Clavius, Christoph - Geometria practica

Clavius, Christoph, Geometria practica

Table of contents

[21.] TRIANGVLORVM RECTILINEORVM RECTAN-gulorum problemata. I. PROPORTIONES LATERVM

[22.] II. LATVS.

[23.] III. LATVS.

[24.] IIII. LATVS.

[25.] V. BASEM.

[26.] VI. BASEM.

[27.] VII. ANGVLVM.

[28.] VIII. ANGVLVM.

[29.] TRIANGVLORVM RECTILINEO-rum obliquangulorum Problemata. IX. SEGMENTA LATERIS A Perpendiculari facta.

[30.] X. LATERA DVO.

[31.] Rurſus

[32.] XI. LATVS.

[33.] XII. LATVS.

[34.] Deinde.

[35.] Hæc autem tangens hoc etiam modo inuenietur, qui priori præferendus videtur.

[36.] Poſt hæc.

[37.] XIII. LATVS.

[38.] XIIII. ANGVLOS DVOS.

[39.] XV. ANGVLOS DVOS.

[40.] XVI. ANGVLOS OMNES TRES. Ex tribus omnibus lateribus perueſtigare.

[41.] Rurſus.

[42.] XVII. PERPENDICVLAREM IN LATVS quodcunque ex angulo oppoſito cadentem. Ex tribus omnibus lateribus efficere notam.

[43.] FINIS LIBRI PRIMI.

[44.] GEOMETRIÆ PRACTICÆ LIBER SECVNDVS.

[45.] PROBLEMA I.

[46.] ALITER

[47.] ALITER

[48.] ALITER

[49.] LEMMA.

[50.] SCHOLIVM.

145115LIBER TERTIVS. differentiæ ſtationum, nota relinquetur altitudo D F, vel d M, quæſita. Inueniri
autem hac ratione rectam AF, demonſtratum eſt in problemate 4. Num. 1.

2. Qvod ſi in vtraque ſtatione latus vmbræ verſæ ſecetur in F, H, vt in 2.
figura problematis 4. hic repetita, inuerſa tamen, habebimus tres vias inueſti-
gandi altitudinem A F, ex qua ſi tollatur latus quadrati A D, manifeſta relin-
quetur quęſita altitudo DF, vel d M. Nam reducta vtraque vmbra verſa ad re-
ctam, ſi fiat,

71[Figure 71]11
Vt I N, differentia vmbra- \\ rum rectarum, # ad A a, differentiam \\ ſtationum: # Ita A D, lat{us} qua- \\ drati 1000. # ad AF.
# Vel ſine reductione.
Vt P, numer{us}, qui fit ex \\ O H, differentia vmbra- \\ rum verſarum in a b, la- \\ t{us} quadrati, # ad numerum, qui fit ex vm- \\ bra verſa b H, maiore in \\ minorem B E, # Ita A a, diffe- \\ rentia ſtatio- \\ num # ad A F,
#### Vel
Vt A a, differentia Quotientum, qui \\ fiunt, ſi lat{us} quadrati per vtram \\ vmbram verſam diuidatur, # ad A a, differentiam ſta- \\ tionum notam in menſu- \\ ra aliqua # Ita A F, \\ vt 1. # ad A F,

procreabitur ſemper altitudo AF, ab oculo inſpectoris A, numerata: quemad-
modumin problemate 4. Num. 2. demonſtratum eſt.

3. Si denique in vna ſtatione ſecetur latus vmbræ verſę in E, & in altera la-
tus vmbrę rectæ in H, vt in 3. figura problematis 4. hic inuerſo ordine repetita:
ſi vtin eodem problemate 4. Num. 3. demonſtrauimus, reducatur vmbra ver-
ſa ad rectam, & fiat,

72[Figure 72]

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