Class lessons on Euclid1882 |
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Сторінка 9
... proved without some knowledge of mathematics , but their truth may be roughly ascertained , in the first in- stance by actual measurement , and in the second thus : - Draw a circle of any size ; draw it in two diameters cutting each ...
... proved without some knowledge of mathematics , but their truth may be roughly ascertained , in the first in- stance by actual measurement , and in the second thus : - Draw a circle of any size ; draw it in two diameters cutting each ...
Сторінка 16
... proving that the truth of any supposition contrary to that in the enuncia- tion being granted , we arrive at untrue or absurd results . The various lines and angles , & c . , made use of in a propo- sition are named from the letters of ...
... proving that the truth of any supposition contrary to that in the enuncia- tion being granted , we arrive at untrue or absurd results . The various lines and angles , & c . , made use of in a propo- sition are named from the letters of ...
Сторінка 23
... proved . SUMMARY OF PROPOSITION IV . , THEOREM 1 . Given : In two triangles two sides and the included angle equal . To be demonstrated : That the triangles are equal in all respects . Cons . - Nil . Proof . - Apply one triangle to the ...
... proved . SUMMARY OF PROPOSITION IV . , THEOREM 1 . Given : In two triangles two sides and the included angle equal . To be demonstrated : That the triangles are equal in all respects . Cons . - Nil . Proof . - Apply one triangle to the ...
Сторінка 24
... prove that two sides and the included angle in one triangle are equal to the corresponding parts in the other . ( 2 ) That the triangle affords a means of comparing angles , for by show- ing the equality of the triangles in the last ...
... prove that two sides and the included angle in one triangle are equal to the corresponding parts in the other . ( 2 ) That the triangle affords a means of comparing angles , for by show- ing the equality of the triangles in the last ...
Сторінка 27
... prove ( 1 ) the larger pair of triangles equal , ( 2 ) the smaller pair of triangles equal . 6 Since the smaller As contain the s on the other side of the base , ' these angles are equal . F D L G E Subtract from the Ls of the larger ...
... prove ( 1 ) the larger pair of triangles equal , ( 2 ) the smaller pair of triangles equal . 6 Since the smaller As contain the s on the other side of the base , ' these angles are equal . F D L G E Subtract from the Ls of the larger ...
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Загальні терміни та фрази
&c.-Q.E.D. PROPOSITION ABCD alternate angles angle ABC angle ACB angles are equal angles equal base BC bisected Cheaper Edition circle cons construction Demy 8vo diameter enunciation equal bases equal in area equal sides equal triangles equilateral triangle Euclid exterior Fcap Frontispiece given angle given line given point given straight line given triangle gnomon gram half the line Illustrations interior and opposite interior angles isosceles triangle Join line equal meet opposite angles opposite sides parallelogram perpendicular Poems problem produced proof Prop rectangle contained rhombus right angles right-angled triangle Second Edition sides equal Small crown 8vo square on AC square on half SUMMARY OF PROPOSITION THEOREM Third Edition Translated triangle ABC triangles are equal twice the rect twice the rectangle vertical angle vols Wherefore whole line
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