silence the contradictions or sophistical
sciences which lead to an everlasting clamour.

[Sidenote: Of Science]

6.

There is no certainty [in science] where one of the mathematical
sciences cannot be applied, or in those [sciences] which are not in
harmony with mathematics.

[Sidenote: From Leonardo's Dictionary]

7.

Syllogism: to speak doubtfully.

Sophism: to speak confusedly; falsehood for truth.

Theory: knowledge without practice.

[Sidenote: Definition of Science]

8.

Science is that discourse of the mind which derives its origin from
ultimate principles beyond which nothing in nature can be found which
forms a part of that science: as in the continued quantity, that is to
say, the science of geometry, which, starting from the surfaces of
bodies, has its origin in the line, which is the end of the
superficies; and we are not satisfied by this, because we know that the
line terminates in the point, and the point is that which is the least
of things. Therefore the point is the first principle of geometry, and
nothing else can exist either {143} in nature or in the human mind from
which the point can issue. Because if you say that the contact between
a surface and the extreme point of an iron instrument is the creation
of the point, it is not true; but let us say that this point of contact
is a superficies which surrounds its centre, and in the centre the
point dwells. And such a point is not a part of the substance of the
superficies, neither it nor all the points of the universe can, even if
combined,--it being granted that they could be combined,--compose any
part of a superficies. And granted, as you imagined, a whole composed
of a thousand points, if we divide any part of this quantity of a
thousand, we can very well say that this part shall equal its whole;
and this we can prove by zero, or naught, that is, the tenth figure of
arithmetic, which is represented by a cipher as being nothing, and
placed after unity it will signify 10, and if two ciphers are placed
after unity it will signify 100, and thus the number will go on
increasing by ten to infinity whenever a cipher is added, and the
cipher in itself is worth nothing more than naught, and all the naughts
in the universe are equal to one naught alone, in regard to their
substance and value.

[Sidenote: True Science based on the Testimony of the Senses]

9.

Knowledge which is the issue of experience is termed mechanical; t