element. One of the four basic substances out of which all terrestrial bodies were thought to be composed: earth, water, air, and fire.
elemental. Pertaining to the four terrestrial elements (earth, water, air, and fire).
epicycle. A circle whose center lies on and moves along the circumference of a larger circle, called deferent. The postulation of epicycles enabled astronomers to analyze the motion of heavenly bodies as a combination of circular motions, so that there would be variations in the distance from the heavenly body to the center of the deferent, as well as in the body’s direction of motion as seen from that center.
equidistance of ratios. If a, b, c, d, … , l is one set of magnitudes, and A, B, C, D, … , L is another, such that a:b = A:B, b:c = B:C, …, and k:l = K:L, then it follows by equidistance of ratios that a:l = A:L.
fixed star. A heavenly body that is visible normally only at night and appears to revolve daily around the earth without changing its position relative to other stars; thus all fixed stars appear to move in unison as if they were fixed on a celestial sphere, whose daily rotation carries them all along. A fixed star corresponds to what is nowadays called simply star, but in Galileo’s time star meant simply heavenly body and stars were divided into fixed and wandering.
force. In modern physics, a force is defined by means of Newton’s second law of motion, and so it is a cause of changes of speed or direction of motion. In Aristotelian physics, a force was a cause of motion and could be internal or external; internal forces caused natural motions, external forces caused violent motions. In Galileo’s work, force had a less clear and less precise meaning that overlaps with both the Aristotelian and the Newtonian concepts, as well as with the concept of energy; although he was groping toward the Newtonian concept, he did not really possess it; Galileo’s notion was also interwoven in confusing ways with his talk of power and moment.
Foscarini, Paolo Antonio (1580–1616). Head of the order of Carmelites in the province of Calabria and professor of theology at the University of Messina. He published in early 1615 a book that attempted to show the compatibility between the Bible and the earth’s motion. This book was condemned and totally banned by the Index’s Decree of 1616.
fourth proportional. Given three quantities A, B, C, the fourth proportional to them is a quantity X such that A:B = C:X.
geokinetic. Pertaining to the earth’s motion or claiming that the earth moves. The geokinetic worldview claims that the earth rotates daily on its axis from west to east and revolves yearly around the sun in the same direction. This term is contrasted with geostatic and may be taken to correspond to Copernican.
gravity. A term used interchangeably with weight and heaviness. In the Aristotelian worldview, gravity is the property of the elements earth and water whereby they tend to move toward the center of the universe; it manifests itself either as weight or free fall; and it is contrasted with a property called levity (or lightness), which is attributed to the elements air and fire, which consists of the tendency to move away from the center of the universe, and which manifests itself as buoyancy or spontaneous upward motion; bodies with gravity are called heavy bodies, and those with levity are called light bodies; it follows that light bodies go up because of their intrinsic property of levity, and not because they weigh less than the surrounding medium; in short, bodies with levity are thought to have no weight. Galileo abandoned the dichotomy between gravity and levity and held that all bodies have weight, thus explaining buoyancy and spontaneous upward motion in terms of the relative weight or specific gravity of the bodies involved; for him gravity was a property belonging to all bodies in the universe (heavenly as well as terrestrial), but consisted of the tendency to go toward the center of the whole of which one was a part, so that a rock on the moon would tend to move toward the center of the moon. Thus for both Aristotle and Galileo gravity could be labeled a universal property, but in different senses; for Aristotle it was universal in the sense that it was defined in terms of the center of the universe, a unique point yielding an absolute frame of reference; for Galileo it was universal in the sense that it characterized all material bodies in the universe; but even Galileo did not conceive of gravity as universal in the sense of Newton’s gravitation, namely, in terms of mutual attraction among all bodies in the universe, and thus as acting between the earth and the moon.
great circle. On a spherical surface, a circle whose center coincides with the center of the sphere. For example, on the earth the equator and the meridians are great circles, but the parallels are not.
Heraclides of Pontus. Ancient Greek who lived in the fourth century B.C.
Hicetas of Syracuse. Ancient Greek who lived about 400 B.C.
impetus. In late medieval physics, the impetus of a projectile was the power to move that had been transferred to it by the projector and that would be gradually lost. Galileo uses the term to refer to the power that a body has due to either the quantity of motion it embodies or the tendency it has to move in a particular way. Thus, the Galilean meaning is inexact and corresponds partly to the late medieval meaning and partly to what modern physics would call either momentum, kinetic energy, or even potential energy.
Index. Short for the Congregation of the Index, the department of the Catholic Church in charge of book censorship. Officially created in 1572 by Pope Gregory XIII, it was meant to formalize the periodic publication of the Index of Prohibited Books, whose first edition had already appeared in 1564 as a result of the Council of Trent. The Congregation was formally abolished by Pope Benedict XV in 1917, when the task of book censorship was taken over by the Inquisition.
Then in 1966 the Inquisition relinquished this task by decreeing that within the Church book regulation is a moral and not a legal issue.
Inquisition. The common name for the Congregation of the Holy Office, the department of the Catholic Church whose purpose was to defend and uphold faith and morals. It was officially instituted in 1542 by Pope Paul III and was meant to take over the suppression of heresies and heretics begun by the medieval Inquisition. By the time of Galileo, the notion of heresy had been given a legal definition, and inquisitorial procedures had been codified. Nowadays this department is called the Congregation for the Doctrine of the Faith.
Jupiter. A planet whose orbit is bigger than the annual orbit and whose period of revolution is about twelve years. In the geostatic system, it is the sixth planet from the earth; in the Copernican system, it is the fifth planet from the sun.
Lincean Academy. Also called Academy of the Linceans (in Italian Accademia dei Lincei, which means literally “academy of those who have lynx eyes”), this was the first modern international scientific academy, founded in 1603 by Prince Federico Cesi (1585–1630), although it fell apart soon after his death. Galileo was made a member in 1611, became a friend of Cesi, and received support from the Academy for the publication of many of his works.
mean proportional. Given two quantities, A and B, their mean proportional is a quantity X such that A:X = X:B.
Medicean Planets or Stars. A term used by Galileo to refer to Jupiter’s satellites, which he discovered. He named the new bodies in honor of Cosimo II de’ Medici, who ruled Florence and the Grand Duchy of Tuscany.
meridian. A circle on the surface of a sphere passing through both poles and cutting the equator at right angles.
Milky Way. Wide band of faint light in the night sky stretching all the way around the celestial sphere. Corresponds to the galaxy of stars in which our solar system is located.
moment. Aside from the obvious connotation of an instant of time, this word is used by Galileo with several other meanings. One is an approximation to the momentum of modern physics. Another is synonymous with the terms magnitude or intensity or degree, as in the phrase “the moment of the speed a body possesses.”
momentum. In classical (Newtonian) physics, momentum is defined as the product of a body’s mass and its velocity, taking velocity as a vector quantity (which has both a num
erical magnitude and a spatial direction). The law of conservation of momentum states that in a closed system the total amount of momentum neither increases nor decreases but remains constant. Galileo’s counterpart of this law is his principle of conservation of motion; but the correspondence is inexact because he had no conception that momentum is a vector and because he did not clearly distinguish between momentum and kinetic energy.
natural motion. In Aristotelian natural philosophy, natural motion is the motion which a body has by nature; that is, motion which the body has because of its nature; namely, motion caused by the moving body’s inherent nature; or again, motion caused by a force internal or inherent to the moving body. Thus, the natural motion of a terrestrial body is the motion it spontaneously tends to undergo in order to reach its natural place of rest, if it is not already there; for example, the natural motion of the elements earth and water is straight toward the center of the universe, and the natural motion of the elements air and fire is straight away from the center of the universe. Natural motion is contrasted with violent motion. Galileo partly accepted and partly modified this notion. He continued to speak of spontaneous (or internally caused) motion as one kind of natural motion, but dissociated it from the doctrine of natural places; so, for him the oscillation of a pendulum on the earth or the free fall of a rock on the moon would be as natural as the free fall of a rock on the earth. He sometimes added another meaning to the concept of natural motion, namely, motion that can last forever. And he contrasted natural motion with violent motion but also spoke of a third kind which is neither natural nor violent and which he labeled indifferent or neutral motion; an example of the latter would be horizontal motion on a frictionless surface.
opposition. A configuration in the apparent position of two heavenly bodies when they appear to be on opposite sides from the observer on earth, namely, 180 degrees apart on the celestial sphere.
For example, a full moon occurs when it and the sun are in opposition.
orb. A term that is partly synonymous with the term orbit, namely, the path followed by one heavenly body around another. The term also refers to the region of the heavens where a given orbital path is located. For example, the lunar orb could refer either to the path of the moon around the earth, or to the region of space surrounding the earth at a distance equal to that between the earth and the moon.
orbit. The path followed by a heavenly body as it moves among the other bodies, usually around some particular body or point that is regarded as the center or focus of the orbit.
palm. A term used in this book to translate literally Galileo’s word palmo. This was an ancient inexact unit of length corresponding to either the width of the palm of a hand, the length of a hand, or the distance from the tip of the thumb to the tip of the little finger when extended.
parabola. In mathematics, a plane curve defined as the set of all points equidistant from a fixed straight line (called the directrix) and a fixed point (called the focus). The shape generated is that of the intersection of a cone and a plane parallel to its side.
parallel. This term has two relevant meanings, as an adjective and as a noun. Two lines lying in the same plane are said to be parallel to each other when they never meet regardless of how far they are extended; similarly, two planes are parallel to each other when they never meet regardless of how far they are extended. Used as a noun, a parallel is a circle on the surface of a sphere (such as the earth or the celestial sphere) that is parallel to the equator; these parallels become smaller and smaller as one moves on the sphere’s surface from the equator to the poles.
perigee. In the orbit of a heavenly body, this is the point closest to the earth.
Peripatetic. A Greek word meaning literally a person who walks around. A nickname given to Aristotelians in Galileo’s time. Peripatetics acquired this nickname because in the school founded by Aristotle the teachers had the habit of walking around while lecturing.
perturbed equidistance of ratios. Given two sets of three magnitudes a, b, c, and A, B, C, such that a:b = B:C and b:c = A:B, it follows by perturbed equidistance of ratios that a:c = A:C.
phases. The phases of a nearby heavenly body (such as the moon and Venus) are the periodic changes in its apparent shape from round disk to semicircle to crescent and back to semicircle and round disk. They are caused by changes in the relative position between the sun, the earth, and the other body: a crescent is seen when the body is in the region between the earth and the sun; a semicircle is seen when the line connecting the three bodies forms an angle close to a right angle; and a full disk is seen when the body’s entire surface illuminated by the sun can be seen from the earth, either because the earth is between the sun and the body (as in the case of the moon) or because the sun is between the earth and the body (as in the case of Venus).
Philolaus of Croton (c. 470–c. 385 B.C.). Greek philosopher from southern Italy who accepted some of Pythagoras’ ideas. He elaborated the view that the earth, together with the other planets (including the sun), moves around the center of the universe, where a central fire is located.
planet. A term originating from Greek and meaning a wandering star. In the geostatic worldview, a planet is a heavenly body that appears to move both around the earth and in relation to other heavenly bodies; that is, a heavenly body that simultaneously performs two motions around the earth, the diurnal motion from east to west every day and another revolution from west to east in a definite period of time varying from one planet to another. There were seven planets, and their arrangement in the order of increasing orbit and period was as follows: moon, one month; Mercury, Venus, and sun, one year; Mars, two years; Jupiter, twelve years; and Saturn, twenty-nine years. In the Copernican view, a planet is a heavenly body that revolves around the sun, again in a definite period of time that varies from one planet to another: Mercury, three months; Venus, seven and a half months; earth, one year; Mars, two years; Jupiter, twelve years; and Saturn, twenty-nine years. In Galileo’s time, the planets Uranus, Neptune, and Pluto had not yet been discovered.
Prime Mobile. A term meant to convey the idea of the “first body in motion.” In Aristotelian natural philosophy, the Prime Mobile was a sphere lying outside the celestial sphere and acted upon by the First Unmoved Mover; by rotating daily, the Prime Mobile carried along all the other heavenly bodies (excluding the earth). The Prime Mobile was needed by those Aristotelians for whom the celestial sphere could not be a source of the diurnal motion; in fact, there was evidence that it had another slower movement in the opposite direction (the precession of the equinoxes), and the idea was to have a distinct sphere for each distinct movement.
Pseudo-Aristotle. The unknown author of a book entitled Questions of Mechanics, wrongly attributed to Aristotle according to a tradition that lasted past Galileo’s time. The book was probably written a generation after Aristotle’s death, by one of his followers.
retrograde motion. Westward motion against the background of the fixed stars which a planet appears to have periodically for a brief period, thus reversing its usually eastward motion (called direct motion). In the geostatic system, it was explained by means of epicycles. In the Copernican system, it is explained in terms of the relative motion between the earth and the planet in question.
Sagredo, Giovanfrancesco (1571–1620). Venetian aristocrat and diplomat who became Galileo’s best friend when Galileo taught at the University of Padua. Sagredo has been immortalized as one of the three speakers in the Dialogue and the Two New Sciences.
Salviati, Filippo (1582–1614). Wealthy Florentine nobleman whose interest in science and philosophy earned him membership in the Lincean Academy in 1612. One of Galileo’s closest friends in Florence, Salviati has been immortalized as one of the three characters in the Dialogue and the Two New Sciences.
save the appearances (or the phenomena). To explain observed natural phenomena by means of assumptions that are taken not to describe real physical processes, but rather to be merely convenient instrumen
ts for making calculations and predictions.
Seleucus. A Babylonian who lived around 150 B.C. and who was a follower of Aristarchus’ geokinetic theory.
Simplicio. One of the three characters in the Dialogue and the Two New Sciences. In Italian, Simplicio denotes both a simpleton and the philosopher Simplicius.
Simplicius. Greek philosopher who lived in the sixth century A.D., famous as one of the greatest commentators of Aristotle.
specific gravity. A term used by Galileo to mean weight per unit volume (the weighing being done presumably in air). This is analogous to the modern concept of density (which means mass per unit volume), except that Galileo did not have a clear concept of mass as distinct from weight. His point is that he wants a concept enabling him to compare the weights of equal volumes of different substances, so as to say, for example, that wax is “specifically” heavier than cork but lighter than lead.
spyglass. Term used by Galileo to refer to the telescope during the first two years that he used the instrument (perspicillum in Latin, occhiale in Italian). In 1611 the term telescopium was coined, and he adopted the new term.
telescope. Optical instrument consisting of an arrangement of lenses, mirrors, or both, that magnifies the image of distant objects so that they appear larger or nearer, thus rendering our vision more powerful and enabling us to see things that cannot be seen by the naked eye. Invented in Holland in 1608, it was significantly improved by Galileo the following year and turned into an effective scientific instrument for acquiring new knowledge about the world. The word (telescopium in Latin) was not coined until 1611, and before 1611 Galileo called the instrument a spyglass.
third proportional. Given two quantities A and B, their third proportional is a quantity X such that A:B = B:X.
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