An Essay On the Relation of the Several Parts of a Mathematical Science to the F
An Essay On the Relation of the Several Parts of a Mathematical Science to the F
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Of space of one dimension or lines we have a twofold division of lines, curved and straight ; and of curved lines we have several species of circles, ellipses, cycloids, curves of double curvature, and so on : and we have figures formed of combinations of straight lines, as e. G. Tri- angles, parallelograms, trapeziums ; and we have parallel straight lines ; and thus there is the most perfect division possible of the several specific forms which the pregnant idea involves, and a most perfect su...bordination of classes from even summum genus down to infima species ; but these many divisions having been made, it be- comes necessary to explain the meaning of the terms we employ ; hence our need of definitions, which are definitions of the several classes; not the same as the axioms, inasmuch as they are not pregnant with consequences, and are not used as premises in any syllogism by means of which we deduce new properties from old ones ; but as many of the specific forms of the original idea involve consequences peculiar to that particular species, it is necessary to enunciate axioms of rather a diflferent kind, which shall state pro- 15 perties, of not the idea in all its generality, but of certain particular species of it, such as the axiom about straight lines "Two straight lines cannot enclose a space ;" that about right angles " All right angles are equal ;" that about parallel straight lines, and so on ; all these differ from the definitions, inasmuch as the defini- tions are definitions only of the words, and do not involve any of the properties of the things whose names they explain.
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To quickly assess the difficulty of the text, read a short excerpt:
Of space of one dimension or lines we have a twofold division of lines, curved and straight ; and of curved lines we have several species of circles, ellipses, cycloids, curves of double curvature, and so on : and we have figures formed of combinations of straight lines, as e. G. Tri- angles, parallelograms, trapeziums ; and we have parallel straight lines ; and thus there is the most perfect division possible of the several specific forms which the pregnant idea involves, and a most perfect su...bordination of classes from even summum genus down to infima species ; but these many divisions having been made, it be- comes necessary to explain the meaning of the terms we employ ; hence our need of definitions, which are definitions of the several classes; not the same as the axioms, inasmuch as they are not pregnant with consequences, and are not used as premises in any syllogism by means of which we deduce new properties from old ones ; but as many of the specific forms of the original idea involve consequences peculiar to that particular species, it is necessary to enunciate axioms of rather a diflferent kind, which shall state pro- 15 perties, of not the idea in all its generality, but of certain particular species of it, such as the axiom about straight lines "Two straight lines cannot enclose a space ;" that about right angles " All right angles are equal ;" that about parallel straight lines, and so on ; all these differ from the definitions, inasmuch as the defini- tions are definitions only of the words, and do not involve any of the properties of the things whose names they explain.
What to read after An Essay On the Relation of the Several Parts of a Mathematical Science to the F?
You can find similar books in the "Read Also" column, or choose other free books by Bartholomew Price to read onlineMoreLess
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