HPSC2100
TUTORIAL 5:
TARTAGLIA’S NOVA
SCIENTIA & PROJECTILE
MOTION
Cindy Hodoba Eric
Semester 1, 2023
cindy.eric@sydney.edu.au
FRONTISPIECE &
DETAILS
BC + CD = Mixed Motion = Metaphysically Impossible
AB = Forced or Violent Motion
DE + EF = Natural Motion
2. Proper places and natural vs violent motion.
• Bodies naturally move towards their
proper place.
• Natural motion: internal cause (& most
fundamental quality of an element).
• Violent or forced motion: external cause.
• Natural and violent motions are
metaphysically contrary. Therefore, they
cannot mix.
• Acceleration: a body moves faster towards
the end of its natural motion because it’s
closer to its proper place.
3. No void/vacuum
1. The aim of Aristotle’s physics is to explain
change.
• The speed of a body moving through a
medium depends on two factors:
• Weight (the heavier it is, the greater its
ability to push the medium aside)
• Density of the medium (its resistance)
• Thus:
• The fall of a body in a medium (air or
water) is inversely proportional to the
medium’s density.
• Speed is proportional to
force or cause (weight) over
resistance.
• Why is a vacuum/void impossible?
What happens to a body when
resistance is zero?
• Without resistance, speed is infinite.
• A body can be in two places at the
same time.
REVIEW: MOTION IS THE
PARADIGM OF CHANGE
‘Tartaglia explains how the angle of the
trajectory can increase the range of projectiles.
Based on mathematical and geometrical
calculations or “Archimedean reasoning” (66), a
shot travels much further in one direction, and
in total distance, than a “point blank” shot. He
also found that different trajectories could
reach the same hit spot (67). How do these
findings fit into the contrary “natural” and
“violent” motions (65)? Do these motions
shape the trajectory of the projectile through
contrary balance? Or is one eventually
extinguished by the other? How do they
interact in different trajectories that reach the
same destination?’(Yining Gao, 2023)
• Philologist & Aristotelian commentator.
• Philoponus questions Aristotle’s reason
why projectiles keep moving after
they’re thrown.
• When the arrow leaves the bowstring,
what should happen to it according to
Aristotle’s laws?
• Why?
Problem: Aristotle’s ad hoc explanation
“the air is employed as a kind of instrument of
the action … that is the reason why an object set
in motion by compulsion continues in motion
even though the mover does not follow it up”
(Aristotle, De Caelo, III.2).
• Problem: if air is a resisting
medium, then how can it provide
both propulsion and resistance
simultaneously?
CRITICAL THINKING &
ABDUCTION VIA JOHN
PHILOPONUS (C . 490–570CE
– LATE ANTIQUITY)
Abduction: forming a fallible
conclusion from known information
(an inference to the best
explanation).
‘Niccolo Tartaglia,
In your plea to have His excellency, The Duke
accepts your proposal of a new method of
determining heights that will be quick as
opposed to the initial methods, you stress
that this new method will add the expert
bombardiers on top of their fine and practical
skills the art of pure reasoning. However, you
mention that you will structure the new
method where only hypotenuse and horizontal
lengths are used to define the heights. How
effective will this method be in enhancing
cognitive ability since it will be banked on only
two parameters which in appear limiting? How
will it include logical reasoning?’ (Shiyuan
Zhang, 2023)
“it is impossible for a heavy body to move with
natural motion and violent motion mixed
together”(Tartaglia, Nova Scientia).
A diagram of a cannonball’s trajectory in Tartaglia,
Nova Scientia, 1537.
“Everything that is in motion [change] must be
moved [changed] by something” (Aristotle, Physics,
VII).
“[T]he air is employed as a kind of instrument of
the action … that is the reason why an object set
in motion by compulsion continues in motion even
though the mover does not follow it up” (Aristotle,
De Caelo, III.2).
Contradiction:
“Every violent trajectory or motion of
uniformly heavy bodies outside the
perpendicular of the horizon [DEF] will
always be partly straight and partly curved,
and the curved part will form part of the
circumference of a circle” (Tartaglia, Nova
Scientia).
TARTAGLIA’S THEORETICAL,
SYMMETRICAL CANNONBALL
TRAJECTORIES (C . 1499/1500–
1557 – THE RENAISSANCE)
Contradiction indirectly resolved:
“truly no violent trajectory or motion of
uniformly heavy body outside the perpendicular
of the horizon can have any part that is perfectly
straight, because of the weight residing in that
body, which continually acts on it and draws it
towards the centre of the world” (Nova Scientia).
• Why is there no motion “outside the
perpendicular of the horizon” here?
Motion
“outside the
perpendicular
of the
horizon”
(Nova Scientia).
CONTRADICTION BETWEEN
THEORY AND PRACTICAL
EXPERIENCE (KNOW-THAT V
KNOW-HOW):
‘Tartaglia's letter of dedication demonstrates the importance of
hierarchs to scientific research. He uses many praise words in
his letter such as"And like every river that flows to approach
and unite with the sea , this will seek to approach and unit with
your greatness..." and "For just as the abundant sea , which has
no need of water , does not disdain to receives a little stream
,so i hope that your excellency will not disdain to accept this",
it suggests that his researchs dependent on the support of
hierarchs, so are there any disadvantages of this kind of
"dependent systems"?’ (Echo Shi, 2023).
Luis Collado de Libraja, Prattica manual
dell’Artiglieria, 1606.
Samuel Sturmy, in Mariner’s Magazine
No. 5: Mathematical and Practical Arts,
1669.