Clavius, Christoph - Geometria practica

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11989LIBER TERTIVS. 49. Min 38. veluti prius. ſolum deſunt ſec. 7. quæ nullius ſunt momenti. Vt au-
5151[Handwritten note 51]5252[Handwritten note 52]5353[Handwritten note 53] tem ſtudioſos moleſtia hac ſupputandi liberem, conſtruxi ſequentem tabulam
pro ſingulis partibus milleſimis vtriuſque vmbræ: In qua ſi centenæ in vertice,
& reliquæ vnitates in latere ſumantur, illico in angulo communi reperientur
gradus, ac Min. pro angulo quæſito: qui videlicet altitudinem Solis aut ſtellæ
11Vſus tabule
gnomonicæ
ſequentis.

indicabit, ſi partes milleſimæ ad vmbram verſam ſpectent: ſi autem partes ad
vmbram rectam pertinent Complementum eius anguli altitu dinem Solis ſtel-
læue oſtendet, vt paulo infra demonſtrabimus. Componetur autẽ tabula hęc,
ſi ſingulis partibus milleſimis vmbræ apponantur ad dextram quinque cifræ, &
22Compoſiti@
tabulæ gno-
monicæfacil-
lima. ex toto illo numero abijciantur tres cifræ: quod idem eſt, ac ſi apponantur tã-
tum duæ cifræ, vt Tangentes angulorum habeantur, Ita factum eſſe vides ſupra:
Nam ad partes vmbræ 850. adiectæ ſunt duæ cifræ, vt Tangens fieret 85000.
Hac enim ratione fit multip licatio vmbræ abſciſſæ per ſinum totum 100000. &
5151[Handwritten note 51]5252[Handwritten note 52]5353[Handwritten note 53] diuiſio per 1000. vtin Arithmetica noſtra practica ſcripſimus. Quod ſi quatuor
cifræ partibus milleſimis apponantur, habentur eadem ratione Tangẽtes, poſi-
to ſinu toto 10000000.

2. Vervm demonſtremus prius, angulum, quem filum perpendiculi, vel
linea fiduciæ ſecans vmbramrectam cum pro ximo latere facit, in vtro que Qua-
drato eſſe complementum altitudinis Solis, ſeu ſtellæ; illum vero, quem filum
5151[Handwritten note 51]5252[Handwritten note 52]5353[Handwritten note 53] aut fiduciæ linea vmbram verſam ſecans efficit, exhibere ipſam altitudinem. Sit
ergo primum quadratum pendulum ABCD, & Quadrans circuli Verticalis per
ſtellam ducti AEF, ita vt AE, Horizonti æquidiſter: ſintq; tres altitudines ſtel-
læ, EG, grad. 45. EH, maior, & EK, minor. Quando ergo latus pinnacidiorum
AB, cum radio GA, coincidit, erit angulus altitudinis ſemirectus GAE, 3327. tertij. qualis eſt ſuo complemento FAG, propter æquales arcus EG, FG, hoc eſt, 4415. primi.

53[Figure 53]55Filum per-
pendiculi ſe-
cansvmbra@
rectam facit
angulum cõ-
plementi alti-
tudinis; ſecans
vero vmbram
verſam angu-
lum conſtituit
ipſi{us} altitu-
dinis.66ſchol 34.
primi. gulo quem filum cumlatere AB, facit. Cum ergo diameter quadrati ſecet an- gulos eius rectos bifariam, in ſemirectos nimirum, tranſibit filum per angulum
C: Ac proinde tam CAB, quam CAD, æqualis tunc erit angulo altitudinis E-
AG. Quando autem pinnacidiorum latus cum radio HA, coincidit, erit angu-
lus altitudinis EAH, ſemirecto maior, & angulus complementi FAH, ſemirecto
minor, cui æqualis eſt angulus IAB: Acpropterea filum vmbram rectam 7715. primi.

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111	81
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116	86
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118	88
119	89
120	90
121	91
122	92
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124	96
125	95
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