Lectures on the Principles of Demonstrative MathematicsA. and C. Black, 1843 - 147 páginas |
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Página 13
... Prop . of the 1st Element of Euclid . From the importance attached to those discoveries , and the joy they are said to have caused , we may infer that none of equal value had been previously known . A similar re- mark will apply to ...
... Prop . of the 1st Element of Euclid . From the importance attached to those discoveries , and the joy they are said to have caused , we may infer that none of equal value had been previously known . A similar re- mark will apply to ...
Página 16
... Prop . 1. Philopponus Comm . in An . Post . l . i . Diog . Laërt in Plat . Proclus in Euc . Prop . 1 . * the latter too . But it is impossible to 16 LECTURE I.
... Prop . 1. Philopponus Comm . in An . Post . l . i . Diog . Laërt in Plat . Proclus in Euc . Prop . 1 . * the latter too . But it is impossible to 16 LECTURE I.
Página 37
... what should have been the definition is very evi- * Euclid , Optica , Prop . 9 . + Compare Cicero de Oratore , ii . 25 , and Topica , 5 . dent to every one who is conversant with the Elements THE PRINCIPLES OF DEMONSTRATIVE GEOMETRY . 37.
... what should have been the definition is very evi- * Euclid , Optica , Prop . 9 . + Compare Cicero de Oratore , ii . 25 , and Topica , 5 . dent to every one who is conversant with the Elements THE PRINCIPLES OF DEMONSTRATIVE GEOMETRY . 37.
Página 39
... Prop . 27 ; but any one who exa- mines the place , will find that it is for comparison , not for demonstration . The definitions , then , are forms of speech intended to convey to the mind simple ideas by reference to the senses , or ...
... Prop . 27 ; but any one who exa- mines the place , will find that it is for comparison , not for demonstration . The definitions , then , are forms of speech intended to convey to the mind simple ideas by reference to the senses , or ...
Página 40
... such a perpendicular is * Archimedes de Æq . i . 1 . In Proclus on Post Creswell , p . 31 , as is done , too , by Proclus in his comment on Prop . 1 , in reply to Zeno . what the mind cannot possibly doubt , and which it 40 LECTURE II .
... such a perpendicular is * Archimedes de Æq . i . 1 . In Proclus on Post Creswell , p . 31 , as is done , too , by Proclus in his comment on Prop . 1 , in reply to Zeno . what the mind cannot possibly doubt , and which it 40 LECTURE II .
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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...