The school edition. Euclid's Elements of geometry, the first six books, by R. Potts. corrected and enlarged. corrected and improved [including portions of book 11,12]. |
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Resultat 1-5 av 71
Side 13
To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let
BAC be the given rectilineal angle . It is required to bisect it . DHE в с In AB take
any point ... Wherefore the angle BAC is bisected by the straight line AF . Q . E . F
...
To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let
BAC be the given rectilineal angle . It is required to bisect it . DHE в с In AB take
any point ... Wherefore the angle BAC is bisected by the straight line AF . Q . E . F
...
Side 18
... the angle ACD is greater than the angle BĂE or BAC . In the same manner , if
the side BC be bisected , and AC be produced to G ; it may be demonstrated that
the angle BCG , that is , the angle ACD , ( 1 . 15 . ) is greater than the angle ABC .
... the angle ACD is greater than the angle BĂE or BAC . In the same manner , if
the side BC be bisected , and AC be produced to G ; it may be demonstrated that
the angle BCG , that is , the angle ACD , ( 1 . 15 . ) is greater than the angle ABC .
Side 61
Shew how a given straight line may be bisected by Euc . 1 . 1 . 43 . In what cases
do the lines which bisect the interior angles of plane triangles , also bisect one ,
or more than one of the corresponding opposite sides of the triangles ? 44 .
Shew how a given straight line may be bisected by Euc . 1 . 1 . 43 . In what cases
do the lines which bisect the interior angles of plane triangles , also bisect one ,
or more than one of the corresponding opposite sides of the triangles ? 44 .
Side 63
lelogram , when its diagonals bisect each other : and when its diagonals divide it
into four triangles , which are equal , two ... same parts , shew that the straight line
joining the vertices of the triangles is bisected by the line containing the bases .
lelogram , when its diagonals bisect each other : and when its diagonals divide it
into four triangles , which are equal , two ... same parts , shew that the straight line
joining the vertices of the triangles is bisected by the line containing the bases .
Side 65
be joined by a straight line AB , and this line be bisected in D , then if a
perpendicular be drawn from the point of bisection , it is manifest that a circle
described with any point in the perpendicular as a center ANCIENT
GEOMETRICAL ...
be joined by a straight line AB , and this line be bisected in D , then if a
perpendicular be drawn from the point of bisection , it is manifest that a circle
described with any point in the perpendicular as a center ANCIENT
GEOMETRICAL ...
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Vanlige uttrykk og setninger
ABCD Algebraically Apply base bisected Book chord circle circumference common construction contained definition demonstrated described diagonals diameter difference distance divided double draw drawn equal equal angles equiangular equilateral triangle equimultiples Euclid extremities fall figure formed four fourth Geometrical given circle given line given point given straight line greater half Hence inscribed intersection isosceles join length less Let ABC line drawn magnitudes manner mean meet multiple parallel parallelogram pass perpendicular plane problem produced Prop proportionals proved Q.E.D. PROPOSITION radius ratio reason rectangle rectangle contained regular remaining respectively right angles segment semicircle shew shewn sides similar solid square straight line taken tangent THEOREM third touch triangle ABC twice units vertex wherefore whole
Populære avsnitt
Side 112 - Guido, with a burnt stick in his hand, demonstrating on the smooth paving-stones of the path, that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.
Side 83 - 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...
Side 48 - If two triangles have two sides of the one equal to two sides of the other, each to each ; and...
Side 238 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Side 198 - A LESS magnitude is said to be a part of a greater magnitude, when the less measures the greater, that is, ' when the less is contained a certain number of times exactly in the greater.
Side 271 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.
Side 81 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Side 115 - angle in a segment' is the angle contained by two straight lines drawn from any point in the circumference of the segment, to the extremities of the straight line which is the base of the segment.
Side 341 - On the same base, and on the same side of it, there cannot be two triangles...
Side 24 - ... twice as many right angles as the figure has sides ; therefore all the angles of the figure together with four right angles, are equal to twice as many right angles as the figure has sides.
Bibliografisk informasjon
| Tittel | The school edition. Euclid's Elements of geometry, the first six books, by R. Potts. corrected and enlarged. corrected and improved [including portions of book 11,12]. |
| Forfatter | Euclides |
| Redaktør | Robert Potts |
| Utgave | 5 |
| distribuert | 1864 |
| Original fra | Oxford University |
| Digitalisert | 7. sep 2006 |
| Eksporter sitat | BiBTeX EndNote RefMan |