Lectures on the Principles of Demonstrative MathematicsA. and C. Black, 1843 - 147 páginas |
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Página 16
... proved that the duplication of the cube depends on the determination of two mean proportionals between two given straight lines . This fact teaches us that the doctrine of proportionals had then made considerable advance . To the school ...
... proved that the duplication of the cube depends on the determination of two mean proportionals between two given straight lines . This fact teaches us that the doctrine of proportionals had then made considerable advance . To the school ...
Página 23
... proved ; not that I entertain any doubt of it . The first author to which I can trace it , is Tzetzes , who wrote in 1176 , according to Gerbelius . The passage is , Πρὸ τῶν προθύρων τῶν αὐτοῦ γράψας ὑπῆρχε πλάτων Μηδεὶς ἀγεωμετρῆτος ...
... proved ; not that I entertain any doubt of it . The first author to which I can trace it , is Tzetzes , who wrote in 1176 , according to Gerbelius . The passage is , Πρὸ τῶν προθύρων τῶν αὐτοῦ γράψας ὑπῆρχε πλάτων Μηδεὶς ἀγεωμετρῆτος ...
Página 35
... proved that all the three angles of a rectilinear triangle are equal to two right angles , this property may be taken as the definition of a species of figure . " Every figure , ( rectilinear or not , ) the sum of whose angles is equal ...
... proved that all the three angles of a rectilinear triangle are equal to two right angles , this property may be taken as the definition of a species of figure . " Every figure , ( rectilinear or not , ) the sum of whose angles is equal ...
Página 45
... prove , which is this : that the equality of all other things is dependent in a secondary manner on equality ( by con- gruity ) of magnitude as its primary . His argument is briefly as follows : Since quantities , and the relative af ...
... prove , which is this : that the equality of all other things is dependent in a secondary manner on equality ( by con- gruity ) of magnitude as its primary . His argument is briefly as follows : Since quantities , and the relative af ...
Página 49
... prove the circle congruous with the triangle , but that a polygon coincides with some other triangle . This species of equality , then , which Barrow ranks under congruity does not by any means belong to it . For it is impossible to ...
... prove the circle congruous with the triangle , but that a polygon coincides with some other triangle . This species of equality , then , which Barrow ranks under congruity does not by any means belong to it . For it is impossible to ...
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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...