DOI Seite / Zitierlink:
https://doi.org/10.11588/diglit.8#0072
( 71 )
angles with it, dividing it into two equal parts : secondly,
it is evident that, from the point in the side of the base
wherein the perpendicular touches and divides it, to the
centre of the square that forms the area of the plan of
the Pyramid, is a length equal to half of the side of the
base, and the termination of this length, meets the lice,
imagined as let down, inside of the Pyramid from it's
apex to the centre of the area, at right angles with it.
Let us now imagine a right angled trigon, one leg where-
of shall be the known line equal to half the side of the
Pyramid's base, i. e. 200 cubits; the other leg the altitude
(of the Pyramid) sought, which I shall call A, and the
hypothenuse is the perpendicular, of the isosceles first
mentioned ; then by Py thagoras's theorem, if we sub-
tract the square of 200 cubits, equal to the short leg,
from the square of 400 cubits, equal to the hypothenuse,
the square root of the remainder must be the other leg
A. the real vertical height of the Pyramid.
Accordingly, from 400 cubits X 400 = 160 000, take
40 000, the product of 200X200, and there will remain
120 000, whereof the square root is 346.41016151376
cubits, the true vertical altitude sought ; which reduced
to English feet, are equal to 631.8521346.---------This is
so near to 625 when increased by the altitude of the top
part wanting, that it must be an unreasonable sceptic
that can doubt any longer of the sides of the Pyramid
being isosceles trigons, whereof the perpendiculars are,
and were intended by the architects of the Pyramid to
be, the whole length of the base : since the altitude they
produce by the vertical junction at top, is so conforma-
ble to the height recorded by the French literati, and
also by others, when due allowance is made for the depth
of sand not taken into their account. For
Pliny
angles with it, dividing it into two equal parts : secondly,
it is evident that, from the point in the side of the base
wherein the perpendicular touches and divides it, to the
centre of the square that forms the area of the plan of
the Pyramid, is a length equal to half of the side of the
base, and the termination of this length, meets the lice,
imagined as let down, inside of the Pyramid from it's
apex to the centre of the area, at right angles with it.
Let us now imagine a right angled trigon, one leg where-
of shall be the known line equal to half the side of the
Pyramid's base, i. e. 200 cubits; the other leg the altitude
(of the Pyramid) sought, which I shall call A, and the
hypothenuse is the perpendicular, of the isosceles first
mentioned ; then by Py thagoras's theorem, if we sub-
tract the square of 200 cubits, equal to the short leg,
from the square of 400 cubits, equal to the hypothenuse,
the square root of the remainder must be the other leg
A. the real vertical height of the Pyramid.
Accordingly, from 400 cubits X 400 = 160 000, take
40 000, the product of 200X200, and there will remain
120 000, whereof the square root is 346.41016151376
cubits, the true vertical altitude sought ; which reduced
to English feet, are equal to 631.8521346.---------This is
so near to 625 when increased by the altitude of the top
part wanting, that it must be an unreasonable sceptic
that can doubt any longer of the sides of the Pyramid
being isosceles trigons, whereof the perpendiculars are,
and were intended by the architects of the Pyramid to
be, the whole length of the base : since the altitude they
produce by the vertical junction at top, is so conforma-
ble to the height recorded by the French literati, and
also by others, when due allowance is made for the depth
of sand not taken into their account. For
Pliny