Euclid and His Modern RivalsMacmillan, 1885 - 275 sider |
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Resultat 1-5 av 31
Side 4
... position GAF , GA having same direction as DC ( Ax . 9 ) ; similarly slide / BCE along AE into position GAC . Then the ext . Zs = CAF , FAG , GAC one revolution = two straight Zs . But the ext . and int . s = 3 straight Zs . Therefore ...
... position GAF , GA having same direction as DC ( Ax . 9 ) ; similarly slide / BCE along AE into position GAC . Then the ext . Zs = CAF , FAG , GAC one revolution = two straight Zs . But the ext . and int . s = 3 straight Zs . Therefore ...
Side 9
... position , without involving risk of circular argument . Euc . Now , in order to secure this uniform logical sequence , we should require to know , as to any particular Proposition , what other Propositions were its logical de ...
... position , without involving risk of circular argument . Euc . Now , in order to secure this uniform logical sequence , we should require to know , as to any particular Proposition , what other Propositions were its logical de ...
Side 24
... positions concerning it . Min . Let us make sure that we understand each other as to those two words . I presume that a ' subject ' will include just so much ' property ' as is needed to indicate the Pair of Lines referred to , i.e. to ...
... positions concerning it . Min . Let us make sure that we understand each other as to those two words . I presume that a ' subject ' will include just so much ' property ' as is needed to indicate the Pair of Lines referred to , i.e. to ...
Side 42
... position of two finite Lines , if all I knew about them was their never meeting however far produced and it would be equally impossible to form any mental picture of the position which a Line , crossing one of them , would have ...
... position of two finite Lines , if all I knew about them was their never meeting however far produced and it would be equally impossible to form any mental picture of the position which a Line , crossing one of them , would have ...
Side 49
... position , to E and F. ' The words ' in its new position ' would be necessary , because you would now have two points in your diagram , both called ' C ' And you would also be obliged to give the points D and E additional names , namely ...
... position , to E and F. ' The words ' in its new position ' would be necessary , because you would now have two points in your diagram , both called ' C ' And you would also be obliged to give the points D and E additional names , namely ...
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Vanlige uttrykk og setninger
adjacent angles alternate angles angles are equal assert assume axiomatic beginners Cambridge Mathematical Tripos Certainly coincide coincidental Lines common point construct Contranominal course curve CUTHBERTSON deduce define Definition demonstration different directions different Lines draw drawn Elementary Geometry equal angles equally inclined equidistant equidistantial Euclid examining finite Lines given Line given point grant HENRICI infinite interior angles interpolated intersectional Lines Legendre less magnitude Manual mathematical mean meet if produced method Modern Rivals NIEMAND reads old proof omitted Pair of Lines parallel perpendicular Petitio Principii phrase Plane Plane Geometry Playfair's Axiom position Pr Pr Pref Problems Prop Propositions prove reductio ad absurdum remark right angles right Line separate point separational Lines sepcodal side straight angle straight Line suppose Syllabus text-book Th Th Theorem tion transversal Triangle true Wilson words writer دو وو
Populære avsnitt
Side 135 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Side 143 - Your geometry states it as an axiom that a straight line is the shortest way from one point to another: and astronomy shows you that God has given motion only in curves.
Side 34 - Thus, for" example, he to whom the geometrical proposition, that the angles of a triangle are together equal to two right angles...
Side 201 - If there are three or more parallel straight lines, and the intercepts made by them on any straight line that cuts them are equal, then the corresponding intercepts on any other straight line that cuts them are also equal.
Side 98 - ... angle. An acute angle is one which is less than a right angle.
Side 203 - The sum of the squares on two sides of a triangle is double the sum of the squares on half the base and on the line joining the vertex to the middle point of the base.
Side 67 - Min. I accept all that. Nie. We then introduce Euclid's definition of ' Parallels. It is of course now obvious that parallel Lines are equidistant, and that equidistant Lines are parallel. Min. Certainly. Nie. We can now, with the help of Euc. I. 27, prove I. 29, and thence I. 32. Min. No doubt. We see, then, that you propose, as a substitute for Euclid's i2th Axiom, a new Definition, two new Axioms, and what virtually amounts to five new Theorems. In point of ' axiomaticity ' I do not think there...
Side 93 - Theorem. In every Triangle the greater side is opposite to the greater angle, and conversely, the greater angle is opposite to the greater side.
Side 203 - To construct a rectilineal Figure equal to a given rectilineal Figure and having the number of its sides one less than that of the given figure ; and thence to construct a Triangle equal to a given rectilineal Figure.
Side 200 - Assuming that the areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles...