„Gib mir einen Punkt, wo ich sicher stehen kann, [einen Hebel, der lang genug ist, ] und ich bewege die Erde mit einer Hand“
"Gib mir einen Punkt, wo ich hintreten kann, und ich hebe die Erde aus den Angeln."
Zitate von Archimedes
4 5
Archimedes
Geburtstag: 287 v.Chr
Todesdatum: 212 v.Chr
Archimedes von Syrakus war ein griechischer Mathematiker, Physiker und Ingenieur. Er gilt als einer der bedeutendsten Mathematiker der Antike. Seine Werke waren auch noch im 16. und 17. Jahrhundert bei der Entwicklung der höheren Analysis von Bedeutung.
Zitate Archimedes
„Ich hab's (gefunden)!“
Der Ausruf ist nach einer von Plutarch und Vitruv überlieferten Anekdote berühmt geworden, derzufolge Archimedes von Syrakus unbekleidet und laut »Heureka!«, rufend durch die Stadt gelaufen sein soll, nachdem er in der Badewanne das nach ihm benannte »Archimedische Prinzip« entdeckt hatte. Original griech.: "Ἑυρηκα!"
„Störe meine Kreise nicht!“
Nach römischer Überlieferung raunte Archimedes diese letzten Worte dem römischen Soldaten zu, der ihn bei der Eroberung von Syrakus in einem stillen Garten entdeckte und erstach. Archimedes grübelte über geometrischen Figuren, die er in den Sand gezeichnet hatte.
Original griech.: "Μή μου τοὺς κύκλους τάραττε!"
Original lat.: "Noli turbare circulos meos!"
„Gib mir einen Punkt, wo ich hintreten kann, und ich bewege die Erde“
So soll er sein Hebelgesetz veranschaulicht haben, belegt in Pappos "Synagoge", einer Sammlung mathematischer Abhandlungen
Original griech.: "δος μοι που στω και κινω την γην" (Dos moi pou sto kai kino taen gaen)
Dorischer Dialekt: "δος μοι πα στω και τα γαν κινάσω"
„If two equal weights have not the same centre of gravity, the centre of gravity of both taken together is at the middle point of the line joining their centres of gravity.“
— Archimedes, buch On the Equilibrium of Planes
Book 1, Proposition 4.
On the Equilibrium of Planes
„Any segment of a right-angled conoid (i. e., a paraboloid of revolution) cut off by a plane at right angles to the axis is 1½ times the cone which has the same base and the same axis as the segment“
— Archimedes, buch The Method of Mechanical Theorems
Proprosition 4.
The Method of Mechanical Theorems
„The centre of gravity of any cylinder is the point of bisection of the axis.“
— Archimedes, buch The Method of Mechanical Theorems
Proposition presumed from previous work.
The Method of Mechanical Theorems
„The centre of gravity of any cone is [the point which divides its axis so that] the portion [adjacent to the vertex is] triple“
— Archimedes, buch The Method of Mechanical Theorems
of the portion adjacent to the base
Proposition presumed from previous work.
The Method of Mechanical Theorems
„The centre of gravity of any parallelogram lies on the straight line joining the middle points of opposite sides.“
— Archimedes, buch On the Equilibrium of Planes
Book 1, Proposition 9.
On the Equilibrium of Planes
„First then I will set out the very first theorem which became known to me by means of mechanics, namely that
Any segment of a section of a right angled cone (i. e., a parabola) is four-thirds of the triangle which has the same base and equal height,
and after this I will give each of the other theorems investigated by the same method. Then at the end of the book I will give the geometrical [proofs of the propositions]…“
— Archimedes, buch The Method of Mechanical Theorems
The Method of Mechanical Theorems
„How many theorems in geometry which have seemed at first impracticable are in time successfully worked out!“
— Archimedes, buch On Spirals
On Spirals (225 B.C.)
„The centre of gravity of any hemisphere [is on the straight line which] is its axis, and divides the said straight line in such a way that the portion of it adjacent to the surface of the hemisphere has to the remaining portion the ratio which 5 has to 3.“
— Archimedes, buch The Method of Mechanical Theorems
Proposition 6.
The Method of Mechanical Theorems
„In any triangle the centre of gravity lies on the straight line joining any angle to the middle point of the opposite side.“
— Archimedes, buch On the Equilibrium of Planes
Book 1, Proposition 13.
On the Equilibrium of Planes
„It follows at once from the last proposition that the centre of gravity of any triangle is at the intersection of the lines drawn from any two angles to the middle points of the opposite sides respectively.“
— Archimedes, buch On the Equilibrium of Planes
Book 1, Proposition 14.
On the Equilibrium of Planes
„Two magnitudes whether commensurable or incommensurable, balance at distances reciprocally proportional to the magnitudes.“
— Archimedes, buch On the Equilibrium of Planes
Book 1, Propositions 6 & 7, The Law of the Lever.
On the Equilibrium of Planes
„I thought fit to… explain in detail in the same book the peculiarity of a certain method, by which it will be possible… to investigate some of the problems in mathematics by means of mechanics. This procedure is… no less useful even for the proof of the theorems themselves; for certain things first became clear to me by a mechanical method, although they had to be demonstrated by geometry afterwards… But it is of course easier, when we have previously acquired, by the method, some knowledge of the questions, to supply the proof than it is to find it without any previous knowledge.“
— Archimedes, buch The Method of Mechanical Theorems
The Method of Mechanical Theorems
„I am persuaded that it [The Method of Mechanical Theorems] will be of no little service to mathematics; for I apprehend that some, either of my contemporaries or of my successors, will, by means of the method when once established, be able to discover other theorems in addition, which have not yet occurred to me.“
— Archimedes, buch The Method of Mechanical Theorems
The Method of Mechanical Theorems
„The centre of gravity of a parallelogram is the point of intersection of its diagonals.“
— Archimedes, buch On the Equilibrium of Planes
Book 1, Proposition 10.
On the Equilibrium of Planes
„I have found it! or I have got it!, commonly quoted as Eureka!“
What he exclaimed as he ran naked from his bath, realizing that by measuring the displacement of water an object produced, compared to its weight, he could measure its density (and thus determine the proportion of gold that was used in making a king's crown); as quoted by Vitruvius Pollio in De Architectura, ix.215;
Original: (el) εὕρηκα [heúrēka]
„Equal weights at equal distances are in equilibrium and equal weights at unequal distances are not in equilibrium but incline towards the weight which is at the greater distance.“
— Archimedes, buch On the Equilibrium of Planes
Book 1, Postulate 1.
On the Equilibrium of Planes
