Full text: Clavius, Christoph: Geometria practica

Iam verò ſi ſumma trium angulorum A, B, K, inuentorum, nimirum grad. 325. min. 56. auferatur ex grad. 540. ſumma omnium 5. angu-
lorum pentagoni, reliqua fiet
ſumma angulorum H, I, grad. 214. min. 4. Acproinde vterque
erit grad. 107. min. 2. minor ve-
rò angulo pentagoni grad. 180. Nonergo æquiangulum eſt Du-
reri pentagonum, ſed ſolum æ-
quilaterum. Omnes tamen 5. anguli cõficiunt ſummam grad. 540. ſicut in pentagono æquila-
tero, atque æquiangulo, vt hæ
formula indicat.

375.1.

Angulus # A # Grad. # 108 # min. # 22
# B # Grad. # 108 # min. # 22
# H # Grad. # 107 # min. # 2
# I # Grad. # 107 # min. # 2
# K # Grad. # 109 # min. # 12
## Summa # # 540 # min. # 0

376. SCHOLIVM.

Svnt alij nonnulli, qui ad interuallum cuiuſuis rectæ AB, deſcriptis ex cẽ-
tris A, B, duobus circulis ſe interſecantibus in C, D, vt in ſuperiori figura, ducunt
rectam AD, affirmantque AD, latus eſſe pentagoni in circulo, cuius ſemidiame-
ter DM, inſcripti. ſed toto cœlo aberrant. Eſt enim AD, minus latere pentago-
ni circuli prædicti. Nam quia latus pentagonipoteſt & latus hexagoni, & la- tus decagoni circuli eiuſdem: Poteſt autem AD, rectas DM, MA; & DM, la- tus eſt hexagoni in circulo, cuius ſemidiameter DM, eſſet AM, latus decagoni in
eodem circulo. quod falſum eſt. Quoniam enim latus decagoni maius eſt ſe-
miſſe lateris pentagoni, quod duo latera decagoniſupra latus Pentagoni con-
ſtituant Iſoſceles in quo duo latera maiora ſunt latere pentagoni: Erit AM, ſe- miſsis ipſius AB, vel AD, minor latere decagoni. Igitur AD, minor eſt latere pẽ-
tagoni; quando quidem latus pentagoni poteſt & latus hexagoni DM, & latus decagoni, quod maius eſt, quam AM, ſemiſsis ipſius AD, vt diximus.

376.1.

10. tertijde-
cimi.
47. primi.
coroll. 15.
quanti.
20. primi.
10. tertijde-
cimi.

377. THEOR. 12. PROPOS. 30.

INVENTIONEM lateris heptagoni in dato circulo non rectè à qui-
buſdam tradi, demonſtrare.

Carolvs Marianus Cremonenſis totum vnum libellũ
edidit de inuentione lateris heptagoni in circulo dato, in
quo probare conatur, latus heptagoni reperiri hac ratione. Sit circulus ABC, cuius centrum D, diameter CA, in qua pro-
ducta capiatur AE, æqualis quartæ parti ſemidiametri AD, ita
vt AE, quinta pars ſit rectæ DE. Deſcripto autem ex E, ad in-
teruallum ſemidiametri AD, circulo ſecante datum circulum
in B, iũgatur recta AB, quam dicit eſſe latus heptagoni, quod
falſum eſſe, ita oſtendemus. Si AB, eſſet verum latus hepta-
goni, & ducta BE, æquali ſemidiametro DB, (quod fiet, ſi ex

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