Apian, Petrus
,
Instrvmentvm Sinvvm, sev primi mobilis
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GENVINVS VSVS
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tudinis huius ſecundiloci tibi propones, ſimiliter & </
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<
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ijs duces in totum, productum diuides in minorem, & </
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<
s
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xml:space
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">arcus quotientis dabit differenti-
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am longitudinis, at iſtud ip ſum in hac re te celare noluimus.</
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<
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<
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<
s
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at hinc etiam intercapedine habita inter utran, differentiam adhuc longi
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tudinum & </
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<
s
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<
s
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</
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<
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<
s
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<
s
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">ſinus cõplemento℞ utriuſ eleuationis poli, gra-
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dus etiã & </
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<
s
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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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<
emph
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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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intercapedo ad 90. </
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<
s
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">gradus nõ adſurgat, cõplemẽtũ alte℞ latitudinis oportere eſſe maius
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intercapedine, ne eſt q̊d in hoc uſu ulterius requiras, plura aũt ſuꝑ hac re inuenies in
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Mereoroſcopijs noſtris, ſiquidẽ duo cõſcripſimus, alte℞ ſpeculare uocauimus, alterũ recti
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linearũ, nũc porrò quæ cœpimus ſic proſequemur. </
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<
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">Numeros illos tres, puta utrun cõ-
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plementũ latitudinũ & </
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<
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">intercapedinis arcũ ita diſpone, ut unũ colloces ſuꝑ alterũ, & </
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<
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iorem quidẽ ſupremo loco, in medio aũt mediũ, & </
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<
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">minimũ inſimo loco, hinc ſubtrahe me
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dium à maximo, & </
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<
s
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">reſiduũ dicet̃ differentia prima. </
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<
s
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">Mox ſubtrahe etiã minorẽ de 90. </
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<
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relinquetur, appellabitur differentia ſecunda. </
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<
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primæ differentiæ, & </
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<
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">inde ſubtrahe ſinum differentiæ ſecundæ, reſiduũ duc in ſinũ cõple-
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menti maioris arcus, ꝓductũ diuide in ſinũ maioris, & </
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<
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">q̊tientẽ adde ad ſinũ arcus primæ
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differentiæ, ſummã illã quadrato, ſimiliter & </
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<
s
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">ſinũ differentiæ ſecundæ, at hinc illa duo
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quadrata ſimul adde in unã ſummã, ex ea quære radicẽ quadratã, arcus deinceps huius ra
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dicis ſubtractus de 90. </
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<
s
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<
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pone & </
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<
s
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">ſinũ cõplementi maioris latitudinis, minorẽ duc in totum, & </
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<
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<
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<
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<
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<
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maiorem, ſic arcus q̊tientis ꝓducet differentiam longitudinis quã primo quærebam. </
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<
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hæc ducito & </
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<
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">ſinũ cõplementi latitudinis minoris in ſinũ differentiæ lõgitudinis, produ-
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ctum diuide in ſinũ totũ, & </
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<
s
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">quotientem rurſus ſepone in aliquẽ locũ, ei´ adiunge ſinum
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intercapedinis minorem duc in totũ, & </
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<
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">ꝓductũ diuide cũ maiori, hinc arcus q̊tientis mon
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ſtrat angulum poſitiõis quæſitúm. </
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<
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">At hæc ita demũ ueritatẽ obtinent, ſi locus ſecũdus
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Auſtralior extiterit, qui ſi ſit Borealior ̈ primus & </
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<
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ſitionis accipitur, tunc quære angulũ poſitionis hoc modo. </
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<
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<
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</
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menti operationis ſuperius inuentũ, & </
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<
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<
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cto in maiorem diuiſo, arcus quotientis angulũ dabit poſitionis à ſeptentrione adortum,
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ſi tamen locus ſecundus ſuerit orientalior, is ſi ſit occidẽtalior, numerandus erit tibi angu-
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PLVM
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<
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<
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<
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Hie
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<
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lus ille à meridiano ſeptentrionali ad occaſum. </
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<
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<
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excutere. </
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<
s
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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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">mi. </
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<
s
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">ab Auguſta etiã uſ in Hieruſalem ſunt 491. </
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<
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<
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<
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<
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<
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nunc aſſumo numeros illos tres, cõplementum minoris latitudinis, at is numerus erit
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maior, complementum latitudinis maioris medium tenebit, & </
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<
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cum, quia minor. </
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<
s
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">Medium porrò ſubtraho à maiori, & </
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<
s
xml:id
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">remanet differentia prima, mi-
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norem uero à 90. </
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<
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<
s
xml:id
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">relinquitur differentia ſecunda, diſponuntur hoc modo.</
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</
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<
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<
s
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">Numerus maior 58. </
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<
s
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">gra. </
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<
s
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<
s
xml:id
="
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">mi. </
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<
s
xml:id
="
echoid-s5689
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">complementum minoris latitudinis.</
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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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<
s
xml:id
="
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<
s
xml:id
="
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">complementum maioris latitudinis.</
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>
<
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</
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<
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<
s
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="
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<
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<
s
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<
s
xml:id
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<
s
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<
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</
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<
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<
s
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="
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">Differentia prima 16. </
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<
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<
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<
s
xml:id
="
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<
s
xml:id
="
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xml:space
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">ſcilicet complementorum latitud.</
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<
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</
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<
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<
s
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<
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<
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<
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<
s
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">hoc eſt complementum diſtantiæ.</
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<
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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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">Iam ꝓpono mihi ſinũ cõplemẽti primæ differentiæ. </
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<
s
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<
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<
s
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">inde ſubtraho ſinũ ſecundæ
<
lb
/>
differentiæ, puta 84119. </
s
>
<
s
xml:id
="
echoid-s5719
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s5720
"
xml:space
="
preserve
">remanent 11679. </
s
>
<
s
xml:id
="
echoid-s5721
"
xml:space
="
preserve
">quẽ numerũ duco in ſinũ cõplementi maio-
<
lb
/>
ris. </
s
>
<
s
xml:id
="
echoid-s5722
"
xml:space
="
preserve
">ſ. </
s
>
<
s
xml:id
="
echoid-s5723
"
xml:space
="
preserve
">52497. </
s
>
<
s
xml:id
="
echoid-s5724
"
xml:space
="
preserve
">ꝓductũ diuido cũ ſinu maioris. </
s
>
<
s
xml:id
="
echoid-s5725
"
xml:space
="
preserve
">ſ. </
s
>
<
s
xml:id
="
echoid-s5726
"
xml:space
="
preserve
">85111. </
s
>
<
s
xml:id
="
echoid-s5727
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s5728
"
xml:space
="
preserve
">quotiens dat 7203. </
s
>
<
s
xml:id
="
echoid-s5729
"
xml:space
="
preserve
">hæc addo ad
<
lb
/>
ſinũ primæ differẽtiæ, puta 28680. </
s
>
<
s
xml:id
="
echoid-s5730
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s5731
"
xml:space
="
preserve
">ꝓueniũt 35883. </
s
>
<
s
xml:id
="
echoid-s5732
"
xml:space
="
preserve
">numerus hic ſi quadretur, ꝓducit
<
lb
/>
1287589689. </
s
>
<
s
xml:id
="
echoid-s5733
"
xml:space
="
preserve
">Mox quadrabis etiã ſinus ſecũdæ differentiæ. </
s
>
<
s
xml:id
="
echoid-s5734
"
xml:space
="
preserve
">ſ. </
s
>
<
s
xml:id
="
echoid-s5735
"
xml:space
="
preserve
">84119. </
s
>
<
s
xml:id
="
echoid-s5736
"
xml:space
="
preserve
">facit 7076106161.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s5737
"
xml:space
="
preserve
">utrun hoc quadratũ cõiungo in unã ſummã, quæ erit 8363605850. </
s
>
<
s
xml:id
="
echoid-s5738
"
xml:space
="
preserve
">radix illius quadra
<
lb
/>
ta eſt 91453. </
s
>
<
s
xml:id
="
echoid-s5739
"
xml:space
="
preserve
">lã ſi arcũ radicis. </
s
>
<
s
xml:id
="
echoid-s5740
"
xml:space
="
preserve
">ſ. </
s
>
<
s
xml:id
="
echoid-s5741
"
xml:space
="
preserve
">66. </
s
>
<
s
xml:id
="
echoid-s5742
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s5743
"
xml:space
="
preserve
">8. </
s
>
<
s
xml:id
="
echoid-s5744
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s5745
"
xml:space
="
preserve
">ſubtraxero à 90. </
s
>
<
s
xml:id
="
echoid-s5746
"
xml:space
="
preserve
">relinquunt̃ 23. </
s
>
<
s
xml:id
="
echoid-s5747
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s5748
"
xml:space
="
preserve
">52. </
s
>
<
s
xml:id
="
echoid-s5749
"
xml:space
="
preserve
">mi.</
s
>
<
s
xml:id
="
echoid-s5750
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>
