Lectures on the Principles of Demonstrative MathematicsA. and C. Black, 1843 - 147 páginas |
Dentro del libro
Resultados 1-5 de 23
Página viii
... requiring an idea of operations algebraic definitions of indices - signs - imaginary quantities — argu- ments in ... requires time for the mastery of its principles - 1 . necessity for extension of methods of comparison 2. development of ...
... requiring an idea of operations algebraic definitions of indices - signs - imaginary quantities — argu- ments in ... requires time for the mastery of its principles - 1 . necessity for extension of methods of comparison 2. development of ...
Página 8
... require no development in the mind . Had this been the case , why was not geometry coëval with humanity ? Why did not the age which produced a Draco ( not to mention a Solomon ) produce also a Euclid ? Why was not a single geometric ...
... require no development in the mind . Had this been the case , why was not geometry coëval with humanity ? Why did not the age which produced a Draco ( not to mention a Solomon ) produce also a Euclid ? Why was not a single geometric ...
Página 16
... require that they should pursue a long and systematic course of reasoning , heaping consequence upon consequence . Each problem terminated in itself , or at most led to a very narrow field of collateral investiga- tion . But in geometry ...
... require that they should pursue a long and systematic course of reasoning , heaping consequence upon consequence . Each problem terminated in itself , or at most led to a very narrow field of collateral investiga- tion . But in geometry ...
Página 31
... require us to ad- mit any conception of an infinitude of parts , leading to * Compare Arist . Phys . Ausc . iv . 2 , with Plato , Timæus , and Philebo , p . 26-7 . Barrow , Lect . ix . Aristotle de gen . et corrup . i . 2 , Our concern ...
... require us to ad- mit any conception of an infinitude of parts , leading to * Compare Arist . Phys . Ausc . iv . 2 , with Plato , Timæus , and Philebo , p . 26-7 . Barrow , Lect . ix . Aristotle de gen . et corrup . i . 2 , Our concern ...
Página 33
... requires hypotheses as to the nature of a probable existence , the former de- mands only communications as to the quality of a con- ception . The principles of Optics , for instance , are very different in this respect from those of ...
... requires hypotheses as to the nature of a probable existence , the former de- mands only communications as to the quality of a con- ception . The principles of Optics , for instance , are very different in this respect from those of ...
Otras ediciones - Ver todas
Lectures on the Principles of Demonstrative Mathematics Philip Kelland Sin vista previa disponible - 2019 |
Términos y frases comunes
admit adopted affections algebra amongst ancients appears applied Apuleius Archimedes argument Aristotle arithmetical arithmetical derivation assume assumption axiom Barrow circle Clavius coincide comparison conceive conception conclusions congruity consequence defined Differential Calculus difficulty discovery doctrine Elements equal equation Euclid Euclid's definition evidence existence express extension fact figure finite former four magnitudes fourth geometry idea important Laërt latter Lect lecture lity Math mathematical method method of exhaustions metical mind multiple nature necessity notation notion objection operations parallels Peacock perty philosophers plane Plato Playfair ples Plutarch possess postulate present PRINCIPLES OF DEMONSTRATIVE Proclus Prop proportion proportionality proposition Pythagoras quantities ratio reason rectilinear reductio ad absurdum reference remark require right angles rule of signs senses simple Simson space square straight line symbols Thales theorem Theory of Equations thing Timæus tion tiple treatise triangle truth whilst writers
Pasajes populares
Página 64 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.
Página 38 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Página 52 - Any two sides of a triangle are together greater than the third side.
Página 96 - ... of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth: or, if the multiple of the first be equal to that of the second, the multiple of the third is also equal to that of the fourth...
Página 122 - Whatever form is algebraically equivalent to another when expressed in general symbols, must continue to be equivalent whatever those symbols denote.
Página 17 - It is certain that from its completeness, uniformity and faultlessness, from its arrangement and progressive character, and from the universal adoption of the completest and best line of argument, Euclid's " Elements " stand preeminently at the head of all human productions.
Página 38 - Of four-sided figures, a square is that which has all its sides equal, and all its angles right angles.
Página 67 - Parallel straight lines are such as are in the same plane, and which being produced ever so far both ways, do not meet.
Página 88 - But when four magnitudes are proportionals, if the first be greater than the third, the second is greater than the fourth ; and if equal, equal; if less, less; (v.
Página 25 - That all our cognition," he says, " begins with experience, there is not any doubt ; for how otherwise should the faculty of cognition be awakened into exercise, if this did not occur through objects which affect our senses...