The English works of Thomas Hobbes of Malmesbury, Volume 01 (of 11)
Thomas Hobbes · en
dispersed through the whole length A B or C D, yet, so that if it were
collected and put together, it would be equal to the same F B or G D.
Wherefore, if two sides which contain an angle, &c.; which was to be
demonstrated.
19. If two transmitted lengths have to their times any other proportion
explicable by number, and the side A B be so divided in E, that A B be
to A E in the same proportion which the lengths transmitted have to the
times in which they are transmitted, and between A B and A E there be
taken a mean proportional A F; it may be shown by the same method, that
the side, which is moved with uniform motion, works as much with its
concourse through the whole length A B, as it would do if the other
motion were also uniform, and the length transmitted in the same time A
C were that mean proportional A F.
And thus much concerning motion by concourse.
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[Illustration:
_Vol. 1. Lat. & Eng._
C. XVI.
_Fig. 1-11_
]
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CHAP. XVII.
OF FIGURES DEFICIENT.
1. Definitions of a deficient figure; of a complete figure; of the
complement of a deficient figure; and of proportions which are
proportional and commensurable to one another.—2. The proportion of
a deficient figure to its complement.—3. The proportions of
deficient figures to the parallelograms in which they are described,
set forth in a table.—4. The description and production of the same
figures.—5. The drawing of tangents to them.—6. In what proportion
the same figures exceed a strait-lined triangle of the same altitude
and base.—7. A table of solid deficient figures described in a
cylinder.—8. In what proportion the same figures exceed a cone of
the same altitude and base.—9. How a plain deficient figure may be
described in a parallelogram, so that it be to a triangle of the
same base and altitude, as another deficient figure, plain or solid,
twice taken, is to the same deficient figure, together with the
complete figure in which it is described.—10. The transferring of
certain properties of deficient figures described in a parallelogram
to the proportions of the spaces transmitted with several degrees of
velocity.—11. Of deficient figures described in a circle.—12. The
proposition demonstrated in art. 2 confirmed from the elements of
philosophy.—13. An unusual way of reasoning concerning the equality
between the superficies of a portion of a sphere and a circle.—14.
How from the description of deficient figures in a parallelogram,
any number of mean proportionals may be found out between two given
strait lines.
[Sidenote: Definition of a deficient figure.]