170150GEOMETRI Æ
pezium, FCMO, eſſe vt compoſita ex, RC, &
, {1/2}, CD, ad
compoſitam ex, MD, & , {1/2}, CD.
compoſitam ex, MD, & , {1/2}, CD.
Nam trapezium, CRGF, ad, GD, eſt vt compoſita ex, RC,
& , {1/2}, CD, ad, RD, inſuper, GD, ad, AM, eſt vt, RD, ad, C
M, & tandem, AM, ad trapezium, FCMO, eſt vt, CM, ad, M
D, cum, {1/2}, CD, ergo ex æquali trapezium, FGRC, ad trape-
zium, FCMO, erit vt, RC, cum, {1/2}, CD, ad, MD, cum, {1/2}, D
C, quod erat demonſtrandum.
& , {1/2}, CD, ad, RD, inſuper, GD, ad, AM, eſt vt, RD, ad, C
M, & tandem, AM, ad trapezium, FCMO, eſt vt, CM, ad, M
D, cum, {1/2}, CD, ergo ex æquali trapezium, FGRC, ad trape-
zium, FCMO, erit vt, RC, cum, {1/2}, CD, ad, MD, cum, {1/2}, D
C, quod erat demonſtrandum.
COROLLARIVM.
_H_Inc patet omnes lineas trapezij, FGRC, regula, RM, ad omnes
11_3. huius._ lineas trapezij, FCMO, regula eadem eſſe, vt, RC, cum, {1/2},
CD, ad, MD, cum, {1/2}, DC, veluti autem in antecedenti oſtendimus,
ſi, CD, ſit æqualis ipſi, DF, omnes lineas trapezij, FGMO, regula,
CM, æquari omnibus abſciſſis ipſius, FD, adiuncta, DM, ita in præ-
ſenti oſtendemus omnes lineas trapezij, FGRC, regula, RD, æquari re-
ſiduis omnium abſciſſarum ipſius, AC, vel, FD, adiuucta, RC; vnde
patebit reſiduas abſciſſarum propoſitæ lineæ, vt, FD, adiuncta, RC, ad
omnes abſciſſas eiuſdem, adiuncta alia linea, vt, DM, eſſe vt compoſi-
tum ex prima adiuncta, & , {1/2}, propoſitæ, CD, ſiue, FD, illi æqualis,
ad compoſitum ex ſecunda adiuncta, & , {1/2}, propoſitæ lineæ, ideſt vt, R
C, cum, {1/2}, CD, vel, DF, ad, MD, cum, {1/2}, CD, vel, DF.
11_3. huius._ lineas trapezij, FCMO, regula eadem eſſe, vt, RC, cum, {1/2},
CD, ad, MD, cum, {1/2}, DC, veluti autem in antecedenti oſtendimus,
ſi, CD, ſit æqualis ipſi, DF, omnes lineas trapezij, FGMO, regula,
CM, æquari omnibus abſciſſis ipſius, FD, adiuncta, DM, ita in præ-
ſenti oſtendemus omnes lineas trapezij, FGRC, regula, RD, æquari re-
ſiduis omnium abſciſſarum ipſius, AC, vel, FD, adiuucta, RC; vnde
patebit reſiduas abſciſſarum propoſitæ lineæ, vt, FD, adiuncta, RC, ad
omnes abſciſſas eiuſdem, adiuncta alia linea, vt, DM, eſſe vt compoſi-
tum ex prima adiuncta, & , {1/2}, propoſitæ, CD, ſiue, FD, illi æqualis,
ad compoſitum ex ſecunda adiuncta, & , {1/2}, propoſitæ lineæ, ideſt vt, R
C, cum, {1/2}, CD, vel, DF, ad, MD, cum, {1/2}, CD, vel, DF.
THE OREMA XXII. PROPOS. XXII.
EXpoſitis duobus vtcunq;
parallelogrammis, in eiſdem-
que ductis diametris, & duobus vtcunq; lateribus pro
regula ſumptis, nempè in vnoquoq; eorum vno: Omnia qua-
drata cuiuſuis dictorum parallelogrãmorum ad omnia qua-
drata cuiuſuis triangulorum per diametrum in ipſo conſtitu-
torum, erunt vt omnia quadrata reliqui parallelogrammi ad
omnia quadrata cuiuſuis triangulorum per diametrum in
iſto ductam pariter conſtitutorum.
que ductis diametris, & duobus vtcunq; lateribus pro
regula ſumptis, nempè in vnoquoq; eorum vno: Omnia qua-
drata cuiuſuis dictorum parallelogrãmorum ad omnia qua-
drata cuiuſuis triangulorum per diametrum in ipſo conſtitu-
torum, erunt vt omnia quadrata reliqui parallelogrammi ad
omnia quadrata cuiuſuis triangulorum per diametrum in
iſto ductam pariter conſtitutorum.
Sint expoſita vtcunque parallelogramma, AS, Τ β, in ijſque du-
ctæ diametri, EO, Z & , regulis ſumptis, ES, Ζβ. Dico omnia
quadrata, AS, ad omnia quadrata trianguli, OES, eſſe vt omnia
quadrata, Τ β, ad omnia quadrata, & Ζ β. Sienim, vtomnia
ctæ diametri, EO, Z & , regulis ſumptis, ES, Ζβ. Dico omnia
quadrata, AS, ad omnia quadrata trianguli, OES, eſſe vt omnia
quadrata, Τ β, ad omnia quadrata, & Ζ β. Sienim, vtomnia
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