6949LIBER I.
quadrata, AE, EG, (quia etiam, AEG, rectus eſt) æquabuntur
tribus quadratis, AE, EF, FG, vnde, ablato communiquadrato,
1148. Primi
El. Def. 6. AE, quadratum, GE, ęquabitur duobus quadratis, GF, FE; pari
ratione autem probabimus quadratum, YT, æquari quadratis, Y
22Vndec. Z, ZT, vnde anguli, GFE, YZT, recti erunt; & eodem modo
33Elem. probabimus eſſe rectos, EPG, TXY, ergo anguli, AFE, KZT,
44Defin. 6.
Vnd. El. erunt anguli inclinationis primorum planorum, BG, LY, cum iu-
biectis planis, HV, & Λ, & ideò inter ſe æquales: Similiter anguli,
APE, KXT, erunt inclinationes ſecundorum planorum, AV, K
Λ, cum eiſdem ſubiectis planis. Quia ergo anguli, AFE, KZT,
ſunt æquales, & , AEF, KTZ, recti, erunt triangula, AFE, K
ZT, inter ſe ſimilia, vt etiam triangula, AFG, KZY, inter ſe,
nam anguli, AGF, KYZ, ſunt quoque æquales, & , AFG, KZ
Y, recti; erit ergo, vt, EF, ad, FA, ſic, TZ, ad, ZK, & vt, A
F, ad, FG, ſic, KZ, ad, ZY, ergo ex æquali, vt, EF, ad, FG,
itaerit, TZ, ad, ZY, & ſunt circa rectos, nempè æquales angu-
556. Sexti
Elem. los, GFE, YZT, ergo triangula, GFE, YZT, pariter ſimilia
erunt, anguli igitur, EGF, TYZ, adæquabuntur, totus autem,
PGF, toti, XYZ, æquatur, ergo reliquus, EGP, erit ęqualis re-
liquo, TYX, & ſunt recti, EPG, TXY, vt probatum eſt, ergo
erunt, GPE, YXT, ſimilia triangula, igitur, vt, PG, ad, GE,
ſic erit, XY, ad, YT, vt verò, GE, ad, GF, ſic eſt, YT, ad, YZ,
& vt, GF, ad, GA, ſic, YZ, ad, YK, ergo ex æquali, PG, ad,
GA, erit vt, XY, ad, YK, habemus ergo duo triangula, APG,
KXY, habentia duos angulos, APG, KXY, ęquales, ſunt. n. re-
cti, circa verò duos, PGA, XYK, latera proportionalia, & reli-
quorum vtrumq; ſimul, PAG, XKY, minorem recto, ergo erunt
667. Sexti
Elem. ſimilia, & anguli, PGA, XYK, ęquales, vnde reliqui, AGV, Κ
Υ Λ, pariter æquales erunt, quod eſt vnum propoſitorum.
tribus quadratis, AE, EF, FG, vnde, ablato communiquadrato,
1148. Primi
El. Def. 6. AE, quadratum, GE, ęquabitur duobus quadratis, GF, FE; pari
ratione autem probabimus quadratum, YT, æquari quadratis, Y
22Vndec. Z, ZT, vnde anguli, GFE, YZT, recti erunt; & eodem modo
33Elem. probabimus eſſe rectos, EPG, TXY, ergo anguli, AFE, KZT,
44Defin. 6.
Vnd. El. erunt anguli inclinationis primorum planorum, BG, LY, cum iu-
biectis planis, HV, & Λ, & ideò inter ſe æquales: Similiter anguli,
APE, KXT, erunt inclinationes ſecundorum planorum, AV, K
Λ, cum eiſdem ſubiectis planis. Quia ergo anguli, AFE, KZT,
ſunt æquales, & , AEF, KTZ, recti, erunt triangula, AFE, K
ZT, inter ſe ſimilia, vt etiam triangula, AFG, KZY, inter ſe,
nam anguli, AGF, KYZ, ſunt quoque æquales, & , AFG, KZ
Y, recti; erit ergo, vt, EF, ad, FA, ſic, TZ, ad, ZK, & vt, A
F, ad, FG, ſic, KZ, ad, ZY, ergo ex æquali, vt, EF, ad, FG,
itaerit, TZ, ad, ZY, & ſunt circa rectos, nempè æquales angu-
556. Sexti
Elem. los, GFE, YZT, ergo triangula, GFE, YZT, pariter ſimilia
erunt, anguli igitur, EGF, TYZ, adæquabuntur, totus autem,
PGF, toti, XYZ, æquatur, ergo reliquus, EGP, erit ęqualis re-
liquo, TYX, & ſunt recti, EPG, TXY, vt probatum eſt, ergo
erunt, GPE, YXT, ſimilia triangula, igitur, vt, PG, ad, GE,
ſic erit, XY, ad, YT, vt verò, GE, ad, GF, ſic eſt, YT, ad, YZ,
& vt, GF, ad, GA, ſic, YZ, ad, YK, ergo ex æquali, PG, ad,
GA, erit vt, XY, ad, YK, habemus ergo duo triangula, APG,
KXY, habentia duos angulos, APG, KXY, ęquales, ſunt. n. re-
cti, circa verò duos, PGA, XYK, latera proportionalia, & reli-
quorum vtrumq; ſimul, PAG, XKY, minorem recto, ergo erunt
667. Sexti
Elem. ſimilia, & anguli, PGA, XYK, ęquales, vnde reliqui, AGV, Κ
Υ Λ, pariter æquales erunt, quod eſt vnum propoſitorum.
Rurſus, quia, PE, ad, EF, eſt vt, XT, ad, TZ;
EF, autem
ad, EA, vt, TZ, ad, TK, ergo ex æquali, PE, ad, EA, erit vt,
XT, ad; TK, & ſunt circa ęquales angulos, PEA, XTK, latera
776. Sexti
Elem. proportionalia, ergo triangula, APE, KXT, ſimil a erunt, nec-
non anguli, APE, KXT, inclinationis ſecundorum planorum, A
V, Κ Λ, cum ſubiectis planis inter ſe æquales, & ad eandem partem
quod etiam demonſtrare propoſitum fuit.
ad, EA, vt, TZ, ad, TK, ergo ex æquali, PE, ad, EA, erit vt,
XT, ad; TK, & ſunt circa ęquales angulos, PEA, XTK, latera
776. Sexti
Elem. proportionalia, ergo triangula, APE, KXT, ſimil a erunt, nec-
non anguli, APE, KXT, inclinationis ſecundorum planorum, A
V, Κ Λ, cum ſubiectis planis inter ſe æquales, & ad eandem partem
quod etiam demonſtrare propoſitum fuit.
THEOREMA XXIV. PROPOS XXVII.
POſita definitione, quam affert Euclides lib 6.
El.
de ſimi-
libus figuris rectilineis, ſequitur pro ipſis etiam defini-
tio geneneralis, quam de omnibus ſimilibus figuris planis
ipſe attuli.
libus figuris rectilineis, ſequitur pro ipſis etiam defini-
tio geneneralis, quam de omnibus ſimilibus figuris planis
ipſe attuli.