Clavius, Christoph - Geometria practica

Clavius, Christoph, Geometria practica

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[Item 1.]

[2.] CHRISTOPHORI CLAVII BAMBER- GENSISE SOCIETATE Iesv. GEOMETRIA PRACTICA.

[3.] Cum gratia & Priuilegio Sac. Cæſ. Maieſtat. Superiorum Permiſu. Mogvntia, Ex Typographeo lOANNIS Albini. ANNO M. DC. VI.

[4.] Perillvstri Ac Generoso D. GEORGIO FVGGERO SENIORI BARONI IN KIRCHBERG, ET VVEISSENHORN Chriſtophorus Clauius è Societate IESV S.P.D.

[5.] Romæ pridie Idvs Septemb. cIↄ. cI. CIIII.

[6.] Clavdivs Aqvaviva Societatis Iesv Præpoſitus Generalis.

[7.] INDEX CAPITVM, PROBLE-MATVM, AC PROPOSITIONVM HORVM VIII. LIBRORVM. PRIMI LIBRI CAPITA.

[8.] SECVNDI LIBRI PROBLEMATA.

[9.] TERTII LIBRI PROBLEMATA.

[10.] QVARTI LIBRI CAPITA.

[11.] QVINTI LIBRI CAPITA.

[12.] SEXTI LIBRI PROPOSITIONES.

[13.] SEP TIMI LIBRI Propoſitiones.

[14.] FINIS.

[15.] PRÆFATIO.

[16.] GEOMETRIÆ PRACTICÆ. LIBER PRIMVS. Tria capita ad dimenſionem linearum ſum-me neceſſaria complectens.

[17.] INSTRVMENTI PARTIVM Conſtructio, atque vſus. CAPVT I.

[18.] CAPVT II.

[19.] SEQVITVR TABELLA.

[20.] PROBLEMATA VARIA TRIANGV-lorum rectilineorum. Capvt III.

[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.

9161LIBER SECVNDVS. rentiam ſtationum, vt eſt P Q, Tangens maior ad diſtantiam N L, vt paulo an-
te oſtenſum eſt, facilius demonſtrabimus, ſi ducatur recta I T, quæ producta
ſecet N L, in S. Nam in triangulis IP T, K O R, duo latera IP, P T, duobus la-
teribus KO, OR, æqualia ſunt, angulo ſque continent æquales, vtp ote rectos.
Igitur anguli T, R, ęquales ſunt; ideo que KL, IS, parallelæ. Et quia 114. primi. I K, æqualis eſt & ipſi SL, & differentiæ ſtationum HG, vel NM, liquido 2228. primi. ſtat, ita eſſe T Q, differentiam Tangentium ad S L, quæ differentię ſtationum
3334. primi. I K, vel H G, æqualis eſt, vt eſt P Q, Tangens maior ad diſtantiam NL,

44ſchol. 4.
ſext.

3. Per ſolos ſinus ita Problema efficiemus. Primum inquiremus hypote-
5532. primi. nuſas I L, K L, hoc modo. Quoniam angulus L K V, duobus angulis L I K, I L K, æqualis eſt; ſi L I K, angulus complementi maioris anguli obſeruationis
L I N, auferatur ex L K V, angulo complementi minoris anguli obſeruationis
L K M, reliquus fiet angulus I K L. Si ergo fiat.

6610. triang.
rectil.77
Vt ſin{us} anguli I K L, dif- \\ ferentiæ inter duos an- \\ gulos complementorum \\ angulorum obſeruatio- \\ num # ad I K, \\ differẽ- \\ tiam \\ ſtatio- \\ num: # Ita ſin{us} anguli I K L, conflati ex \\ recto, & angulo obſeruationis \\ minore, vel # ad I L,
# # Ita ſin{us} anguli LIK, complemen- \\ ti maioris anguli obſeruationis. # ad K L,
88Hypotenu-
ſarum inuẽ-
tio.

euadet nota tam I L, quam K L, in menſura differentiæ ſtationum. Igitur ſi fiat,

9910. triang.
rectil.1010
Vt ſin{us} tot{us} \\ angulire- \\ cti N, # ad Hypotenuſam \\ proxime inuen- \\ tam I L, # Ita ſin{us} anguli I L N, complementi \\ maioris anguli obſeruationis # ad I N,
#### Vel
Vt ſin{us} tot{us} an- \\ guli recti M, # ad hypotenuſam K L, \\ nuper inuentam: # Ita ſin{us} anguli K L M, complemen- \\ ti minoris anguli obſeruationis # ad \\ K M,
1111Altitudinis
inuentio per
ſolos ſinus.

cognita fiet altitudò I N, vel KM, ex qua ſi dematur ſtatura menſoris, altitudo
quæſita relinquetur H N, vel G M, hoc eſt, E F.

Distantia autem vtraque N L, M L, reperietur, ſi fiat.

121210. triang.
rectil.1313Diſtantiæ in-
uentio per
ſolos ſinus.1414
Vt ſin{us} tot{us} \\ anguli recti \\ N, vel M, # ad Hypotenuſam \\ inuentam I L, \\ vel K L, # Ita ſin{us} anguli maioris ob- \\ ſeruati NIL, vel \\ ad N L, diſtan- \\ tiam
# # Ita ſin{us} anguli minoris ob- \\ ſeruati M K L, # ad M L, diſtan- \\

Sine numeris eædem rectæ IN, N L, IL, K L, & c. reperientur, vt in ſupe-
1515Quo pacto
problema
conficiatur ſi-
ne numeris. rioribus: ſi nimirum (vtemur figura huius problematis, ne nouam conſtruere
cogamur) ſumptarecta IK, tot partium, quot palmi, pedeſuein differentia ſta-
tionum exiſtunt, fiant anguli VKL, VIL, complementorum angulorum MKL,
NIL, obſeruationum, & concurſus L, notetur, ex quo ducatur LN, ipſi IK, pa-
rallela, & ad hanc perpendicularis in I, excitetur IN, & c. Vel ſi angulus rectus
conſtituatur INL, & in aſſumpto puncto L, vbi concurſum eſſe volumus,

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