The first six books of the Elements of Euclid, with numerous exercises |
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Αποτελέσματα 6 - 10 από τα 36.
Σελίδα 30
produced ; let them meet in k , and through k draw kl , parallel to e a or fh , and produce ha , gb to the points 1 , m : then hlkf is a parallelogram , of which the diameter is hk , and ag , me are the parallelograms about hk ; and lb ...
produced ; let them meet in k , and through k draw kl , parallel to e a or fh , and produce ha , gb to the points 1 , m : then hlkf is a parallelogram , of which the diameter is hk , and ag , me are the parallelograms about hk ; and lb ...
Σελίδα 33
Given a finite straight line to describe a square of which that line shall be the diameter . 14. To construct a triangle that shall be equal to any given rectilineal . figure . D. SECT . II . — THEOREMS . 15. There cannot Exercises.
Given a finite straight line to describe a square of which that line shall be the diameter . 14. To construct a triangle that shall be equal to any given rectilineal . figure . D. SECT . II . — THEOREMS . 15. There cannot Exercises.
Σελίδα 34
The diameters of a rectangle are equal to one another . 25. If any number of parallelograms be inscribed in a given parallelogram , the diameters of all the figures shall cut one another in the same point . 26.
The diameters of a rectangle are equal to one another . 25. If any number of parallelograms be inscribed in a given parallelogram , the diameters of all the figures shall cut one another in the same point . 26.
Σελίδα 35
In every parallelogram , any of the e d parallelograms about a diameter , together with the two complements , is called a gnomon . Thus the parallelogram hg , together with the complements a f , fc , is the gnomon , which is more ...
In every parallelogram , any of the e d parallelograms about a diameter , together with the two complements , is called a gnomon . Thus the parallelogram hg , together with the complements a f , fc , is the gnomon , which is more ...
Σελίδα 37
From the demonstration , it is manifest that the parallelograms about the diameter of a square are likewise squares . e PROPOSITION V. - THEOREM . If a straight line be divided into two equal parts , and also into two unequal parts ...
From the demonstration , it is manifest that the parallelograms about the diameter of a square are likewise squares . e PROPOSITION V. - THEOREM . If a straight line be divided into two equal parts , and also into two unequal parts ...
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a b c angle a b c angle bac base base bc bc is equal bisected centre circle circumference common compounded definition demonstrated describe diameter divided double draw equal angles equal to f equiangular equilateral equimultiples exterior angle extremity fall fore four fourth given straight line greater half ILLUSTRATED inscribe join less likewise magnitudes manner meet multiple parallel parallelogram pass perpendicular produced proportionals PROPOSITION ratio reason rectangle contained rectilineal figure remaining angle right angles segment shewn sides similar square square of a c straight line a b Take taken third touches the circle triangle triangle a b c wherefore whole