Rational Geometry: A Text-book for the Science of Space; Based on Hilbert's FoundationsJ. Wiley & Sons, 1904 - 285 Seiten |
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Seite 2
A Text-book for the Science of Space; Based on ... given , then this third is explicitly and uniquely given . If A lies on a and besides on another straight b we use also the expression : " the straights " a “ and ” b " have the point ...
A Text-book for the Science of Space; Based on ... given , then this third is explicitly and uniquely given . If A lies on a and besides on another straight b we use also the expression : " the straights " a “ and ” b " have the point ...
Seite 3
... use also the expressions : A , B , C " lie in " a , A , B , C , " are points of " a , etc. I 4. ANY three non - costraight points A , B , C of a plane a determine THIS plane a . I 5. If two points A , B of a straight a lie in a plane a , ...
... use also the expressions : A , B , C " lie in " a , A , B , C , " are points of " a , etc. I 4. ANY three non - costraight points A , B , C of a plane a determine THIS plane a . I 5. If two points A , B of a straight a lie in a plane a , ...
Seite 4
... a straight and a point not on it there is always one and only one plane . Proof . On the straight there are ( by I 2 ) two points . These two with the point not on the straight determine ( by I 3 ) a plane , in which ( by I 5 ) they and the ...
... a straight and a point not on it there is always one and only one plane . Proof . On the straight there are ( by I 2 ) two points . These two with the point not on the straight determine ( by I 3 ) a plane , in which ( by I 5 ) they and the ...
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... point within the sect AB , it must always go either through a point of the sect BC or through a point of the sect AC . Deductions from the assumptions of ... points of 1 a straight are given , then they can always 6 RATIONAL GEOMETRY.
... point within the sect AB , it must always go either through a point of the sect BC or through a point of the sect AC . Deductions from the assumptions of ... points of 1 a straight are given , then they can always 6 RATIONAL GEOMETRY.
Seite 7
... FIG . 4 . 22. Theorem . Every straight a , which lies in a plane a , separates the other points of this plane a into two regions , of the following character : every point A of the one region determines with every point BETWEENNESS .
... FIG . 4 . 22. Theorem . Every straight a , which lies in a plane a , separates the other points of this plane a into two regions , of the following character : every point A of the one region determines with every point BETWEENNESS .
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adjacent angles altitude angle h angles opposite assumptions axis base bisection-point bisector bisects called chord circle circumcenter congruent congruent angles Construction coplanar copunctal Corollary costraight Definition determine diagonals diameter dicular draw edges end-points Engineering equilateral equivalent by completion face-angles Find the locus frustum Geometry given angle given plane given point given sect given straight greater gruent hypothenuse hypothesis inscribed inscribed angle intersection Inverse isosceles triangle joining Manual median meet meters minor arc morocco opposite sides orthocenter pair parallel parallelogram part-tetrahedra perigon perpen perpendicular point in common polar pole polygon polyhedron prismatoid Problem Proof proportional prove pyramid quad quadrant quadrilateral radius right angles sphere spherical angle spherical polygon spherical triangle square st's straightest summits supplemental symmetrical tangent Text-book Theorem third side transversal partitions Treatise triangle ABC trihedral unit sect vertex vertices
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