Lectures on the Principles of Demonstrative MathematicsA. and C. Black, 1843 - 147 páginas |
Dentro del libro
Resultados 1-5 de 16
Página 5
... kind ; and many of you must have cast a thought towards the explanation . But , be- ing totally ignorant of the fundamental idea on which optics is founded , you probably never conceived it possi- ble that , with a little knowledge of ...
... kind ; and many of you must have cast a thought towards the explanation . But , be- ing totally ignorant of the fundamental idea on which optics is founded , you probably never conceived it possi- ble that , with a little knowledge of ...
Página 6
... kind ) emanates from the eye towards objects . + On the other hand , the Atomists and Epicureans supposed that images ‡ detach themselves from objects and travel to the eye . § Plato || appears to unite the two theories ; Euclid ...
... kind ) emanates from the eye towards objects . + On the other hand , the Atomists and Epicureans supposed that images ‡ detach themselves from objects and travel to the eye . § Plato || appears to unite the two theories ; Euclid ...
Página 11
... kind , we are not surprised that its very existence should have been forgotten by those who , in truth , derived am- ple benefit from it . Do we find modern philosophers anxious to trace the origin of their ideas ? Quite the contrary ...
... kind , we are not surprised that its very existence should have been forgotten by those who , in truth , derived am- ple benefit from it . Do we find modern philosophers anxious to trace the origin of their ideas ? Quite the contrary ...
Página 23
... kind , that the principles of demonstrative geometry be clearly understood and carefully taught . When , from investigating the grounds of certainty , we content our- * Plato de Rep . B. vii . Diog . Laert . in Xenoc . Proclus , Com ...
... kind , that the principles of demonstrative geometry be clearly understood and carefully taught . When , from investigating the grounds of certainty , we content our- * Plato de Rep . B. vii . Diog . Laert . in Xenoc . Proclus , Com ...
Página 40
... kind . For the purpose of carrying on reasoning merely , simpli- city is no requisite in a postulate . If the mind can con- ceive the existence of a parabola as well as of a circle , the admission of the use of the one is quite as ...
... kind . For the purpose of carrying on reasoning merely , simpli- city is no requisite in a postulate . If the mind can con- ceive the existence of a parabola as well as of a circle , the admission of the use of the one is quite as ...
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...