Syllabus of Plane Geometry: (corresponding to Euclid, Books I-VI) ...Macmillan & Company, 1876 - 58 sider |
Inni boken
Resultat 1-5 av 5
Side 42
... whence ( Def . 6 ) A : C > B : C ; Also , since C > mB while nC is not > mA ( Def . 6 ) C : B > C : A or C : A < C : B. If A < B , then B > A and therefore B : C > A : C , that is A : C < B : C. and so also C : A > C : B. Hence the ...
... whence ( Def . 6 ) A : C > B : C ; Also , since C > mB while nC is not > mA ( Def . 6 ) C : B > C : A or C : A < C : B. If A < B , then B > A and therefore B : C > A : C , that is A : C < B : C. and so also C : A > C : B. Hence the ...
Side 43
... whence if A be a multiple , part , or multiple of a part of B , P is the same multiple , part , or multiple of a ... whence BD . Also if A > C , A : B > C : B , and therefore C : D > C : B , whence B > D. Again if A < C , A : B < C : B ...
... whence if A be a multiple , part , or multiple of a part of B , P is the same multiple , part , or multiple of a ... whence BD . Also if A > C , A : B > C : B , and therefore C : D > C : B , whence B > D. Again if A < C , A : B < C : B ...
Side 44
... whence ( Th . 7 ) mA > = or < nC , as mB > = or < nD , and this being true for all values of m and » , AC : B D ... whence it follows that so also is mA + mC + mE > = or < nB + nD + nF and therefore so is m ( A + C + E ) > = or < n ( B + ...
... whence ( Th . 7 ) mA > = or < nC , as mB > = or < nD , and this being true for all values of m and » , AC : B D ... whence it follows that so also is mA + mC + mE > = or < nB + nD + nF and therefore so is m ( A + C + E ) > = or < n ( B + ...
Side 46
... whence P > R. B :: R : Q , Similarly if A = C or if A < C. Hence the lemma is proved . By Theor . 6 , mA : mB :: mP : mQ , and by Theor . 11 , mB : nC :: mQ : nR , whence by the lemma as mA > = or < nC , so is mP > = or < nR , and ...
... whence P > R. B :: R : Q , Similarly if A = C or if A < C. Hence the lemma is proved . By Theor . 6 , mA : mB :: mP : mQ , and by Theor . 11 , mB : nC :: mQ : nR , whence by the lemma as mA > = or < nC , so is mP > = or < nR , and ...
Side 49
... whence the rectangle AC : the rectangle BC :: base OA base OB . ] COR . Parallelograms or triangles of the same altitude are to one another as their bases . THEOR . 5. In the same circle or in equal circles angles at the centre and ...
... whence the rectangle AC : the rectangle BC :: base OA base OB . ] COR . Parallelograms or triangles of the same altitude are to one another as their bases . THEOR . 5. In the same circle or in equal circles angles at the centre and ...
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Syllabus of Plane Geometry: (corresponding to Euclid, Books I-VI) ... Association for the improvement of geometrical teaching Uten tilgangsbegrensning - 1876 |
Vanlige uttrykk og setninger
adjacent angles adjoining sides angles are equal angles equal angles opposite antecedent bisects Book called centre chord circle a regular circumference circumscribe conjugate angles consequent construct a triangle contrapositive diagonal distance divided internally equal altitude equal angles equal circles equimultiples exterior angle given angle given point given ratio given rectilineal figure given straight line greater angle hypotenuse identically equal inscribe interior angles intersect less lines are proportional Loci locus middle point minor arcs multiple obtuse angle opposite angles parallel straight lines parallelogram perpendicular PLANE GEOMETRY point of contact point of division polygon PROB quadrilateral radii radius ratio compounded ratios are equal rectangle contained right angles Rule of Conversion Rule of Identity SECTION segments side opposite Similar rectilineal figures square straight angle straight line drawn straight line joining subtended Superposition SYLLABUS OF PLANE THEOR Theorem triangles are identically unequal vertex whence whole numbers