Euclid and His Modern RivalsMacmillan, 1885 - 275 sider |
Inni boken
Resultat 1-5 av 41
Side 55
... straight Line . 6 Nie . As the shortest path from one point to another . ' Min . This does not seem to me to embody the primary idea which the word ' straight ' raises in the mind . Is not the natural process of thought to realise first ...
... straight Line . 6 Nie . As the shortest path from one point to another . ' Min . This does not seem to me to embody the primary idea which the word ' straight ' raises in the mind . Is not the natural process of thought to realise first ...
Side 56
... straight Line between two points is the shortest " is a synthetical Proposition . For my conception of straight contains no notion of quan- tity , but is merely qualitative . The conception of the shortest is therefore wholly an ...
... straight Line between two points is the shortest " is a synthetical Proposition . For my conception of straight contains no notion of quan- tity , but is merely qualitative . The conception of the shortest is therefore wholly an ...
Side 57
... Line made up of straight Lines . Nie . That is true . Min . And all cases of broken Lines may be deduced from their simplest case , which is Euclid's I. 20 . Nie . Well , we will abate our claim and simply ask to have I. 20 granted us ...
... Line made up of straight Lines . Nie . That is true . Min . And all cases of broken Lines may be deduced from their simplest case , which is Euclid's I. 20 . Nie . Well , we will abate our claim and simply ask to have I. 20 granted us ...
Side 63
... straight Lines AB , CD , are cut by a third straight Line EF , they make with it the alternate angles AGH , GHD , equal ; and also the two internal angles at the same side BGH , GHD equal to two right angles . A E D For AGH and EGB are ...
... straight Lines AB , CD , are cut by a third straight Line EF , they make with it the alternate angles AGH , GHD , equal ; and also the two internal angles at the same side BGH , GHD equal to two right angles . A E D For AGH and EGB are ...
Side 65
... straight Lines cannot have a common segment . ' B H For if two straight Lines ABC , ABH could have a common segment AB ; then the straight Line ABC might be turned about its extremity A , towards the side on which BH is , so as to cut ...
... straight Lines cannot have a common segment . ' B H For if two straight Lines ABC , ABH could have a common segment AB ; then the straight Line ABC might be turned about its extremity A , towards the side on which BH is , so as to cut ...
Andre utgaver - Vis alle
Vanlige uttrykk og setninger
adjacent angles admit 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 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...