293263LIBER SEXTVS.partes æquales, detrahenda primum erit per lineam rectam ex dato puncto du-
ctam pars denominata à numero partium, in quas diuidendum eſt triangulum.
197[Figure 197]
Deinde duæ tales partes:
poſtea tres, atque ita deinceps, donec tot partes, vna
minus, detractæ ſint, in quot partes diuidendum proponitur triangulum. Vt ſi
triangulum ABC, ex puncto D, diuidendum ſit in quinque partes æquales, diui-
demus latus BC, in quo datum punctum eſt, in quinque partes æquales, in pun-
ctis E, F, G, H. Iuncta deinderecta DA, ducemus ei parallelas EI, FK, GL, HM.
Sinamque connectantur rectæ D I, D K, D L, D M, diuiſum erit triangulum in
quinque partes æquales. Nam vt in dicta propoſ. 14. ſcholij propoſ. 33. lib. 6.
Euclid. oſtenſum eſt, triangulum DBI, eſt {@/5}. totius trianguli, hoc eſt, ita ſe ha-
bet DBI, ad ABC, vt BE, ad BC. Triangulum autem DBK, continet {2/3}. totius
trianguli, id eſt, ita ſe habet D B K, ad A B C, vt B F, ad B C. At vero triangulum
DBL, complectitur {3/5}. totius trianguli, id eſt, ita ſe habet DBL, ad ABC, vt BG,
ad BC. Quadrilaterum denique ABDM, comprehendit {4/5}. totius trianguli, hoc
eſt, ita ſe habet ABDM, ad ABC, vt B H, ad B C. Ex quo fit, reliquum triangu-
lum DMC, eſſe {1/5}. eiuſdem trianguli ABC.
ctam pars denominata à numero partium, in quas diuidendum eſt triangulum.
minus, detractæ ſint, in quot partes diuidendum proponitur triangulum. Vt ſi
triangulum ABC, ex puncto D, diuidendum ſit in quinque partes æquales, diui-
demus latus BC, in quo datum punctum eſt, in quinque partes æquales, in pun-
ctis E, F, G, H. Iuncta deinderecta DA, ducemus ei parallelas EI, FK, GL, HM.
Sinamque connectantur rectæ D I, D K, D L, D M, diuiſum erit triangulum in
quinque partes æquales. Nam vt in dicta propoſ. 14. ſcholij propoſ. 33. lib. 6.
Euclid. oſtenſum eſt, triangulum DBI, eſt {@/5}. totius trianguli, hoc eſt, ita ſe ha-
bet DBI, ad ABC, vt BE, ad BC. Triangulum autem DBK, continet {2/3}. totius
trianguli, id eſt, ita ſe habet D B K, ad A B C, vt B F, ad B C. At vero triangulum
DBL, complectitur {3/5}. totius trianguli, id eſt, ita ſe habet DBL, ad ABC, vt BG,
ad BC. Quadrilaterum denique ABDM, comprehendit {4/5}. totius trianguli, hoc
eſt, ita ſe habet ABDM, ad ABC, vt B H, ad B C. Ex quo fit, reliquum triangu-
lum DMC, eſſe {1/5}. eiuſdem trianguli ABC.
Qvando punctum datum eſt in vno angulo, manifeſtum eſt, ſi latus op-
poſitum in tot partes ſecetur, in quot triangulum diuidendum eſt, rectas 111. ſexti. eo angulo ad puncta diuiſionum eductas ſecare triangulum in propoſitas par-
tes æquales.
poſitum in tot partes ſecetur, in quot triangulum diuidendum eſt, rectas 111. ſexti. eo angulo ad puncta diuiſionum eductas ſecare triangulum in propoſitas par-
tes æquales.
PROBL. 6. PROPOS. 11.
DATVM triangulum per lineas vni lateri parallelas in quotlibet æ-
quales partes diuidere,
quales partes diuidere,
Sit triangulum A B C, diuidendum verbi gratia in quatuor partes æquales
perlineas lateri BC, æquidiſtantes. Secetur vtrumuis reliquorum laterum ni-
198[Figure 198]
mirum A B, in 4.
partes æquales, in tot videlicet, in quot triangulũ diuidendum
eſt, in punctis D, E, F. Etinter A B, A D, inuenta media proportionali A E;
perlineas lateri BC, æquidiſtantes. Secetur vtrumuis reliquorum laterum ni-
eſt, in punctis D, E, F. Etinter A B, A D, inuenta media proportionali A E;
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