Full text: Clavius, Christoph: Geometria practica

LIBER QVARTVS. Quo ſegmento 6. dempto ex latere B C, 21. remanebit alterum ſegmentum
C D, 15.

172.1.

18. primi.
13. ſecundi.
Note:
13. ſecundi.
Note:

Deinde in poſteriori triangulo ABD, ducenda ſit perpendicularis ad latus
A B, non maximum. Et quia latus DB, latere AD, maius eſt; erit angulus A, maior angulo B. Cum ambo ergo ſimul ſint duobus rectis minores, erit ſaltem minor B, acutus: ac proinde quadratum rectæ AD, minus erit quadratis recta- rum A B, B D, rectangulo bis comprehenſo ſub latere AB, & ſegmento inter B,
& perpendicularem. Siergo quadratum rectę AD, 121. ſubtrahatur ex ſumma
quadratorum rectarum AB, B D, id eſt, ex 544. reliquum fiet rectangulum bis
comprehenſum ſub A B, & ſegmento, inter B, & perpendicularem, nimirum
423. ideoque eius ſemiſsis 211 {1/2}. æqualis erit illi rectangulo ſemel ſumpto. Qua-
re ſi rectangulum hoc 211 {1/2}. diuidatur per latus AB, 12. dabit Quotiens 17 {5/8}. ſe-
gmentum inter B, & perpendicularem. quod quia maius eſt latere A B, argu-
mento eſt, perpendicularem DC, cadere extra triangulum: ac proinde angu-
lum A, obtuſum eſſe. Quod ſi ex hoc ſegmento 17 {5/8}. dematur latus AB, 12. re-
manebit exterius ſegmentum 5 {5/8}.

172.1.

18. primi.
17. primi.
13. primi.
Note:
Note:

Qvando conſtat, angulum A, eſſe obtuſum, ideoque perpendicularem
DC, extra triangulum cadere, reperiemus eadem ſegmenta BC, CA, hoc etiam
modo. Quoniam quadratum lateris BD, ſuperat quadrata laterum A B, AD, rectangulo bis comprehenſo ſub latere A B, & ſegmento exteriore AC; ſi ſum-
mam quadratorum rectarum AB, AD, 265. detrahatur ex quadrato lateris BD,
400. reliquum erit rectangulum 135. bis comprehenſum ſub AB, AC: & eius ſe-
miſsis 67 {1/2}. illi rectangulo ſemel ſumpto æqualis erit; ac proinde hocrectan-
gulo 67 {1/2}. diuiſo per latus A B, 12. indicabit Quotiens 5 {5/8}. ſegmentum exterius
CD; cui ſi addatur latus A B, 12. conflabitur ſegmentum BC, 17 {5/8}. Sed prior
ratio, quæ exlibr. 2. Euclid. non pendet, expeditior eſt, ac proinde tenenda: quamuis auctores alij poſteriorem hanc viam plerunque ſequantur.

172.1.

12. ſecundi.
Note:
Quæ ratio te-
nenda in ſe-
gmentis ex-
quirendis.
Perpendicu-
laris in trian-
gulo quo pa-
cto reperia-
tur.

Inventis ſegmentis à perpendiculari factis, ita magnitudinem perpendi-
cularis cognoſcemus.

DIFFERENTIA inter vtrumuis ſegmentum, & lat{us} adiacens ducatur in
ſummam ex eodem ſegmento & later@ conflatam. Radix enim quadrata nume-
ri producti perpendicularem exhibebit notam, vt lib. 1. cap. 3. Num. 17. demonſtra-
uim{us}.

Verbi gratia. In priori triangulo ABC, ſi differentia 4. inter ſegmentum B D,
& latus AB, hoc eſt, inter 6. & 10. multip licetur per 16. nempe per ſummam eiuſ-
dem ſegmenti BD, & lateris AB; gignetur numerus 64. cuius radix quadrata
8. dabit perpendicularem AD. Pari ratione ſi diſſerentia 2. inter ſegmentum
CD, & latus AC, hoc eſt, 15. & 17. ducaturin 32. id eſt, in ſummam eiuſdem ſeg-
menti CD, & lateris AC: procreabitur numerus 64. cuius radix quadrata 8. præbebit perpendicularem AD, vt prius.

172.1.

Note:

In poſteriori autem triangulo ABD, ſi differentia 5 {3/8}. inter
ſegmentum AC, & latus AD, nimirũ inter 5 {5/8}. & 11. ducatur
in 16 {5/8}. hoc eſt, in ſum̃am eiuſdem ſegmenti AC, & latus AD: producetur numerus {5719/64}. ſiue 89 {23/64}. cuius radix quadrata
in numeris exhiberi non poteſt, ſed paulo maior eſt, quãap-
poſita fractio cuius numerator eſt 75 {94/151}. denominator aũt 8.

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