Clavius, Christoph
,
Geometria practica
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LIBER QVARTVS.
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<
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xml:space
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">DE AREA MVLTIL ATERARVM
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figurarum irregularium.</
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>
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<
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IV.</
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<
s
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xml:space
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">1. </
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<
s
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xml:space
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">FIGVRAS multilateras irregulares, quæ videlicet plura latera habent
<
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<
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xlink:label
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note-201-01
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xlink:href
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note-201-01a
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xml:space
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">Area multi
<
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lateræ figuræ.</
note
>
inæqualia, quam quatuor, etiamſi valdè irregulares ſint, metiemur, vt
<
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/>
trapezia irregularia, reſoluendo nimirum illasin triangula, & </
s
>
<
s
xml:id
="
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xml:space
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">ſingulorũ
<
lb
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triangulorum areas inueſtigando. </
s
>
<
s
xml:id
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echoid-s7121
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xml:space
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preserve
">Nam omnes hæ areæ in vnam ſummam col-
<
lb
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lectæ æquales ſunt areæ totius figuræ propoſitæ. </
s
>
<
s
xml:id
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echoid-s7122
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xml:space
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preserve
">Vt ſi figura ſeptem laterum A-
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BCDEFG, reſoluatur in quin que triangula ABG, GBD, DBC, DEF, FDG, ita
<
lb
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xlink:label
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note-201-02
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xlink:href
="
note-201-02a
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xml:space
="
preserve
">Quando figu-
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/>
ra in triangu-
<
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/>
la reſolui po-
<
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/>
teſt, quo m@-
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/>
do ei{us} area
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/>
colligatur.</
note
>
vteorum latera ſe mutuo non interſecent, in quirendæ ſunt areæ ſingulorũ hoc
<
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/>
<
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number
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129
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201-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/201-01
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modo. </
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<
s
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xml:space
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">Quando omnia latera triangulorum nota effici poſſunt per aliquam
<
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/>
menſuram, ſiue figura agrum aliquem repræſentet, ſiue in charta ſolum ſit de-
<
lb
/>
ſcripta, demittantur ex angulis ad latera oppoſita perpendiculares AH, DI, CK,
<
lb
/>
DM, FL, ſingulæ in ſingulis triangulis. </
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>
<
s
xml:id
="
echoid-s7124
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xml:space
="
preserve
">Deinde in triangulo ABG,
<
note
symbol
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a
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position
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right
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xlink:label
="
note-201-03
"
xlink:href
="
note-201-03a
"
xml:space
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preserve
">9. triang. re-
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ctil.</
note
>
ex tribus lateribus notis ſegmenta B H, H G; </
s
>
<
s
xml:id
="
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xml:space
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">& </
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>
<
s
xml:id
="
echoid-s7126
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xml:space
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">ex his perpendicularis A H, vt
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cap. </
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<
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>
<
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xml:space
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">huius lib. </
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<
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">Num. </
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<
s
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">2. </
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>
<
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">declarauimus. </
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>
<
s
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xml:space
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">Nam AH, in ſemiſſem baſis B G, ducta
<
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/>
producet aream trianguli A B G. </
s
>
<
s
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="
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xml:space
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preserve
">Eadem que ratione aliorum triangulorum areæ
<
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perueſtigentur: </
s
>
<
s
xml:id
="
echoid-s7134
"
xml:space
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preserve
">atque omnes areæ in vnam redigantur ſummam, vt area toti-
<
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/>
us figuræ habeatur. </
s
>
<
s
xml:id
="
echoid-s7135
"
xml:space
="
preserve
">Quod ſi malueris, poteris omnium triangulorum areas in-
<
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dagare ex tribus lateribus cognitis, per ea, quæ capit. </
s
>
<
s
xml:id
="
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xml:space
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">2. </
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>
<
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">Numer. </
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<
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">1. </
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<
s
xml:id
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xml:space
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">ſcripſimus,
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etiamſi neque perpendiculares ductæ ſint, neque ſegmenta B H, G H, in-
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/>
uenta.</
s
>
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</
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<
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<
s
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xml:space
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">2. </
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>
<
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<
emph
style
="
sc
">Qvando</
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>
latera triangulorum interiora menſurarinequeunt, immo ne-
<
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/>
<
note
position
="
right
"
xlink:label
="
note-201-04
"
xlink:href
="
note-201-04a
"
xml:space
="
preserve
">Quando figu-
<
lb
/>
ra in triangu-
<
lb
/>
la reſolui non
<
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/>
poteſt quo mo
<
lb
/>
do ei{us} area
<
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/>
deprehenda-
<
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/>
tur.</
note
>
que duci, vt non raro accidit in campis, aut agris, qui vel propter arbores, vel
<
lb
/>
paludes interiectas, rectis itineribus pertranſirinon poſſunt; </
s
>
<
s
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xml:space
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">alia ratione ſco-
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pum attingemus, hac videlicet. </
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>
<
s
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xml:space
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">Cognitis lateribus figuram ambientibus
<
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per aliquam menſuram, inueſtigentur quoque anguli ab ipſis comprehenſi
<
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/>
beneficio quadrantis alicuius in gradus diuiſi. </
s
>
<
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xml:id
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xml:space
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preserve
">In propoſita figura angulus
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C D E, indagandus non eſt, quod ſit extra figuram. </
s
>
<
s
xml:id
="
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xml:space
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preserve
">Reſoluta deinde figura
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mente. </
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>
<
s
xml:id
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xml:space
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preserve
">aut cogitatione in triangula, ac ſi latera interiora ducta eſſent, vt p@us:</
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>
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