The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 115
... is equal to , greater , or less , according as the first and second are equal to , greater , or less than each other . BOOK VI . DEFINITIONS . I. SIMILAR rectilineal figures are BOOK V. EXERCISES . 115 Propositions 91 Exercises.
... is equal to , greater , or less , according as the first and second are equal to , greater , or less than each other . BOOK VI . DEFINITIONS . I. SIMILAR rectilineal figures are BOOK V. EXERCISES . 115 Propositions 91 Exercises.
Σελίδα 116
Euclides. BOOK VI . DEFINITIONS . I. SIMILAR rectilineal figures are those which have their several angles equal , each to each , and the sides about the equal angles proportionals . Definition I. II . Reciprocal figures , viz ...
Euclides. BOOK VI . DEFINITIONS . I. SIMILAR rectilineal figures are those which have their several angles equal , each to each , and the sides about the equal angles proportionals . Definition I. II . Reciprocal figures , viz ...
Σελίδα 124
... similar ( vi . def . 1 ) : in the like man- ner it may be demonstrated , that the tri- angle a dc is equiangular and similar to the triangle abc : and the tri- angles abd , a cd , being both equiangular and similar to abc , are ...
... similar ( vi . def . 1 ) : in the like man- ner it may be demonstrated , that the tri- angle a dc is equiangular and similar to the triangle abc : and the tri- angles abd , a cd , being both equiangular and similar to abc , are ...
Σελίδα 129
... similar , and similarly situated , to a given rectilineal figure . LET a b be the given straight line , and c def the given rectilineal figure of four sides ; it is required upon the given straight line ab to describe a rectilineal ...
... similar , and similarly situated , to a given rectilineal figure . LET a b be the given straight line , and c def the given rectilineal figure of four sides ; it is required upon the given straight line ab to describe a rectilineal ...
Σελίδα 130
... similar to one another ( vi . def . 1 ) . Next , let it be required to describe upon a given straight line ab , a rectilineal figure similar , and similarly situated , to the rectilineal figure cdkef . Join de , and upon the given ...
... similar to one another ( vi . def . 1 ) . Next , let it be required to describe upon a given straight line ab , a rectilineal figure similar , and similarly situated , to the rectilineal figure cdkef . Join de , and upon the given ...
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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 circumference bc 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 inscribe less LET abc LET the straight likewise multiple opposite angle parallel parallelogram perpendicular produced Q. E. D. PROPOSITION rectangle a d rectangle contained remaining angle right angles segment semicircle shewn square of a c straight line a b straight line ab straight line bc tiple touches the circle triangle abc triangle def twice the rectangle