Clavius, Christoph, Geometria practica

Table of Notes

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8555LIBER SECVNDVS. includantur. Atque tot palmos, aut pedes quælibet illarum rectarum comple-
ctetur, quot particulæ in earum interuallis deprehenſæ fuerint.
ALITER
7. Idem aſſequentur via quadam generali, quæ in omnes dimenſiones
quadrat, videlicet.
Fiat angulus quicunque B A C. Deinde ſumpta verbigra-
tia, in exemplum regula trium Num.
1. huius propoſitionis, accipiatur primæ
quantitati O P, (hoc eſt, differentiæ Tangentium angulorum obſeruatorum)
21[Figure 21] æqualis;
vel ſi nimis parua eſt, multiplex A D.
11Problema hoc
1. qua ratione
aliter ſine nu-
meris abſolua
tur
(Nos duplam accepimus) Item ſecũ dæ P N, (hoc
eſt, Tangenti minoris anguli) æqualis, vel ęque
multiplex cum A D, nimirum D B.
Poſt hæc ex
inſtrumento partium capiantur tot particulę A E,
quot palmi, aut pedes in ED, differentia ſtationum
continentur.
Ducta autemrecta D E, agatur ei pa-
rallela BC.
Nam quot partes inſtrumenti partium includetinteruallum EC, tot
palmos, aut pedes diſtantia DF, complectetur;
cum quatuor quantitates 224. Sexti. DB, AE, EC, proportionales ſint.
Eodem modo procedes in alijs exemplis, hoc obſeruato, vt quando ſinus
alicuius anguli in regula trium reperitur, accipias ex tabula ſinuum ſinum, abie-
ctis quinque figuris, vtſinus totus ſit 100.
Verbi gratia. In vltimo exemplo
Num.
4. recta AD, ſumenda eſſet æqualis 100. particulis inſtrumenti partium, ni-
mirum ſinui tori.
At D B, æqualis hypotenuſę E G, vel D G, in figura Num. 6.
Et A E, ſi angulus E, eſt grad. 30. Min. 15. æqualis 50 {4/10}. ferme particulis: quia
tantus eſt ſinus grad.
30. Min. 15. Vel ſi angulus G D F, eſt grad. 53. Min. 20. ac-
cipienda eſſet AE, æqualis particulis 80 {3/10}.
fere. Ita enim interuallum E C,
dabit tot palmos, aut pedes rectę F G, quot particulę in eo comprehenduntur,
Et ſic de cęteris.
Qvando autem tota regula 100. partium eſt nimis longa, ſumi poteſt pro
ſinu toto quoduis interuallum inter 100, &
100. dummodo reſpectu huius ſi-
nus totius accipiantur poſtea ſinus, vt cap.
1. lib. 1. Num. 12. declarauimus.
Poteris autem nonnunquam ordinemimmutare, ponendo nimirum ſe-
cundamquantitatem DB, in recta AC;
& tertiam AE, in recta DB, prout videli-
cetid expedire cognoueris ad parallelas DE, BC, ducendas.
LEMMA.
DATIS duabus rectis ad inuicem inclinatis, punctum, in quo con-
ueniant, inuenire.
QVOD hic proponitur, demonſtratum à
22[Figure 22] nobis fuit lẽmate 13.
lib. 1. noſtri Aſtrolabij plu-
rib{us} viis.
Sed quia ei{us} inſignis eſt vtilit{as} in
puncto concurſ{us} duarum rectarum exquiren-
do demonſtrabim{us} illud ipſum hoc loco paulo
aliter.
Sint ergo duærectæ A B, C D, oblique
ſe in concurſu B, ſecant{es}.
Ex quotli-
lib{et} punctis E, F, G, vtcunque in

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