240220GEOMETRIÆ
pro axiſumptum eſt) &
curua circuli, vel ellipſis contine-
tur, erunt proximè, vt baſis eiuſdem parallelogrammi ad ſui
reliquum, demptis ab ea, {11/14}, rectæ lineæ, quæ ſit æqualis
dimidiæ ſecundæ diametri Prædicti circuli, vel ellipſis, ſi-
mul cum exceſſu, quo dicti, {11/14}, excedunt, {2/3}, tertiæ propor-
tionalis duarum, quarum prima eſt dicta baſis, ſecunda au-
tem dicta ſecundæ diametri dimidia.
tur, erunt proximè, vt baſis eiuſdem parallelogrammi ad ſui
reliquum, demptis ab ea, {11/14}, rectæ lineæ, quæ ſit æqualis
dimidiæ ſecundæ diametri Prædicti circuli, vel ellipſis, ſi-
mul cum exceſſu, quo dicti, {11/14}, excedunt, {2/3}, tertiæ propor-
tionalis duarum, quarum prima eſt dicta baſis, ſecunda au-
tem dicta ſecundæ diametri dimidia.
Sit parallelogrammum, FD, &
circa latus, FB, vtcunque tam-
quam circa diametrum (intellige autem ſemper diametrum hic, &
in ſequentibus, vt eſt nomen commune diametro, & axi) integri ſic
deſcriptus ſemicirculus, vel ſemiellipſis, FQB, cuius curua, FQB,
neque tangat, neque ſecet latus, ZD, oppoſitum lateri, FB, bifa-
riam autem diuiſa, FB, in, A, & per, A, ipſi, BD, baſi ducta pa-
rallela, AP, ſeceturà curua, FQB, vtcunq; in, Q; erit autem, A
Q, dimidia ſecundæ axis circuli, vel ellipſis, cuius centrum, A; du-
catur inſuperper, Q, ipſi, FB, parallela, HC, quæ tanget circu-
1117.1.Con. lum dictum, vel ellipſim, & erit, BC, æqualis ipſi, AQ; fiat dein-
de, vt, DB, ad, BC, ita, BC, ad, BI, & ſumatur, BR, quæ ſit,
{2/3}, BI, & , BE, quæ fit, {11/14}, ipſius, CB, & , EV, quæ ſit æqualis
150[Figure 150]
ipſi, ER, regula verò ſit, BD.
Dico er-
go omnia quadrata parallelogrammi, FD,
ad omnia quadrata figuræ, quæ compre-
henditur tribus lateribus, FZ, ZD, DB,
& curua, FQB, eſſe, vt, BD, ad, DV,
proximè. Omnia . n. quadrata parallelo-
grammi, FD, ad rectangula ſub paralle-
logrammo, FD, & ſemicirculo, vel ſemi-
22Coroll.1.
26.lib.2. ellipſis, FQB, ſunt vt parallelogram-
mum, FD, ad eundem ſemicirculum, vel
ſemiellipſim, FQB; quia verò parallelo-
grammum, FD, ad parallelogrammum, FC, eſt vt, DB, ad, BC,
& item parallelogrammum, FC, ad ſemicirculum, vel ſemiellipſim,
335. Lib.2.
Arch. de
Dim.Cir. FQB, eſt proximè vt 14. ad 11. ideſt vt, CB, ad, BE, ergo ex
æquali parallelogrammum, FD, ad ſemicirculum, vel ſemiellipſim,
FQB, erit vt, DB, ad, BE, & ideò omnia quadrata parallelogram-
mi, FD, ad rectangula ſub parallelogrammo, FD, & ſemicirculo,
445.Lib.2. vel ſemiellipſi, FQB, erunt vt, DB, ad, BE,. i. ſumpta, DB, com-
muni altitudine erunt, vt quadratum, DB, ad rectangulum ſub, D
B, BE, quodſerua.
quam circa diametrum (intellige autem ſemper diametrum hic, &
in ſequentibus, vt eſt nomen commune diametro, & axi) integri ſic
deſcriptus ſemicirculus, vel ſemiellipſis, FQB, cuius curua, FQB,
neque tangat, neque ſecet latus, ZD, oppoſitum lateri, FB, bifa-
riam autem diuiſa, FB, in, A, & per, A, ipſi, BD, baſi ducta pa-
rallela, AP, ſeceturà curua, FQB, vtcunq; in, Q; erit autem, A
Q, dimidia ſecundæ axis circuli, vel ellipſis, cuius centrum, A; du-
catur inſuperper, Q, ipſi, FB, parallela, HC, quæ tanget circu-
1117.1.Con. lum dictum, vel ellipſim, & erit, BC, æqualis ipſi, AQ; fiat dein-
de, vt, DB, ad, BC, ita, BC, ad, BI, & ſumatur, BR, quæ ſit,
{2/3}, BI, & , BE, quæ fit, {11/14}, ipſius, CB, & , EV, quæ ſit æqualis
go omnia quadrata parallelogrammi, FD,
ad omnia quadrata figuræ, quæ compre-
henditur tribus lateribus, FZ, ZD, DB,
& curua, FQB, eſſe, vt, BD, ad, DV,
proximè. Omnia . n. quadrata parallelo-
grammi, FD, ad rectangula ſub paralle-
logrammo, FD, & ſemicirculo, vel ſemi-
22Coroll.1.
26.lib.2. ellipſis, FQB, ſunt vt parallelogram-
mum, FD, ad eundem ſemicirculum, vel
ſemiellipſim, FQB; quia verò parallelo-
grammum, FD, ad parallelogrammum, FC, eſt vt, DB, ad, BC,
& item parallelogrammum, FC, ad ſemicirculum, vel ſemiellipſim,
335. Lib.2.
Arch. de
Dim.Cir. FQB, eſt proximè vt 14. ad 11. ideſt vt, CB, ad, BE, ergo ex
æquali parallelogrammum, FD, ad ſemicirculum, vel ſemiellipſim,
FQB, erit vt, DB, ad, BE, & ideò omnia quadrata parallelogram-
mi, FD, ad rectangula ſub parallelogrammo, FD, & ſemicirculo,
445.Lib.2. vel ſemiellipſi, FQB, erunt vt, DB, ad, BE,. i. ſumpta, DB, com-
muni altitudine erunt, vt quadratum, DB, ad rectangulum ſub, D
B, BE, quodſerua.
Aduerte nunc, quodrectangula ſub parallelogrammo, FD, &
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