Clavius, Christoph
,
Geometria practica
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LIBER QVARTVS.
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Quo ſegmento 6. </
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<
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<
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C D, 15.</
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</
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<
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<
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<
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">Deinde</
emph
>
in poſteriori triangulo ABD, ducenda ſit perpendicularis ad latus
<
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<
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xlink:label
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note-193-01
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xml:space
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">18. primi.</
note
>
A B, non maximum. </
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>
<
s
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xml:space
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">Et quia latus DB, latere AD, maius eſt; </
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>
<
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xml:space
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"> erit angulus
<
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xlink:label
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note-193-02
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xlink:href
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note-193-02a
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xml:space
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">17. primi.</
note
>
maior angulo B. </
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>
<
s
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xml:space
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"> Cum ambo ergo ſimul ſint duobus rectis minores, erit
<
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xlink:label
="
note-193-03
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xlink:href
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note-193-03a
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xml:space
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">13. primi.</
note
>
minor B, acutus: </
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<
s
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="
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"
xml:space
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"> ac proinde quadratum rectæ AD, minus erit quadratis
<
handwritten
xlink:label
="
hd-193-1
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xlink:href
="
hd-193-1a
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number
="
64
"/>
<
handwritten
xlink:label
="
hd-193-1
"
xlink:href
="
hd-193-1a
"
number
="
66
"/>
<
handwritten
xlink:label
="
hd-193-1
"
xlink:href
="
hd-193-1a
"
number
="
67
"/>
rum A B, B D, rectangulo bis comprehenſo ſub latere AB, & </
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>
<
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xml:space
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">ſegmento inter B,
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& </
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<
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">perpendicularem. </
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>
<
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echoid-s6465
"
xml:space
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">Siergo quadratum rectę AD, 121. </
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>
<
s
xml:id
="
echoid-s6466
"
xml:space
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">ſubtrahatur ex ſumma
<
lb
/>
quadratorum rectarum AB, B D, id eſt, ex 544. </
s
>
<
s
xml:id
="
echoid-s6467
"
xml:space
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">reliquum fiet rectangulum bis
<
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comprehenſum ſub A B, & </
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>
<
s
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xml:space
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>
<
s
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xml:space
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">perpendicularem, nimirum
<
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423. </
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>
<
s
xml:id
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echoid-s6470
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xml:space
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">ideoque eius ſemiſsis 211 {1/2}. </
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>
<
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xml:space
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">æqualis erit illi rectangulo ſemel ſumpto. </
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>
<
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xml:space
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">Qua-
<
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re ſi rectangulum hoc 211 {1/2}. </
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<
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xml:space
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">diuidatur per latus AB, 12. </
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<
s
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">dabit Quotiens 17 {5/8}. </
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>
<
s
xml:id
="
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xml:space
="
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">ſe-
<
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gmentum inter B, & </
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>
<
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xml:id
="
echoid-s6476
"
xml:space
="
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">perpendicularem. </
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>
<
s
xml:id
="
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"
xml:space
="
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">quod quia maius eſt latere A B, argu-
<
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mento eſt, perpendicularem DC, cadere extra triangulum: </
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>
<
s
xml:id
="
echoid-s6478
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xml:space
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">ac proinde angu-
<
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/>
lum A, obtuſum eſſe. </
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>
<
s
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="
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xml:space
="
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">Quod ſi ex hoc ſegmento 17 {5/8}. </
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>
<
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"
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="
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">dematur latus AB, 12. </
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>
<
s
xml:id
="
echoid-s6481
"
xml:space
="
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">re-
<
lb
/>
manebit exterius ſegmentum 5 {5/8}.</
s
>
<
s
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="
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xml:space
="
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</
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>
<
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="
65
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<
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<
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<
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style
="
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">Qvando</
emph
>
conſtat, angulum A, eſſe obtuſum, ideoque perpendicularem
<
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/>
DC, extra triangulum cadere, reperiemus eadem ſegmenta BC, CA, hoc etiam
<
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<
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symbol
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xml:space
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">12. ſecundi.</
note
>
modo. </
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>
<
s
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xml:space
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"> Quoniam quadratum lateris BD, ſuperat quadrata laterum A B,
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<
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66
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<
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rectangulo bis comprehenſo ſub latere A B, & </
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>
<
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">ſegmento exteriore AC; </
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<
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xml:space
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">ſi ſum-
<
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mam quadratorum rectarum AB, AD, 265. </
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>
<
s
xml:id
="
echoid-s6487
"
xml:space
="
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">detrahatur ex quadrato lateris BD,
<
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400. </
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>
<
s
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="
echoid-s6488
"
xml:space
="
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">reliquum erit rectangulum 135. </
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>
<
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echoid-s6489
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xml:space
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">bis comprehenſum ſub AB, AC: </
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<
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">& </
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<
s
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">eius ſe-
<
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miſsis 67 {1/2}. </
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>
<
s
xml:id
="
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"
xml:space
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">illi rectangulo ſemel ſumpto æqualis erit; </
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>
<
s
xml:id
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gulo 67 {1/2}. </
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<
s
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">diuiſo per latus A B, 12. </
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>
<
s
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">indicabit Quotiens 5 {5/8}. </
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>
<
s
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<
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<
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="
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xlink:label
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note-193-05a
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xml:space
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">Quæ ratio te-
<
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nenda in ſe-
<
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gmentis ex-
<
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quirendis.
<
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/>
Perpendicu-
<
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laris in trian-
<
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gulo quo pa-
<
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cto reperia-
<
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tur.</
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>
CD; </
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>
<
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<
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<
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<
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ratio, quæ exlibr. </
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<
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<
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<
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</
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<
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<
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ſegmentis à perpendiculari factis, ita magnitudinem perpendi-
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cularis cognoſcemus.</
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<
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<
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">lat{us} adiacens ducatur in
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ſummam ex eodem ſegmento & </
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<
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<
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ri producti perpendicularem exhibebit notam, vt lib. </
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<
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<
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<
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<
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uim{us}.</
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<
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<
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<
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style
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>
gratia. </
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<
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xml:space
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">In priori triangulo ABC, ſi differentia 4. </
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<
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xml:space
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">inter ſegmentum B D,
<
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<
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xlink:label
="
hd-193-1
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xlink:href
="
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number
="
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<
handwritten
xlink:label
="
hd-193-1
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xlink:href
="
hd-193-1a
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number
="
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"/>
<
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xlink:label
="
hd-193-1
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xlink:href
="
hd-193-1a
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number
="
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& </
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>
<
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xml:id
="
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">latus AB, hoc eſt, inter 6. </
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<
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">& </
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<
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>
<
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">multip licetur per 16. </
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>
<
s
xml:id
="
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xml:space
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">nempe per ſummam eiuſ-
<
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dem ſegmenti BD, & </
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>
<
s
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xml:space
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">lateris AB; </
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>
<
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="
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">gignetur numerus 64. </
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>
<
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xml:id
="
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"
xml:space
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<
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8. </
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>
<
s
xml:id
="
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xml:space
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">dabit perpendicularem AD. </
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>
<
s
xml:id
="
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"
xml:space
="
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">Pari ratione ſi diſſerentia 2. </
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>
<
s
xml:id
="
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xml:space
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">inter ſegmentum
<
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/>
CD, & </
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>
<
s
xml:id
="
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"
xml:space
="
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">latus AC, hoc eſt, 15. </
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>
<
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="
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">& </
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<
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="
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">17. </
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>
<
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="
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">ducaturin 32. </
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>
<
s
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="
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"
xml:space
="
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">id eſt, in ſummam eiuſdem ſeg-
<
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/>
menti CD, & </
s
>
<
s
xml:id
="
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"
xml:space
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">lateris AC: </
s
>
<
s
xml:id
="
echoid-s6538
"
xml:space
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">procreabitur numerus 64. </
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>
<
s
xml:id
="
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"
xml:space
="
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">cuius radix quadrata 8.
<
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</
s
>
<
s
xml:id
="
echoid-s6540
"
xml:space
="
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">præbebit perpendicularem AD, vt prius.</
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>
<
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="
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</
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>
<
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>
<
s
xml:id
="
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"
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="
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<
emph
style
="
sc
">In</
emph
>
poſteriori autem triangulo ABD, ſi differentia 5 {3/8}. </
s
>
<
s
xml:id
="
echoid-s6543
"
xml:space
="
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">inter
<
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/>
ſegmentum AC, & </
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>
<
s
xml:id
="
echoid-s6544
"
xml:space
="
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">latus AD, nimirũ inter 5 {5/8}. </
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>
<
s
xml:id
="
echoid-s6545
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
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xml:space
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">11. </
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>
<
s
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"
xml:space
="
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">ducatur
<
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/>
<
figure
xlink:label
="
fig-193-01
"
xlink:href
="
fig-193-01a
"
number
="
124
">
<
image
file
="
193-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/193-01
"/>
</
figure
>
in 16 {5/8}. </
s
>
<
s
xml:id
="
echoid-s6548
"
xml:space
="
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">hoc eſt, in ſum̃am eiuſdem ſegmenti AC, & </
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>
<
s
xml:id
="
echoid-s6549
"
xml:space
="
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">latus AD:
<
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/>
</
s
>
<
s
xml:id
="
echoid-s6550
"
xml:space
="
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">producetur numerus {5719/64}. </
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>
<
s
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<
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in numeris exhiberi non poteſt, ſed paulo maior eſt, quãap-
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poſita fractio cuius numerator eſt 75 {94/151}. </
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<
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echoid-s6553
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">denominator aũt 8.</
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