Clavius, Christoph, Geometria practica

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332302GEOMETR. PRACT.& anguli K, H, recti, ideoque & reliqui KBM, HLM, æquales. Igitur 1132. primi. dratum ex FK, GH, tanquam ex vna linea, deſcriptum, & quadratum ex KC,
CH
, tanquam ex vna linea deſcriptum, hoc eſt, quadratum K H, vtraque ſi-
mul
, maiora ſunt quadrato ex BK, D H, tanquam ex vna linea, deſcripto, &

quadrato
ex K M, M H, tanquam ex vna linea deſcripto, hoc eſt, quadrato
KH
, vtriſque ſimul.
Ablato ergo communi quadrato KH, erit quadratum ex
FK
, GH, tanquam ex vna linea, deſcriptum maius quadrato ex BK, DH, tan-
quam
ex vna linea, deſcripto;
ideoque maiores erunt rectæ lineæ FK, GH, ſi-
mul
rectis BK, DH, ſimul;
Acpropterea, demptis communibus BK, GH, erit
FB
, reliqua maior, quam reliqua D G.
Eſt autem & K C, maior quam H C,
quod
tota A C, cuius dimidium eſt K C, maior ponitur quam tota C E, cuius
dimidium
eſt HC.
Quapropter rectangulum ſub FB, KC, contentum, maius
erit
rectangulo ſub DG, HC, contento.
Et quoniam triangulum FBC, dimi-
dium
eſt rectanguli ſub FB, KC, contenti;
(Nam ſi ſuper F B, conſtituatur re-
ctangulum
altitudinem habens K C, ita vt triangulum, &
rectangulum inter
225[Figure 225]2241. primi. eaſdem ſint parallelas;
erit triangulum parallelo grammi dimidium. quod quidem parallelo grammumidem eſt, quod rectangulum ſub FB, KC, conten-
tum
, vt conſtat.)
Triangulum verò DGC, dimidium eſt rectanguli contenti
ſub
DG, HC;
(Sienim ſuper D G, conſtituatur rectangulum altitudinem ha-
3341. primi. bens H C, ita vt triangulum, &
rectangulum inter eaſdem ſint parallelas: erit triangulum parallelogrammi dimidium. quod quidem parallelo grammum
idem
eſt, quod rectangulum ſub DG, HC, contentum, vt conſtat.)
erit quo-
que
triangulum F B C, maius triangulo D G C;
ac propterea duplum trianguli
F
B C, nimirum rectilineum AFCBA, maius erit duplo trianguli D G C, vtpote
rectilineo
CDEGC.
Quocirca, addito communi compoſito ex triangulis
ABC
, CGE;
erunt triangula AFC, CGE, vtra que ſimul maiora triangulis ABC,
C
D E, vtriſque ſimul.
Duo ergo triangula Iſoſcelia ſimilia ſuper inæ-
qualibus
baſibus conſtituta, &
c. quod oſtenden-
dum
eſt.

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