Salusbury, Thomas - Mathematical collections and translations (Tome I)

1Motion along D B after the Fall from A. About the whole A B de
ſcribe a Semicircle A E B, and from

112[Figure 112]
C let fall C E, a Perpendicular to A
B, and draw a Line from A to E;
which ſhall be greater than E C.
Let E F be out equall to E C: I ſay,
that the remainder F A is the Time
of the Motion along D B. For be
cauſe A E is a Mean-proportional be
twixt B A and and A C, and A C
is the Time of the Fall along A C;
A E ſhall be the Time along the
Whole A B. And becauſe C E is a
Mean-proportional betwixt D A and
A C, (for D A is equal to B C)
C E, that is E F ſhall be the Time
along A D: Therefore the Remainder A F ſhall be the Time along the
Remainder B B: Which is the Propoſition.

COROLLARY.

Hence is gathered, that if the Time of any Space ex quiete be
as the ſaid Spaec, the Time thereof after another Space is ad
ded ſhall be the exceſſe of the Mean-proportional betwixt
the Addition and Space taken together, and the ſaid Space
above the Mean-proportional betwixt the firſt Space and the
Addition.

As for example, it being ſuppoſed that the Time along

113[Figure 113]
A B, out of Reſt in A, be A B; A S being another Space
added, The Time along A B after S A ſhall be the exceſſe of
the Mean-proportional betwixt S B and B A above the
Mean-proportional betwixt B A and A S.

PROBL VII. PROP. XX.

Any Space and a part therein after the begining
of the Motion being given, to find another
part towards the end that ſhall be paſt in the
ſame Time as the firſt part given.

Let the Space be C B, and let the part in it given after the begin
ing of the Motion in C be C D. It is required to find another
part towards the end B, which ſhall be paſt in the ſame Time as

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