Lectures on the Principles of Demonstrative MathematicsA. and C. Black, 1843 - 147 páginas |
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Página 34
... 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 principles differently , with an especial reference to geometry . I am , however ...
... 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 principles differently , with an especial reference to geometry . I am , however ...
Página 37
... express more : or are not super- Auous . 3. That it be impossible they should express any thing else or that they are unambiguous . And 4. That they have a necessary consistency with themselves . 1. Many instances may be found of ...
... express more : or are not super- Auous . 3. That it be impossible they should express any thing else or that they are unambiguous . And 4. That they have a necessary consistency with themselves . 1. Many instances may be found of ...
Página 45
... express what the learned author intends to 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 ...
... express what the learned author intends to 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 ...
Página 52
... express all the affections which our conceptions of the thing taught us to expect from it . When we designate as a straight line that which possesses a quality in common with another , we bar ourselves from considering what it is in ...
... express all the affections which our conceptions of the thing taught us to expect from it . When we designate as a straight line that which possesses a quality in common with another , we bar ourselves from considering what it is in ...
Página 58
... express only a property or affection of it . Amongst the former may be mentioned Wolfius , || ones . * Proclus in Def . † Euc . Catop . Thesis , 1. ἧς τὰ μέσα πάντα τοῖς ἄκροις ἐπιπροσθει . De Sphærâ et Cylindro Præf . § Varignon Géom ...
... express only a property or affection of it . Amongst the former may be mentioned Wolfius , || ones . * Proclus in Def . † Euc . Catop . Thesis , 1. ἧς τὰ μέσα πάντα τοῖς ἄκροις ἐπιπροσθει . De Sphærâ et Cylindro Præf . § Varignon Géom ...
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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...