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Página 15
... means of the axiom - Things that are equal to the same thing are equal to each other ; then , when A , B , C , D , are relations , the equality of the first and last can be shown only by means of the axiom - Relations that are equal to ...
... means of the axiom - Things that are equal to the same thing are equal to each other ; then , when A , B , C , D , are relations , the equality of the first and last can be shown only by means of the axiom - Relations that are equal to ...
Página 25
... means ; whence results the truism- 2xy = 2xy2 . This clearly shows that the mental act determining each algebraic transformation , is one in which the relation ex- pressed by the new form of the equation is recognized as equal to the ...
... means ; whence results the truism- 2xy = 2xy2 . This clearly shows that the mental act determining each algebraic transformation , is one in which the relation ex- pressed by the new form of the equation is recognized as equal to the ...
Página 31
... mean- time the building containing the standard measure A , has been burnt . Nevertheless , by purchasing another measure C , which had also been made to match the standard A , the surveyor is enabled to complete his work ; and knows ...
... mean- time the building containing the standard measure A , has been burnt . Nevertheless , by purchasing another measure C , which had also been made to match the standard A , the surveyor is enabled to complete his work ; and knows ...
Página 35
... mean between the first and third ; and the other group to that species in which the pro- portion subsists between four separate magnitudes . Thus the axiom- " Things which are equal to the same thing are equal to each other , " may , if ...
... mean between the first and third ; and the other group to that species in which the pro- portion subsists between four separate magnitudes . Thus the axiom- " Things which are equal to the same thing are equal to each other , " may , if ...
Página 38
... means of the equal spaces traversed by an index , or the descent of equal quantities ( space - fulls ) of sand or water . Equal units of weight were obtained through the aid of a lever having equal arms ( scales ) . The problems of ...
... means of the equal spaces traversed by an index , or the descent of equal quantities ( space - fulls ) of sand or water . Equal units of weight were obtained through the aid of a lever having equal arms ( scales ) . The problems of ...
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Términos y frases comunes
accompanying actions æsthetic antecedent Anti-Realistic argument arise asserted attri attributes axiom become body cause changes chapter coexistent positions cognition cohesion colour common complex conceived conception conclusion connatural connexions considered correlative definite degree distinguished elements emotion equal established evolution excited existence experiences express external fact faint feelings further genesis greater Hence ideas implies impressions inconceivable inference intuition involved kind known less magnitudes manifest mental metaphysicians mind motion muscular tension nature nervous ness nexions Objective Science observe pain particular perceived perception phenomena pleasure possible predicate premiss present produced proposition reached Realism recognized reflex action rela relation of coexistence relation of ideas representation represented resistance respect retina riences sciousness sensations sentiments sequence sequent simultaneously Sir William Hamilton subject and object successive suppose syllogism symbols sympathy tactual things thought tion truth unlike visual visual perceptions vivid aggregate words
Pasajes populares
Página 203 - The sense of space, and in the end the sense of time, were both powerfully affected. Buildings, landscapes, &c. were exhibited in proportions so vast as the bodily eye is not fitted to receive. Space swelled, and was amplified to an extent of unutterable infinity.
Página 30 - ANY two sides of a triangle are together greater than the third side.
Página 26 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Página 351 - Propositions of this kind are discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe.
Página 64 - All men are mortal, Socrates is a man, therefore Socrates is mortal, the subject and predicate of the major premise are connotative terms, denoting objects and connoting attributes.
Página 333 - By the term impression, then, I mean all our more lively perceptions, when we hear, or see, or feel, or love, or hate, or desire, or will. And impressions are distinguished from ideas, which are the less lively perceptions, of which we are conscious, when we reflect on any of those sensations or movements above mentioned.
Página 325 - I can imagine a man with two heads, or the upper parts of a man joined to the body of a horse. I can consider the hand, the eye, the nose, each by itself abstracted or separated from the rest of the body. But then, whatever hand or eye I imagine, it must have some particular shape and colour.
Página 326 - I cannot by any effort of thought conceive the abstract idea above described. And it is equally impossible for me to form the abstract idea of motion distinct from the body moving...
Página 25 - The angles at the base of an isosceles triangle are equal to each other; and if the equal sides be produced, the angles on the other side of the base shall be equal.
Página 408 - Accordingly, no geometrical proposition, as, for instance, that any two sides of a triangle are greater than the third side, can ever be derived from the general conceptions of line and triangle, but only from perception.