Lectures on the Principles of Demonstrative MathematicsA. and C. Black, 1843 - 147 páginas |
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Página 4
... assume the character of a spontaneous growth . Be- sides , the mode by which such truths are generally ac- quired is the very reverse of the order of discovery . They 3 are introduced to us as fitting into facts with which 4 LECTURE I.
... assume the character of a spontaneous growth . Be- sides , the mode by which such truths are generally ac- quired is the very reverse of the order of discovery . They 3 are introduced to us as fitting into facts with which 4 LECTURE I.
Página 38
... sides equal , and all its angles right angles . " Not only is there a superfluity in this expression , " all its angles right angles , " but it is a superfluity which is not of ne- cessity consistent with itself . There is no reason why ...
... sides equal , and all its angles right angles . " Not only is there a superfluity in this expression , " all its angles right angles , " but it is a superfluity which is not of ne- cessity consistent with itself . There is no reason why ...
Página 42
... sides are equal each to each by constructing a triangle having three sides equal to those of another , and assert- ing that there can be but one such triangle on the same side of the base . Now , although this method may suffice for ...
... sides are equal each to each by constructing a triangle having three sides equal to those of another , and assert- ing that there can be but one such triangle on the same side of the base . Now , although this method may suffice for ...
Página 52
... sides of a triangle are together greater than the third side ; " and this without requiring from you any notion of a straight line at all . But I must stop here . I cannot require you to admit that the line in which a stone de- scends ...
... sides of a triangle are together greater than the third side ; " and this without requiring from you any notion of a straight line at all . But I must stop here . I cannot require you to admit that the line in which a stone de- scends ...
Página 59
... sides are equal , and each of its angles less than a right angle , is to commit a similar error , but one greatly less injurious in its conse- quences . Colonel Thompson¶ has skilfully endeavoured to remove this objection by proving ...
... sides are equal , and each of its angles less than a right angle , is to commit a similar error , but one greatly less injurious in its conse- quences . Colonel Thompson¶ has skilfully endeavoured to remove this objection by proving ...
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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...