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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per Φ, ducamus ad A E, perpendicularem φ χ, accipiamuſ{q́ue} φ χ, vmbræ A B, æqualem, dabit recta
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χ E, producta ad S, amplitudinem Solis ortiuam, vel occiduam C S. </
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<
s
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xml:space
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">Cum enim planum F D, ſit in plano
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Meridiani, erit gnomon A E, pars communis ſectionis verticalis proprie dicti, & </
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<
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<
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xml:space
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">Si igitur
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circulus A B C D, pro Horizonte ſumatur, intelligatur{q́ue} tabulæ F D, applicari, ita vt punctum φ, in
<
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A, & </
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<
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xml:space
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">χ, in B, cadat, ob æqua
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litatẽ rectarum A B, φ χ, ca-
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det centrũ E, in extremũ ſtyli
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E, propter æqualitatẽ rectarũ
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A E, φ E. </
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<
s
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xml:space
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">Quare linea recta
<
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χ E, cõgruet radio Solis B
<
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E,
<
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<
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">10</
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ac propterea producta cadet
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in S, punctum ortus, vel occa-
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ſus in Horizonte. </
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>
<
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xml:space
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">Igitur arcus
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C S, amplitudo erit ortiua,
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vel occidua. </
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<
s
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xml:space
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">Aduertendum ta
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men est, ſi matutino tempore
<
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obſeruatio fiat, vmbra{q́ue} cadat
<
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in rectam A F, ſolem eſſe bo-
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realẽ. </
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<
s
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xml:space
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">vnde amplitudo ſumen-
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da tunc erit à C, verſus par-
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<
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xlink:label
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">20</
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tes ſeptentrionales, nempe ver
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ſus D: </
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<
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xml:space
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">Si autem vmbra cadat
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in rectam A G, Solem eſſe au
<
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ſtralẽ. </
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<
s
xml:id
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xml:space
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">Quare amplitudo nume
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rãda erit à C, verſus auſtrales
<
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partes, hoc eſt, uerſus B. </
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<
s
xml:id
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xml:space
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">Con-
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trariũ intelligatur, ſi obſerua-
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tio fiat tẽpore veſpertino. </
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<
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xml:id
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xml:space
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">Vm-
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bra enim cadẽte in rectã AG,
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Sol borealis eſt, auſtralis vero,
<
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<
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xlink:label
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">30</
note
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umbra cadente in rectã A F,
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vt perſpicuum eſt.</
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<
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xml:space
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">POSTREMO, vt omnia hæc facili{us}, & </
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<
s
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xml:space
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">rectius fiant, ducendæ erunt in circulo A B C D, ante-
<
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quam ſtylus infigatur, aliquot rectę lineæ pro communibus ſectionibus Verticalium circulorum, & </
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<
s
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xml:space
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culi A B C D. </
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<
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xml:space
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">Vt in figura ducta eſt F G, diſtans ab A C, grad. </
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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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">K L, grad. </
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">& </
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</
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<
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">30. </
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<
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xml:space
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">& </
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<
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xml:space
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">c. </
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<
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xml:space
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">Nam cadente vmbrę extremitate in aliquam dictarum linearum, ſciemus, in quonam Ver-
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ticali circulo Sol ſit. </
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<
s
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xml:space
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">Vnde accepta tunc eius altitudine, progrediemur vt prius. </
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<
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xml:space
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">Hoc autem idcirco
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fieri debet, quoniam ſtylus, ſi prius infigatur, antequàm lineæ per centrum ducantur ex puncto extremo in
<
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vmbra notato, impedimento eſt, ne per centrum dictæ lineæ rectę duci poſſint. </
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<
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xml:space
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">At vero ſi pro ſtylo vſur-
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pemus inſtrumentum in principio ſcholij propoſ. </
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<
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">23. </
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<
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<
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">deſcriptum, hac cautione opus non erit,
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<
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">40</
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cum illud instrumentum poſt obſeruationem vmbrę amoueri queat, vt lineæ per centrum E, poſſint duci
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ſine impedimento.</
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<
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">IAM verò ſi per doctrinam ſinuum quantitatem anguli P R Q, altitudinis poli metiri volueri-
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<
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">Altitudo poli
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ſupra Horizon-
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tem qua ratio-
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ne ſupputetur
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per ſinus</
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mus, efficiemus id hoc modo. </
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<
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xml:space
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">Quoniam arcus G H, altitudinis Solis notus eſt, cognitus erit eius comple-
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menti ſinus E I. </
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<
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xml:space
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">Quia verò & </
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<
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">angulus C E G, notus eſt, ex vmbræ obſeruatione, (Cum enim vmbra ca-
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dat in E F, metientur gradus arcus A F, angulum A E F, hoc eſt, C E G,) erit & </
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<
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xml:space
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">alternus E I O, il
<
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<
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xml:space
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">29. primi.</
note
>
li æqualis, in triangulo rectangulo E I O, notus. </
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<
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xml:space
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">Igitur & </
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<
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xml:space
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">E O, ſinus anguli E I O, notus erit in parti-
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bus ſinus totius E I. </
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<
s
xml:id
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xml:space
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">Quòd ſi fiat, vt E I, ſinus totus ad E I, quatenus nota eſt in partibus ſinus totius
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E G, ita E O, quatenus ſinus eſt anguli E I O, ad aliud, nota fiet E O, in partibus ſinus totius E G, vel
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E B. </
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<
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">Eadem ratione in eiſdem partibus not a fiet E P. </
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<
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xml:space
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">Detracta ergo E O, ex E P, nota fiet O P, in eiſ-
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<
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">50</
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dem partibus. </
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<
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xml:space
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">Ducta autem recta Q ω, ex Q, ad P R, perpendiculari, erit tam Q ω, ipſi O P, quàm
<
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<
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xml:space
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">34. primi.</
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P ω, ipſi O Q, æqualis. </
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<
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">Igitur & </
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<
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">Q ω, in partibus ſinus totius E B, not a erit. </
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<
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xml:space
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">Sunt autem in eiſdem par
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tibus notæ rectæ O Q, hoc eſt, P ω, & </
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<
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xml:space
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">P R, cum ſint æquales ſinubus rectis I H, N M, altitudinum So-
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lis notarum. </
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<
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xml:space
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">Detracta ergo recta P ω, ex P R, erit & </
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<
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">reliqua ω R, in eiſdem partib{us} nota. </
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<
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xml:space
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">Cum igi-
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tur quadrata rectarum ω Q, ω R, æqualia ſint quadrato rectæ Q R, fiet quoque Q R, in eiſdem parti-
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<
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xml:space
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">47. primi.</
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bus nota. </
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<
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">Quapropter ſi fiat, vt Q R, quatenus nota in partibus ſinus totius E B, ad ſe ipſam, quatenus
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eſt ſinus totus, ita Q ω, quatenus nota in partibus ſinus totius E B, ad aliud, nota fiet Q ω, in partibus
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ſinus totius Q R, hoc eſt, quatenus ſinus est anguli Q R ω, altitudinis poli quæſitæ, & </
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<
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<
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">QVOD ſi vnum punctum inuentum ſit ex vmbra in recta E B, vt P, alterum autem in recta
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E D, vt θ, addenda erit E θ, ipſi E P, vt tota θ P, not a fiat. </
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<
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<
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">λ a, ipſi θ P, æqualis not a
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">34. primi.</
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erit. </
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<
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">Ex θ λ, autem vel P a, nota erit a R. </
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<
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">Igitur vt prius, angulus a R λ, in triangulo a R λ, </
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