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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LIBER PRIMVS.
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altitudinis poli, & </
s
>
<
s
xml:id
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xml:space
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">arcus anguli A.) </
s
>
<
s
xml:id
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"
xml:space
="
preserve
">ad ſinum arcus k M, declinationis, ita ſinus anguli recti M,
<
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hoc eſt, ita ſinus totus ad ſinum arcus A K, altitudinis poli. </
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>
<
s
xml:id
="
echoid-s8579
"
xml:space
="
preserve
">Quare ſi fiat, vt ſinus altitudinis poli
<
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ad ſinum declinationis, ita ſinus totus ad aliud, reperietur rurſus ſinus altitudinis Solis in Vertica-
<
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li circulo. </
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>
<
s
xml:id
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xml:space
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preserve
">Quod etiam ſupra demonſtrauimus ſine triangulis ſphæricis.</
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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">INSVPER cum Sol in parallelis borealibus diſtat à meridie ſex horis, vt in ſexta figura, nul
<
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/>
<
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position
="
right
"
xlink:label
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note-0155-01
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xlink:href
="
note-0155-01a
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xml:space
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preserve
">Altitudo Solis,
<
lb
/>
cum Sol ſex ho-
<
lb
/>
ris abeſt à meri-
<
lb
/>
die in parallelis
<
lb
/>
borealibus, qua
<
lb
/>
rati one per ſphę
<
lb
/>
rica triangula
<
lb
/>
inueſtiganda.</
note
>
lius erit negotij altitudinem eius in ueſtigare. </
s
>
<
s
xml:id
="
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xml:space
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preserve
">Quia enim in ſphærico triangulo E L N, figuræ
<
lb
/>
ſextæ angulus N, rectus eſt, per propoſ. </
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<
s
xml:id
="
echoid-s8584
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xml:space
="
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">15. </
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>
<
s
xml:id
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xml:space
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">lib. </
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>
<
s
xml:id
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xml:space
="
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">1. </
s
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<
s
xml:id
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"
xml:space
="
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">Theodoſij, quòd maximus circulus N A, per A,
<
lb
/>
polum Meridiani ductus ſit; </
s
>
<
s
xml:id
="
echoid-s8588
"
xml:space
="
preserve
">erit per propoſ. </
s
>
<
s
xml:id
="
echoid-s8589
"
xml:space
="
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">19. </
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>
<
s
xml:id
="
echoid-s8590
"
xml:space
="
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">lib 4. </
s
>
<
s
xml:id
="
echoid-s8591
"
xml:space
="
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">Ioan. </
s
>
<
s
xml:id
="
echoid-s8592
"
xml:space
="
preserve
">Regiom. </
s
>
<
s
xml:id
="
echoid-s8593
"
xml:space
="
preserve
">de triangulis, vel per pro-
<
lb
/>
poſ. </
s
>
<
s
xml:id
="
echoid-s8594
"
xml:space
="
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">15. </
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>
<
s
xml:id
="
echoid-s8595
"
xml:space
="
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">lib. </
s
>
<
s
xml:id
="
echoid-s8596
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s8597
"
xml:space
="
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">Gebri, vel per propoſ. </
s
>
<
s
xml:id
="
echoid-s8598
"
xml:space
="
preserve
">43. </
s
>
<
s
xml:id
="
echoid-s8599
"
xml:space
="
preserve
">noſtrorum triangulorum ſphæricorum, vt ſinus comple-
<
lb
/>
menti arcus E N, hoc eſt, vt ſinus arcus E F, altitudinis poli, ad ſinum totum, ita ſinus comple-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0155-02
"
xlink:href
="
note-0155-02a
"
xml:space
="
preserve
">10</
note
>
menti arcus E L, hoc eſt, ita ſinus arcus L O, altitudinis Solis, ad ſinum complementi arcus N L,
<
lb
/>
id eſt, ad ſinum arcus L A, declinationis. </
s
>
<
s
xml:id
="
echoid-s8600
"
xml:space
="
preserve
">Conuertendo ergo erit quoque, vt ſinus totus ad ſinum
<
lb
/>
altitudinis poli, ita ſinus declinationis ad ſinum altitudinis Solis. </
s
>
<
s
xml:id
="
echoid-s8601
"
xml:space
="
preserve
">Quocirca ſi fiat, vt ſinus totus ad
<
lb
/>
ſinum altitudinis poli, ita ſinus declinationis ad aliud, habebitur linus altitudinis Solis. </
s
>
<
s
xml:id
="
echoid-s8602
"
xml:space
="
preserve
">Quod
<
lb
/>
etiam ſupra demonſtrauimus ſine triangulis ſphęricis.</
s
>
<
s
xml:id
="
echoid-s8603
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s8604
"
xml:space
="
preserve
">ADHVC ſole puncta æquinoctiorũ poſſidente, ſine magno labore ex hora cognita, ſiue ex
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0155-03
"
xlink:href
="
note-0155-03a
"
xml:space
="
preserve
">Altitudo Solis
<
lb
/>
in ęquiuoctiis,
<
lb
/>
quo pacto ex da
<
lb
/>
ta hora per triã
<
lb
/>
gula ſphęrica in
<
lb
/>
daganda.</
note
>
diſtantia Solis à meridie, altitudinem Solis eliciemus per ſphęrica triãgula hoc modo. </
s
>
<
s
xml:id
="
echoid-s8605
"
xml:space
="
preserve
">Intelligatur
<
lb
/>
in quinta figura Aequator eſle G H I, & </
s
>
<
s
xml:id
="
echoid-s8606
"
xml:space
="
preserve
">Sol exiſtere in k, ne cogamur nouam figurã deſcribere.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s8607
"
xml:space
="
preserve
">Quia igitur in triangulo ſphærico E H K, angulus H, rectus eſt, erit per propoſ. </
s
>
<
s
xml:id
="
echoid-s8608
"
xml:space
="
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">19. </
s
>
<
s
xml:id
="
echoid-s8609
"
xml:space
="
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">lib. </
s
>
<
s
xml:id
="
echoid-s8610
"
xml:space
="
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">4. </
s
>
<
s
xml:id
="
echoid-s8611
"
xml:space
="
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">Ioan. </
s
>
<
s
xml:id
="
echoid-s8612
"
xml:space
="
preserve
">
<
lb
/>
Regiom. </
s
>
<
s
xml:id
="
echoid-s8613
"
xml:space
="
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">vel per propoſ. </
s
>
<
s
xml:id
="
echoid-s8614
"
xml:space
="
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">15. </
s
>
<
s
xml:id
="
echoid-s8615
"
xml:space
="
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">lib. </
s
>
<
s
xml:id
="
echoid-s8616
"
xml:space
="
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">1. </
s
>
<
s
xml:id
="
echoid-s8617
"
xml:space
="
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">Gebri, vel per propoſ. </
s
>
<
s
xml:id
="
echoid-s8618
"
xml:space
="
preserve
">43. </
s
>
<
s
xml:id
="
echoid-s8619
"
xml:space
="
preserve
">noſtrorum triangulorum ſphærico-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0155-04
"
xlink:href
="
note-0155-04a
"
xml:space
="
preserve
">20</
note
>
rum, vt ſinus complementiarcus E H, hoc eſt, vt ſinus arcus H B, altitudinis Aequatoris, vel com
<
lb
/>
plementi altitudinis poli, ad ſinum totum, ita ſinus complementi arcus E K, id eſt, ita ſinus arcus
<
lb
/>
K A, altitudinis Solis, ad ſinum complementi arcus H K, diſtantie Solis à meridie. </
s
>
<
s
xml:id
="
echoid-s8620
"
xml:space
="
preserve
">Quare erit etiã
<
lb
/>
conuertendo, vt ſinus totus ad ſinum complementi altitndinis poli, ita ſinus complementi diſtan-
<
lb
/>
tię Solis à meridie, ad ſinum altitudinis Solis; </
s
>
<
s
xml:id
="
echoid-s8621
"
xml:space
="
preserve
">Ac propterea ſi fiat, vt ſinus totus ad ſinum com-
<
lb
/>
plementi altitudinis poli, ita ſinus complementi diſtantię Solis à meridiead aliud, cognitus erit
<
lb
/>
ſinus altitudinis Solis.</
s
>
<
s
xml:id
="
echoid-s8622
"
xml:space
="
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"/>
</
p
>
<
p
>
<
s
xml:id
="
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"
xml:space
="
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">ALIA quoque ratione per triangula ſphęrica, & </
s
>
<
s
xml:id
="
echoid-s8624
"
xml:space
="
preserve
">commodius fortaſſe, ſine circulo A L P, repe
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0155-05
"
xlink:href
="
note-0155-05a
"
xml:space
="
preserve
">Altitudo Solis
<
lb
/>
quomodo aliter
<
lb
/>
per ſphærica
<
lb
/>
triangula ex da-
<
lb
/>
ta hora inueſti-
<
lb
/>
ganda.</
note
>
riemus altitudinem Solis ex hora cognita, quæ eiuſmodi eſt. </
s
>
<
s
xml:id
="
echoid-s8625
"
xml:space
="
preserve
">Producatur circulus declinationis
<
lb
/>
N L, ad partes L, donec Horizontem ſecet in Q. </
s
>
<
s
xml:id
="
echoid-s8626
"
xml:space
="
preserve
">Et quoniam angulus F N M, diſtantiæ Solis à
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0155-06
"
xlink:href
="
note-0155-06a
"
xml:space
="
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">30</
note
>
meridie cognitus eſt, erit & </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Q N D, reliquus duorum rectorum notus. </
s
>
<
s
xml:id
="
echoid-s8628
"
xml:space
="
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">Cum ergo in triangulo
<
lb
/>
ſphęrico D N Q, cuius angulus D, rectus, & </
s
>
<
s
xml:id
="
echoid-s8629
"
xml:space
="
preserve
">D N Q, notus eſt, vnà cum arcu D N, altitudinis po-
<
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/>
li, ſit per propoſ. </
s
>
<
s
xml:id
="
echoid-s8630
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xml:space
="
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">18 lib. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">4. </
s
>
<
s
xml:id
="
echoid-s8632
"
xml:space
="
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">Ioan. </
s
>
<
s
xml:id
="
echoid-s8633
"
xml:space
="
preserve
">Regiom. </
s
>
<
s
xml:id
="
echoid-s8634
"
xml:space
="
preserve
">de triangulis, vel per propoſ. </
s
>
<
s
xml:id
="
echoid-s8635
"
xml:space
="
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">14. </
s
>
<
s
xml:id
="
echoid-s8636
"
xml:space
="
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">lib. </
s
>
<
s
xml:id
="
echoid-s8637
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s8638
"
xml:space
="
preserve
">Gebri, vel per pro-
<
lb
/>
poſ. </
s
>
<
s
xml:id
="
echoid-s8639
"
xml:space
="
preserve
">42. </
s
>
<
s
xml:id
="
echoid-s8640
"
xml:space
="
preserve
">noſtrorum triangulorum ſphæricorum, vt ſinus anguli D N Q, ad ſinum totum, ita ſinus
<
lb
/>
complementi anguli D Q N, ad ſinum complementi arcus D N, altitudinis poli; </
s
>
<
s
xml:id
="
echoid-s8641
"
xml:space
="
preserve
">erit conuerten-
<
lb
/>
do, vt ſinus totus ad ſinum anguli D N Q, ita ſinus complementi arcus D N, altitudinis poli
<
lb
/>
ad ſinum complementi anguli D Q N: </
s
>
<
s
xml:id
="
echoid-s8642
"
xml:space
="
preserve
">atque adeo angulus ipſe D Q N, cognitus erit. </
s
>
<
s
xml:id
="
echoid-s8643
"
xml:space
="
preserve
">Rurſus
<
lb
/>
quia in eodem triangulo ſphęrico D N Q, eſt per propoſ. </
s
>
<
s
xml:id
="
echoid-s8644
"
xml:space
="
preserve
">19. </
s
>
<
s
xml:id
="
echoid-s8645
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s8646
"
xml:space
="
preserve
">4. </
s
>
<
s
xml:id
="
echoid-s8647
"
xml:space
="
preserve
">Ioan. </
s
>
<
s
xml:id
="
echoid-s8648
"
xml:space
="
preserve
">Regiom. </
s
>
<
s
xml:id
="
echoid-s8649
"
xml:space
="
preserve
">de triangulis, vel
<
lb
/>
per propoſ. </
s
>
<
s
xml:id
="
echoid-s8650
"
xml:space
="
preserve
">13. </
s
>
<
s
xml:id
="
echoid-s8651
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s8652
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s8653
"
xml:space
="
preserve
">Gebri, vel per propoſ. </
s
>
<
s
xml:id
="
echoid-s8654
"
xml:space
="
preserve
">41. </
s
>
<
s
xml:id
="
echoid-s8655
"
xml:space
="
preserve
">noſtrorum triangulorum ſphæricorum, vt ſinus an-
<
lb
/>
guli D Q N, noti iam facti ad ſinum arcus D N, altitudinis poli, ita ſinus totus anguli recti D, ad
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0155-07
"
xlink:href
="
note-0155-07a
"
xml:space
="
preserve
">40</
note
>
ſinum arcus N Q; </
s
>
<
s
xml:id
="
echoid-s8656
"
xml:space
="
preserve
">cognitus erit ſinus arcus N Q, ex quo perueſtig@bimus arcũ ipſum N Q, hac
<
lb
/>
ratione. </
s
>
<
s
xml:id
="
echoid-s8657
"
xml:space
="
preserve
">Quando in ſignis borealibus diſtantia Solis à meridie maior fuerit, quàm hor. </
s
>
<
s
xml:id
="
echoid-s8658
"
xml:space
="
preserve
">6. </
s
>
<
s
xml:id
="
echoid-s8659
"
xml:space
="
preserve
">vt in
<
lb
/>
tertia figura accidit, dabit arcus ex tabula ſinum erutus arcum N Q; </
s
>
<
s
xml:id
="
echoid-s8660
"
xml:space
="
preserve
">quia arcus N Q, minor
<
lb
/>
quadrante tunc eſt, propterea quòd arcus ex polo N, per Q, vſque ad Aequatorem productus qua-
<
lb
/>
drans eſt. </
s
>
<
s
xml:id
="
echoid-s8661
"
xml:space
="
preserve
">Quando vero diſtantia Solis à meridie minor fuerit, quàm hor. </
s
>
<
s
xml:id
="
echoid-s8662
"
xml:space
="
preserve
">6. </
s
>
<
s
xml:id
="
echoid-s8663
"
xml:space
="
preserve
">vt in figura prima, ſe-
<
lb
/>
cunda, & </
s
>
<
s
xml:id
="
echoid-s8664
"
xml:space
="
preserve
">quarta apparet, in quocunque parallelo ſiue boreali, ſiue auſtrali Sol commoretur, erit
<
lb
/>
arcus N Q, quadrante maior: </
s
>
<
s
xml:id
="
echoid-s8665
"
xml:space
="
preserve
">quoniam vero, vt in tractatu ſinuum oſtendimus, idem ſinus eſt ar-
<
lb
/>
cus N Q, & </
s
>
<
s
xml:id
="
echoid-s8666
"
xml:space
="
preserve
">reliqui ex ſemicirculo, auferemus arcum ſinus inuenti ex ſemicirculo, vt habeamus
<
lb
/>
arcum N Q. </
s
>
<
s
xml:id
="
echoid-s8667
"
xml:space
="
preserve
">Quando denique diſtantia Solis à meridie comprehendit hor. </
s
>
<
s
xml:id
="
echoid-s8668
"
xml:space
="
preserve
">6. </
s
>
<
s
xml:id
="
echoid-s8669
"
xml:space
="
preserve
">nihil hic pręcipi-
<
lb
/>
mus, quia tunc, vt in fra docebimus, multo facilius altitudo Solis inquiritur: </
s
>
<
s
xml:id
="
echoid-s8670
"
xml:space
="
preserve
">Eſſet tamen tuncarcus
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0155-08
"
xlink:href
="
note-0155-08a
"
xml:space
="
preserve
">50</
note
>
NQ, quadrans, quia punctũ Q, caderet in punctũ A Inuento autem hac ratione arcu N Q, repe
<
lb
/>
riendus eſt ex eo arcus L Q, hoc modo. </
s
>
<
s
xml:id
="
echoid-s8671
"
xml:space
="
preserve
">In parallelis borealibus ex arcu inuento N Q, detrahatur
<
lb
/>
arcus N L, cõplementi declinationis; </
s
>
<
s
xml:id
="
echoid-s8672
"
xml:space
="
preserve
">In auſtralibus autem parallelis ex eodem arcu inuento N Q,
<
lb
/>
auferatur arcus N L, compoſitus ex quadrante N M, & </
s
>
<
s
xml:id
="
echoid-s8673
"
xml:space
="
preserve
">arcu declinationis M L, vt in quarta figura
<
lb
/>
apparet. </
s
>
<
s
xml:id
="
echoid-s8674
"
xml:space
="
preserve
">Semper enim reliquus erit arcus L Q. </
s
>
<
s
xml:id
="
echoid-s8675
"
xml:space
="
preserve
">Iam vero quoniam in triangulo ſphærico L O Q,
<
lb
/>
angulus O, rectus eſt, & </
s
>
<
s
xml:id
="
echoid-s8676
"
xml:space
="
preserve
">L Q O, notus paulo ante factus, vna cum arcu L Q; </
s
>
<
s
xml:id
="
echoid-s8677
"
xml:space
="
preserve
">eſtq́; </
s
>
<
s
xml:id
="
echoid-s8678
"
xml:space
="
preserve
">per propoſ.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s8679
"
xml:space
="
preserve
">16. </
s
>
<
s
xml:id
="
echoid-s8680
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s8681
"
xml:space
="
preserve
">4. </
s
>
<
s
xml:id
="
echoid-s8682
"
xml:space
="
preserve
">Ioan. </
s
>
<
s
xml:id
="
echoid-s8683
"
xml:space
="
preserve
">Regiom. </
s
>
<
s
xml:id
="
echoid-s8684
"
xml:space
="
preserve
">de triangulis, vel per propoſ. </
s
>
<
s
xml:id
="
echoid-s8685
"
xml:space
="
preserve
">13. </
s
>
<
s
xml:id
="
echoid-s8686
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s8687
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s8688
"
xml:space
="
preserve
">Gebri, vel per propoſ. </
s
>
<
s
xml:id
="
echoid-s8689
"
xml:space
="
preserve
">41. </
s
>
<
s
xml:id
="
echoid-s8690
"
xml:space
="
preserve
">noſtrorũ
<
lb
/>
triangulorum ſphæricorum, vt ſinus totus anguli recti O, ad ſinum arcus L Q, noti, ita ſinus an-
<
lb
/>
guli L Q O. </
s
>
<
s
xml:id
="
echoid-s8691
"
xml:space
="
preserve
">noti ad ſinum arcus L O, altitudinis Solis; </
s
>
<
s
xml:id
="
echoid-s8692
"
xml:space
="
preserve
">cognita fiet Solis altitudo. </
s
>
<
s
xml:id
="
echoid-s8693
"
xml:space
="
preserve
">
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0155-09
"
xlink:href
="
note-0155-09a
"
xml:space
="
preserve
">Inuentum pri-
<
lb
/>
mum.</
note
>
</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s8694
"
xml:space
="
preserve
">ITAQVE ſi fiat, vt ſinus totus ad ſinum anguli D N Q, qui relinquitur, ablato angulo di-
<
lb
/>
ſtantiæ Solis à meridie ex duobus rectis, ita ſinus complementi altitudinis poli ad aliud, </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>