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Conic sections can be regarded as plane sections of a right circular cone (see the figure).
The critical notions constituting solids out of their plane sections and assigning weights to geometric figures were not formally valid within the standard conceptions of Greek geometry, and Archimedes admitted this.
He employed the bold notion of constituting solids from the plane figures formed as their sections (e.g., the circles that are the plane sections of spheres, cones, cylinders, and other solids of revolution), assigning to such figures a weight proportional to their area.
A new analytical (non-finite element) model for simulation of tubular hydroforming plane sections has been introduced.
The plane sections remain plane after deformation (Navier-Bernoulli hypothesis); The distribution of deformations in the mounting section is linear.
Serial, sagittal plane sections of 10-μm thickness were obtained using a Leica RM 2165 microtome (Leica Biosystems, Nussloch, Germany).
Similar(31)
A further analytical study was then conducted based on the test results and plane section theory.
The plane section assumption was used by the top and bottom rigid beams.
The assumption that a plane section remained planar under bending was suitable for a crack joint produced by the load.
We wish to estimate f from the circular profiles of the spheres intersecting a plane section through the material.
It is assumed that the plane section hypothesis is valid and layers do not slip with respect to each other.
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