179
[Commentary:
The instructions on this page refer to the diagram on Add MS
f. . The proof that the point lies on the ellipse is to be found on subsequent pages labelled A.5. ]
Iisdem positis: centro , et intervallo agatur periferia circuli
ad partes lineæ , quæ necessario secabit lineam ,
quia ut demonstrandum fuit, est maior quam . Sit punctum
intersectionis . Deinde continuetur linea ad partes
et fiat æqualis . Iam intelligantur rectum esse maiorem
axem seu diametrum elipseos et dimidium diametri secunda
et sit ipsu elipsis descripta .
Dico quod punctum est in
[Translation: Supposing the same things: with centre and radius , there is constructed the circumference of a circle to the line , which will necessarily cut the line because, as was demonstrated, is smaller than . Let the point of intersection be . Then the line is continued to , and made equal to . Now it is understood that the line is the greater axis or diameter of the ellipse, and is half the second diameter, and the described ellipse is .
I say that the point is on the ellipse.
ad partes lineæ , quæ necessario secabit lineam ,
quia ut demonstrandum fuit, est maior quam . Sit punctum
intersectionis . Deinde continuetur linea ad partes
et fiat æqualis . Iam intelligantur rectum esse maiorem
axem seu diametrum elipseos et dimidium diametri secunda
et sit ipsu elipsis descripta .
Dico quod punctum est in
[Translation: Supposing the same things: with centre and radius , there is constructed the circumference of a circle to the line , which will necessarily cut the line because, as was demonstrated, is smaller than . Let the point of intersection be . Then the line is continued to , and made equal to . Now it is understood that the line is the greater axis or diameter of the ellipse, and is half the second diameter, and the described ellipse is .
I say that the point is on the ellipse.