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nempe angulo A E C, &
eſt æqualis angulo A F D, eo quod C E,
B D ſunt parallelæ, ergo anguli D A C, A F D ſunt æquales, & in
duobus triangulis D A F, A H D ſunt duo auguli A F D, H A D æquales,
& angulus D communis, propterea erit rectãgulum F D in D H æquale
512[Figure 512]
quadrato D A, immo quadrato D C, &
quia proportio F D ad D C eſt
eadem proportioni C D ad D H, & angulus D communis, erunt triangula
D F C, D C H ſimilia, & angulus D F C æqualis D C H, qui æqualis
eſt angulo D A H, & hic eſt æqualis angulo A F D, ergo duo anguli A
F D, C F D ſunt æquales, & D F C æqualis angulo F C E, & erat D
F A æqualis angulo A E C, ergo in triangulo F E C ſunt duo anguli C,
E æquales, & duo anguli G recti, & latus G F commune, propterea
eri@ C G æqualis ipſi G E, ergo C E bifariam ſecatur in G, & hoc eſt,
quod voluimus,
B D ſunt parallelæ, ergo anguli D A C, A F D ſunt æquales, & in
duobus triangulis D A F, A H D ſunt duo auguli A F D, H A D æquales,
& angulus D communis, propterea erit rectãgulum F D in D H æquale
eadem proportioni C D ad D H, & angulus D communis, erunt triangula
D F C, D C H ſimilia, & angulus D F C æqualis D C H, qui æqualis
eſt angulo D A H, & hic eſt æqualis angulo A F D, ergo duo anguli A
F D, C F D ſunt æquales, & D F C æqualis angulo F C E, & erat D
F A æqualis angulo A E C, ergo in triangulo F E C ſunt duo anguli C,
E æquales, & duo anguli G recti, & latus G F commune, propterea
eri@ C G æqualis ipſi G E, ergo C E bifariam ſecatur in G, & hoc eſt,
quod voluimus,
PROPOSITIO XI.
SI mutuo ſe ſecuerint in circulo duæ lineæ A B, C D ad an-
gulos rectos in E, quod non ſit in centro, vtique omnia
quadrata A E, B E, E C, E D æqualia ſunt quadrato diametri.
gulos rectos in E, quod non ſit in centro, vtique omnia
quadrata A E, B E, E C, E D æqualia ſunt quadrato diametri.
Educamus diametrum A F,
513[Figure 513]&
iungamus lineas A C, A D,
C F, D B; Et quia angulus A
E D eſt rectus, erit æqualis an-
gulo A C F, & angulus A D C
æqualis A F C, eo quod ſunt
ſuper arcum A C, & remanent
in duobus triangulis A D E, A
F C duo anguli C A F, D A E
æquales erunt pariter duo arcus
C F, D B æquales immo, &
duæ cordæ eorum æquales, &
duo quadrata D E, E B æquantur quadrato B D, nempe C F, &
C F, D B; Et quia angulus A
E D eſt rectus, erit æqualis an-
gulo A C F, & angulus A D C
æqualis A F C, eo quod ſunt
ſuper arcum A C, & remanent
in duobus triangulis A D E, A
F C duo anguli C A F, D A E
æquales erunt pariter duo arcus
C F, D B æquales immo, &
duæ cordæ eorum æquales, &
duo quadrata D E, E B æquantur quadrato B D, nempe C F, &
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