Lectures on the Principles of Demonstrative MathematicsA. and C. Black, 1843 - 147 páginas |
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Página viii
... straight line , LECTURE IV . ON RATIO AND PROPORTION . Page 51 Measure - ratio - incommensurable magnitudes - proportion - Euclid's doctrine how developed - arithmetical ideas - lead to a common pro- perty - that property made the ...
... straight line , LECTURE IV . ON RATIO AND PROPORTION . Page 51 Measure - ratio - incommensurable magnitudes - proportion - Euclid's doctrine how developed - arithmetical ideas - lead to a common pro- perty - that property made the ...
Página 18
... straight line and the circle , the immediate offspring of the rule and compass , were the only lines discussed . But now , the symmetry of the curves formed by cutting a cone led to the investigation of their properties , and at once ...
... straight line and the circle , the immediate offspring of the rule and compass , were the only lines discussed . But now , the symmetry of the curves formed by cutting a cone led to the investigation of their properties , and at once ...
Página 34
... straight line or a circle , but that such a definition be sought out as shall express what is meant , with sufficient clearness to call up the idea of it in the mind . And accordingly Aristotle in the same treatise di- vides his ...
... straight line or a circle , but that such a definition be sought out as shall express what is meant , with sufficient clearness to call up the idea of it in the mind . And accordingly Aristotle in the same treatise di- vides his ...
Página 36
... straight , but that , beholding what is partially so , the perception of what it is may be con- veyed to the mind ... straight line for its definition . Lecture viii . § Beddoes , Observations on the Nature of Demonstrative Evidence , p ...
... straight , but that , beholding what is partially so , the perception of what it is may be con- veyed to the mind ... straight line for its definition . Lecture viii . § Beddoes , Observations on the Nature of Demonstrative Evidence , p ...
Página 38
... straight line drawn through the centre and terminated both ways by the circumference - dividing the circle into two ... line which is nei- ther straight nor composed of straight lines is a curve . ' This is not the geometric definition ...
... straight line drawn through the centre and terminated both ways by the circumference - dividing the circle into two ... line which is nei- ther straight nor composed of straight lines is a curve . ' This is not the geometric definition ...
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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...