echoid-s6230
"
xml:space
="
preserve
">19. </
s
>
<
s
xml:id
="
echoid-s6231
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s6232
"
xml:space
="
preserve
">33. </
s
>
<
s
xml:id
="
echoid-s6233
"
xml:space
="
preserve
">inter Meridianum Horizontis, & </
s
>
<
s
xml:id
="
echoid-s6234
"
xml:space
="
preserve
">circulum maximum in-
<
lb
/>
reriectus, qui inclinationem plani ad Horizontem dimetitur. </
s
>
<
s
xml:id
="
echoid-s6235
"
xml:space
="
preserve
">Dato ergo plano ad Meridianum
<
lb
/>
inclinato, quãtus ſit arcus ipſins interceptus inter circulum maximum, qui per polos ipſius, & </
s
>
<
s
xml:id
="
echoid-s6236
"
xml:space
="
preserve
">per
<
lb
/>
polos Horizontis tranſit, metiturq́; </
s
>
<
s
xml:id
="
echoid-s6237
"
xml:space
="
preserve
">eius inclinationem ad Horizontem, & </
s
>
<
s
xml:id
="
echoid-s6238
"
xml:space
="
preserve
">tam Meridianum pro-
<
lb
/>
prium ipſius, &</
s
>
<
s
xml:id
="
echoid-s6239
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s6240
"
xml:space
="
preserve
">Quod erat faciendum.</
s
>
<
s
xml:id
="
echoid-s6241
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>