Clavius, Christoph, Geometria practica

Table of contents

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[231.] IIII.
[232.] DE AREA SEGMENTO-rum ſphæræ. Capvt VI.
[233.] ALITER.
[234.] DE AREA SPHÆROIDIS, EIVSDEM-que portionum. Capvt VII.
[235.] DE AREA CONOIDIS parabolici. Capvt VIII.
[236.] DE AREA CONOIDIS Hyperbolici. Capvt IX.
[237.] DE AREA DOLIORVM. Capvt X.
[238.] DE AREA CORPORVM. omnino irregularium. Capvt XI.
[239.] DE SVPERFICIE CONVEXA coni & cylindri recti. Capvt XII.
[240.] FINIS LIBRI QVINTI.
[241.] GEOMETRIÆ PRACTICÆ LIBER SEXTVS.
[242.] THOREMA 1. PROPOSITIO 1.
[243.] PROBLEMA 1. PROPOSITIO 2.
[244.] PROBL. 2. PROPOS. 3.
[245.] ALITER.
[246.] ALITER.
[247.] PROBL. 3. PROPOS. 4.
[248.] SCHOLIVM.
[249.] PROBLEMA 4. PROPOSITIO 5.
[250.] ALITER.
[251.] ALITER.
[252.] SCHOLIVM.
[253.] THEOREMA 2. PROPOS. 6.
[254.] THEOR. 3. PROPOS. 7.
[255.] THEOR. 4. PROPOS. 8.
[256.] COROLLARIVM.
[257.] THEOR. 5. PROPOS. 9.
[258.] PROBL. 5. PROPOS. 10.
[259.] PROBL. 6. PROPOS. 11.
[260.] PROBL. 7. PROPOS. 12.
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page |< < (148) of 450 > >|
178148GEOMETR. PRACT. quæ ſeorſum in charta aliqua ſit deſcripta, productis lineis, quæ illos angulos in
K
, &
L, efficiunt vt in 2. figura apparet. Si namque puncta, vbi dictæ lineæ ex
109[Figure 109] K, &
L, prodeuntes concurrunt, lineis rectis coniungantur, deſcripta erit figu-
ra
O P Q R S, ſimilis omnino figuræ campi A B C D E, Quod ſic demonſtro.
Triangula AGF, OLK, ſimilia ſunt, quòd anguli AGF, AFG, angulis OLK,
OKL
, æquales ſint, ex conſtructione.
Igitur erit AG, ad GF, vt OL, ad LK. 114. ſexti. Eademque ratione, ob ſimilitudinem triangulorum FGE, KLS, erit GF, ad GE,
vt
LK, ad LS:
ac proinde exæquo erit AG, ad GE, vt OI, ad LS. Cum ergo &
anguli
AGE, OLS, circa quos latera illa ſunt proportionalia, æquales ſint,
quippe
cum angulo AGE, factus ſit æ-
110[Figure 110] qualis ex conſtructione angulus O L S:
ſimilia erunt triangula AGE, OLS, 226. ſexti. eſt, æquiangula. Pari ratione ob ſimili-
tudinem
triangulorum FGD, KLR, 334. ſexti. GD, ad GF, vt LR, ad LK.
Item ob ſimi-
litudinem
triangulorum FGE, KLS, erit
FG
, ad GE, vt KL, ad LS.
Igitur erit ex
æquo
GD, ad GE, vt LR, ad LS:
Ac
proinde
cum anguli DGE, RLS, ex con-
ſtructione
ſint æquales;
æquiangula quoque erunt triangula D G E, R L S. 444. ſexti. Non aliter oſtendemus, triangula CGD, BGC, AGB, triangulis, QLR, PLQ,
OLP
, eſſe æquiangula.
Immo eiſdem argumentis concludemus, quamuis non
ſitneceſſarium
, triangula, quæ in F, ſupra latera campi conſtructa ſunt, æqui-
angula
eſſe triangulis in K, ſupra latera figuræ O P Q R S, conſtitutis.
Ex his
ſequitur
, figuram A B C D E, figuræ O P Q R S, æquiangulam eſſe:
quippe cum
earum
anguli coagmentati ſint ex angulis æqualibus, nimirum angulus AED,
ex
angulis AEG, GED, ipſum componentibus, qui angulis OSL, LSR, an-
gulum
OSR, componentibus æquales ſunt;
& ſic de cæteris. Sequitur et-
iam
latera earundem figurarum circa æquales angulos eſſe proportionalia.
Nam propter triangulorum ſimilitudinem, eſt AE, ad EG, vt OS, ad SL: 554. ſexti.

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