Class lessons on Euclid1882 |
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Сторінка 3
... meet our glance are either modifications of , or combinations of the simple figures , and having studied the pro- portions of the elementary figures in the abstract we shall be able to apply them to all the surrounding objects of life ...
... meet our glance are either modifications of , or combinations of the simple figures , and having studied the pro- portions of the elementary figures in the abstract we shall be able to apply them to all the surrounding objects of life ...
Сторінка 6
... meet in a point ( def . 3 ) which obviously has no size or magnitude ( def . 1 ) . To these definitions an objection is frequently urged which we must briefly examine . It is said that defs . 1 , 2 , and 5 are incorrect , since any ...
... meet in a point ( def . 3 ) which obviously has no size or magnitude ( def . 1 ) . To these definitions an objection is frequently urged which we must briefly examine . It is said that defs . 1 , 2 , and 5 are incorrect , since any ...
Сторінка 7
... meet at all , and it consequently cannot be said to have any size whatever . We must then admit that these ... meet together but are not in the same direction . ' 9. A plane rectilineal angle is the inclination of two straight lines to ...
... meet at all , and it consequently cannot be said to have any size whatever . We must then admit that these ... meet together but are not in the same direction . ' 9. A plane rectilineal angle is the inclination of two straight lines to ...
Сторінка 12
... meet . NOTE . The parts of the circle enumerated in defs . 17 , 18 , 19 , are not referred to afterwards in Book I. , and the figures defined in Nos . 31 , 32 , 33 , are spoken of generally as parallelograms . THE POSTULATES . The ...
... meet . NOTE . The parts of the circle enumerated in defs . 17 , 18 , 19 , are not referred to afterwards in Book I. , and the figures defined in Nos . 31 , 32 , 33 , are spoken of generally as parallelograms . THE POSTULATES . The ...
Сторінка 13
Marianne Nops. 6. ' That if a straight line meet two others , so as to make the two interior angles on the same side of it , taken together , less than two right angles , these straight lines being con- tinually produced , shall at length ...
Marianne Nops. 6. ' That if a straight line meet two others , so as to make the two interior angles on the same side of it , taken together , less than two right angles , these straight lines being con- tinually produced , shall at length ...
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&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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