214194GEOMETRIÆ.
n.
nabemus parallelepipedum ſub, AB, &
rectangulo, ADC, &
ſub, AB, & rectingulo, BCD,. . ſub, BC, & rectangulo ſub, A
B, CD, cui ſi iunxeris parallelepipedum ſub, BC, & rectangulo ſub,
BD, DC, componeour parallelepipedum ſub, BC, & rectangulo,
129[Figure 129]
ADC, quod additum parallele-
pipedo ſub, AB, & eodem re-
ctangulo, ADC, componet pa-
1135. huius. rallelepipedum ſub, AC, & re-
ctangulo, ADC, quod quidem
æquale erit alteri ſummæ prædi-
ctæ, nempè parallelepipedo ſub,
BC, & rectangulo ſub, BD, D
C, vna cum, {1/3}, cubi, BC, ergo & eorum tripla æqualia erunt ſci-
licet parallelepipedum ter ſub, AC, & rectangulo, ADC, ſeu ter
22Schol. 35.
huius. ſub, AD, & rectangulo, ACD, æquabitur parallelepipedo ter ſub,
BC, & rectangulo, BDC, ſeu ter ſub, BD, & rectangulo, BCD,
cum cubo, BC, additis verò communibus cubis, AC, CD, fiet pa-
3338. huius. rallelepipedum ter ſub, AD, & rectangulo, ACD, cum cubis, A
C, CD, ideſt totus cubus, AD, æqualis parallelepipedo ter ſub, B
4438. huius. D, & rectangulo, BCD, cum cubis, BC, CD, (quæ integrant
cubum, BD,) & cum cubo, AC, eſt igitur cubus, AD, æqualis
duobus cubis, AC, BD. Poſſibile eſt ergo facere, quod propoſi-
tum fuit.
ſub, AB, & rectingulo, BCD,. . ſub, BC, & rectangulo ſub, A
B, CD, cui ſi iunxeris parallelepipedum ſub, BC, & rectangulo ſub,
BD, DC, componeour parallelepipedum ſub, BC, & rectangulo,
pipedo ſub, AB, & eodem re-
ctangulo, ADC, componet pa-
1135. huius. rallelepipedum ſub, AC, & re-
ctangulo, ADC, quod quidem
æquale erit alteri ſummæ prædi-
ctæ, nempè parallelepipedo ſub,
BC, & rectangulo ſub, BD, D
C, vna cum, {1/3}, cubi, BC, ergo & eorum tripla æqualia erunt ſci-
licet parallelepipedum ter ſub, AC, & rectangulo, ADC, ſeu ter
22Schol. 35.
huius. ſub, AD, & rectangulo, ACD, æquabitur parallelepipedo ter ſub,
BC, & rectangulo, BDC, ſeu ter ſub, BD, & rectangulo, BCD,
cum cubo, BC, additis verò communibus cubis, AC, CD, fiet pa-
3338. huius. rallelepipedum ter ſub, AD, & rectangulo, ACD, cum cubis, A
C, CD, ideſt totus cubus, AD, æqualis parallelepipedo ter ſub, B
4438. huius. D, & rectangulo, BCD, cum cubis, BC, CD, (quæ integrant
cubum, BD,) & cum cubo, AC, eſt igitur cubus, AD, æqualis
duobus cubis, AC, BD. Poſſibile eſt ergo facere, quod propoſi-
tum fuit.
COROLLARIVM.
EX hoc manifeſtum eſt, ſi, AC, ſit latus dati cubi, &
ſit etiam da-
tarecta linea, vt, AB, minor, AC, poſſibile eſſe inuenire duos
eubos, vt, AD, DB, ita vt eorum differentia ſit æqualis cubo dato,
AC, & laterun cubicorum, AD, DB, ſcilicet, AB, pariter diffe-
rentia ſit data, eſt. n. cubus, AC, æqualis dictæ cuborum, AD, DB,
differentiæ, vt eſtenſum eſt. Cum verò ſimilia ſolida quæunq; ſint in
tripla ratione linearum, ſeu later um bomologorum eorumdem, ideò
erunt, vt cubi ipſarum linearum, ſeu laterum bomologoroum, & ideò
eandem rationem, quam babet cubus, AD, ad cubum, DB, babebit
ex. gr. Icoſaedrum deſcriptum latere, AD, ad Icoſaedrum deſoriptum
latere, BD, prædicto bomologo, & vt cubus, AD, ad cubum, AC,
ita erit Icoſaedrum, AD, ad Icoſaedrum, AC, nec non colligendo, vt
cubus, AD, ad cubos, AC, BD, ita erit Icoſaedrum, AD, ad Ico-
ſaedra, AC, BD, ergo Icoſaedrum, AD, æquabitur Icoſaedris, AC,
BD, & ſuperabit Icoſaedrum, BD, Icoſaedro, AC, ergo ſi datum
tarecta linea, vt, AB, minor, AC, poſſibile eſſe inuenire duos
eubos, vt, AD, DB, ita vt eorum differentia ſit æqualis cubo dato,
AC, & laterun cubicorum, AD, DB, ſcilicet, AB, pariter diffe-
rentia ſit data, eſt. n. cubus, AC, æqualis dictæ cuborum, AD, DB,
differentiæ, vt eſtenſum eſt. Cum verò ſimilia ſolida quæunq; ſint in
tripla ratione linearum, ſeu later um bomologorum eorumdem, ideò
erunt, vt cubi ipſarum linearum, ſeu laterum bomologoroum, & ideò
eandem rationem, quam babet cubus, AD, ad cubum, DB, babebit
ex. gr. Icoſaedrum deſcriptum latere, AD, ad Icoſaedrum deſoriptum
latere, BD, prædicto bomologo, & vt cubus, AD, ad cubum, AC,
ita erit Icoſaedrum, AD, ad Icoſaedrum, AC, nec non colligendo, vt
cubus, AD, ad cubos, AC, BD, ita erit Icoſaedrum, AD, ad Ico-
ſaedra, AC, BD, ergo Icoſaedrum, AD, æquabitur Icoſaedris, AC,
BD, & ſuperabit Icoſaedrum, BD, Icoſaedro, AC, ergo ſi datum
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