| 3.
Definition |
Surd quantities, or vnexplicable by number, are
said to be defined, or expressed by numbers very neere, when they
are defined or expressed by great numbers which differ not so much
as one vnite from the true value of the Surd quantities.
As for example. Let the semidiameter, or whole
sine be the rational number 10000000 the sine of 45 degrees shall be
the square root of 50,000,000,000,000, which is surd, or irrationall
and inexplicable by any number, & is included between the limits of
7071067 the lesse, and 7071068 the greater: therfore, it differeth
not an vnite from either of these. Therefore that surd sine of 45
degrees, is said to be defined and expressed very neere, when it is
expressed by the whole numbers, 7071067, or 7071068, not regarding
the fractions. For in great numbers there ariseth no sensible error,
by neglecting the fragments, or parts of an vnite.
|
| 4. Definition |
Equall-timed motions are those which are made
together, and in the same time.
As in the figures following, admit that B
be moued from A to C, in the same time, wherin b
is moued from a to c the right lines
AC & ac, shall be sayd to be described with an
equall-timed motion. |
| 5.
Definition |
Seeing that there may bee a slower and a swifter
motion giuen then any motion, it shall necessarily follow, that
there may be a motion giuen of equall swiftnesse to any motion
(which wee define to be neither swifter nor slower.)
|
| 6. Definition |
The Logarithme therfore of any sine
is a number very neerely expressing the line, which increased
equally in the meane time, whiles the line of the whole sine
decreased proportionally into that sine, both motions being
equal-timed, and the beginning equally swift. |
|
