Full text: Clavius, Christoph: Geometria practica

LIBER TERTIVS. nacidiorum conſpiciatur) vertatur dioptra, donec per eam punctum quo que
C, appareat, & vmbra abſciſſa notetur, per quam ex problem. 1. anguli C G D,
magnitudo addiſcatur. Quod ſi alterum latus quadrati vltra rectam G C, exi-
ſtat, erit angulus CGD, acutus: ſi verò citra rectam GC, extiterit, dictus angu-
lus erit obtuſus: quem cognoſcemus, ſi ad rectum adiiciemus reliquum angu-
lum, inter alterum illud latus, & rectam GC; quem quidem inueſtigabimus, vt
de acuto C G D, diximus, ſi nimirum in recta CD, mente notemus punctum, in
quod alterum illud latus productum incideret. Nam ſi tunc latus illud rectæ
G C, congruat, & dioptra ad punctum notatum vergat, indicabit vmbra inter
latus illud, & lineam fiduciæ angulum prædictum reliquum, vt in problemate 1. dictum eſt. Si denique alterum illud latus præcisè rectæ GC, congruat, angulus
CGD, rectus erit. His peractis, quia in triangulo CGD, latera GC, GD, nota
continent angulum G, etiam cognitum; cognoſcetur quoque tertium latus CD, quod quæritur.

133.1.

157-01
12. triang.
rectil.

2. Vervm inuentis diſtantiis GC, G D, in aliqua menſura, vna cum an-
gulo G, fa cilius, licet non tam certò, interuallum CD, co [?] gnoſcemus hoc pacto. Deſcripto angulo G, ſeorſum ſumatur in GC, portio quotlibet partium late-
ris quadrati, verbi gratia 500. id eſt, ſemiſsis lateris. Et fiat, vt diſtantia inuen-
ta G C, ad diſtantiam inuentam G D, ita partes acceptæ 500. ad aliud. Nam
Quotiens dabit numerum quartum proportionalem earundem partium la-
teris quadrati; quibus ſi capiatur in G D, portio æqualis, erit interuallum inter extrema puncta dictarum portionum, æquidiſtans interuallo CD; vt con-
ſtat, ſi illæ portiones in rectas GC, GD, in figura transferrentur; propterea ꝙ in
illis extremis punctis rectæ GC, GD, ſectæ eſſent proportionaliter. Quare ſi il-
lud interuallum circino menſuretur in eiſdem partibus lateris quadrati, con-
tinebit interuallum C D, totidem particulas rectæ G C, in 500. partes æqua-
les diuiſæ, quot in illo interuallo comprehen duntur ex particulis lateris qua-
drati: cum ſit vt portio particularum 500. ad interuallum illud, ita G C, di-
uiſa in partes æquales 500. ad CD. Quæ particulæ reducentur ad menſuram, in
qua inuentæ ſunt GC, GD: ſi fiat, vt GC, quatenus 500. ad menſuras in G C,
inuentas, ita C D, inuenta in particulis rectæ GC, in 500. partes diuiſæ, ad
aliud.

133.1.

2. ſexti.

Qvia verò vix per circinum accurate reperiri poteſt interuallum illud inter
extremitates proportionalium, magis ex quiſitè, licet laborioſius, interuallum
propoſitum cognoſcetur per 12. triang. rectilineorum.

INTERVALLVM tranſuerſum in Horizonte, cuius vtrumque ex-
tremum videri poteſt, per quadratum metiri.

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