Galilei, Galileo - The systems of the world

Galilei, Galileo, The systems of the world, 1661

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produced from the term A to any other part of the oppoſite line
C D.

SALV. Your choice, and the reaſon you bring for it in my judg
ment is moſt excellent; ſo that by this time we have proved that
the firſt dimenſion is determined by a right line, the ſecond name
ly the breadth with another line right alſo, and not onely right,
but withall, at right-angles to the other that determineth the
length, and thus we have the two dimenſions of length and
breadth, definite and certain. But were you to bound or termi
nate a height, as for example, how high this Roof is from the pave
ment, that we tread on, being that from any point in the Roof,
we may draw infinite lines, both curved, and right, and all of di
verſe lengths to infinite points of the pavement, which of all theſe
lines would you make uſe of?

SAGR. I would faſten a line to the Seeling, and with a plummet
that ſhould hang at it, would let it freely diſtend it ſelf till it
ſhould reach well near to the pavement, and the length of ſuch a
thread being the ſtreighteſt and ſhorteſt of all the lines, that could
poſsibly be drawn from the ſame point to the pavement, I would
ſay was the true height of this Room.

SALV. Very well, And when from the point noted in the pave
ment by this pendent thread (taking the pavement to be levell
and not declining) you ſhould produce two other right lines, one
for the length, and the other for the breadth of the ſuperficies of
theſaid pavement, what angles ſhould they make with the ſaid
thread?

SAGR. They would doubtleſs meet at right angles, the ſaid
lines falling perpendicular, and the pavement being very plain and
levell.

SALV. Therefore if you aſſign any point, for the term from whence
to begin your meaſure; and from thence do draw a right line, as
the terminator of the firſt meaſure, namely of the length, it will
follow of neceſſity, that that which is to deſign out the largeneſs
or breadth, toucheth the firſt at right-angles, and that that which is
to denote the altitude, which is the third dimenſion, going from the
ſame point formeth alſo with the other two, not oblique but right
angles, and thus by the three perpendiculars, as by three lines, one,
certain, and as ſhort as is poſſible, you have the three dimenſions
A B length, A C breadth, and A D height; and becauſe, clear it
is, that there cannot concurre any more lines in the ſaid point, ſo
as to make therewith right-angles, and the dimenſions ought to
be determined by the ſole right lines, which make between them
ſelves right-angles; therefore the dimenſions are no more but
three, and that which hath three hath all, and that which hath all,
is diviſible on all ſides, and that which is ſo, is perfect, &c.

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