Jungatur enim EOſecans arcum Parabolicum ABCin Y,& aga
tur μXquæ tangat eundem arcum in vertice μ & actæ EOoccur
rat in X; & erit area curvilinea AEXμAad aream curvilineam
ACYμAut AEad AC.Ideoque cum triangulum ASEſit
ad triangulum ASCin eadem ratione, erit area tota ASEXμA
ad aream totam ASCYμAut AEad AC.Cum autem ξO
ſit ad SOut 3 ad 1, & EOad XOin eadem ratione, erit SX
ipſi EBparallela: & propterea ſi jungatur BX,erit triangulum
SEBtriangulo XEBæquale. Unde ſi ad aream ASEXμA
addatur triangulum EXB,& de ſumma auferatur triangulum
SEB,manebit area ASBXμAareæ ASEXμAæqualis,
atque adeo ad aream ASCYμAut AEad AC.Sed areæ
ASBXμAæqualis eſt area ASBYμAquamproxime, & hæc
area ASBYμAeſt ad aream ASCYμA,ut tempus deſcripti
arcus ABad tempus deſcripti arcus totius AC.Ideoque AE
eſt ad ACin ratione temporum quamproxime. Q.E.D.
tur μXquæ tangat eundem arcum in vertice μ & actæ EOoccur
rat in X; & erit area curvilinea AEXμAad aream curvilineam
ACYμAut AEad AC.Ideoque cum triangulum ASEſit
ad triangulum ASCin eadem ratione, erit area tota ASEXμA
ad aream totam ASCYμAut AEad AC.Cum autem ξO
ſit ad SOut 3 ad 1, & EOad XOin eadem ratione, erit SX
ipſi EBparallela: & propterea ſi jungatur BX,erit triangulum
SEBtriangulo XEBæquale. Unde ſi ad aream ASEXμA
addatur triangulum EXB,& de ſumma auferatur triangulum
SEB,manebit area ASBXμAareæ ASEXμAæqualis,
atque adeo ad aream ASCYμAut AEad AC.Sed areæ
ASBXμAæqualis eſt area ASBYμAquamproxime, & hæc
area ASBYμAeſt ad aream ASCYμA,ut tempus deſcripti
arcus ABad tempus deſcripti arcus totius AC.Ideoque AE
eſt ad ACin ratione temporum quamproxime. Q.E.D.
LIBER
TERTIUS.
TERTIUS.
Corol.Ubi punctum Bincidit in Parabolæ verticem μ, eſt AE
ad ACin ratione temporum accurate.
ad ACin ratione temporum accurate.
Scholium.
Si jungatur μξ ſecans ACin δ & in ea capiatur ξnquæ ſit
ad μBut 27 MIad 16 Mμ: acta Bnſecabit chordam ACin
ratione temporum magis accurate quam prius. Jaceat autem
punctum nultra punctum ξ, ſi punctum Bmagis diſtat a vertice
principali Parabolæ quam punctum μ; & citra, ſi minus diſtat ab
eodem vertice.
ad μBut 27 MIad 16 Mμ: acta Bnſecabit chordam ACin
ratione temporum magis accurate quam prius. Jaceat autem
punctum nultra punctum ξ, ſi punctum Bmagis diſtat a vertice
principali Parabolæ quam punctum μ; & citra, ſi minus diſtat ab
eodem vertice.
LEMMA IX.
RectæIμ & μM & longitudo (AIC/4Sμ) æquantur inter ſe.
Nam 4Sμ eſt latus rectum Parabolæ pertinens ad verti
cem μ.
cem μ.