The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Αποτελέσματα 11 - 15 από τα 24.
Σελίδα 115
... proportionals are proportionals also . 3. If there be four proportional magnitudes of which the first is a mul- tiple of the second , then the third is the same multiple of the fourth . ( Prove also that if the second be a multiple of ...
... proportionals are proportionals also . 3. If there be four proportional magnitudes of which the first is a mul- tiple of the second , then the third is the same multiple of the fourth . ( Prove also that if the second be a multiple of ...
Σελίδα 116
... proportionals . Definition I. II . Reciprocal figures , viz . triangles and parallelograms , are such as have their sides about two of their angles proportionals in such manner that a side of the first figure is to a side of the other ...
... proportionals . Definition I. II . Reciprocal figures , viz . triangles and parallelograms , are such as have their sides about two of their angles proportionals in such manner that a side of the first figure is to a side of the other ...
Σελίδα 120
... proportionals ; and those which are opposite to the equal angles are homologous sides , that is , are the antecedents or consequents of the ratios . LET abc , dce be equiangular triangles , having the angle abc equal to the angle dce ...
... proportionals ; and those which are opposite to the equal angles are homologous sides , that is , are the antecedents or consequents of the ratios . LET abc , dce be equiangular triangles , having the angle abc equal to the angle dce ...
Σελίδα 121
... proportionals , the triangles shall be equiangular , and have their equal angles opposite to the homologous sides . LET the triangles abc , def have their sides proportionals , so that ab is to be as de to ef ; and bc to ca as efto fd ...
... proportionals , the triangles shall be equiangular , and have their equal angles opposite to the homologous sides . LET the triangles abc , def have their sides proportionals , so that ab is to be as de to ef ; and bc to ca as efto fd ...
Σελίδα 122
... proportionals ; that is , ba to a c , as ed to df ; the triangles a bc , def are equiangular , and have the angle a b c equal to the angle def , and a cb to dfe . b a с е d f G : At the points d , f , in the straight line df , make ( i ...
... proportionals ; that is , ba to a c , as ed to df ; the triangles a bc , def are equiangular , and have the angle a b c equal to the angle def , and a cb to dfe . b a с е d f G : At the points d , f , in the straight line df , make ( i ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
a b c abcd adjacent angles angle a cb angle abc angle bac angle edf angle equal base bc bc is equal bisected centre circle abc describe diameter double draw equal angles equal straight lines equal to f equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given straight line gnomon greater ratio greater than f ILLUSTRATED LONDON inscribe less LET abc LET the straight likewise multiple opposite angle parallel parallelogram pentagon perpendicular Q. E. D. PROPOSITION rectangle a d rectangle contained remaining angle right angles segment shewn square of a c square of eg straight line a b straight line ab straight line bc tiple touches the circle triangle abc triangle def twice the rectangle
Δημοφιλή αποσπάσματα
Σελίδα 2 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another : XVI.
Σελίδα 42 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Σελίδα 4 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 21 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Σελίδα 29 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Σελίδα 38 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together with the square of...
Σελίδα 15 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle. Let...
Σελίδα 13 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Σελίδα 4 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Σελίδα 126 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.