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 87
Side 9
Then shall the base BC be equal to the base EF ; and the triangle ABC to the
triangle DEF ; and the other angles to which the equal sides are opposite shall be
equal , each to each , viz . the angle ABC to the angle DEF , and the angle ACB
to ...
Then shall the base BC be equal to the base EF ; and the triangle ABC to the
triangle DEF ; and the other angles to which the equal sides are opposite shall be
equal , each to each , viz . the angle ABC to the angle DEF , and the angle ACB
to ...
Side 10
and the triangle AFC is equal to the triangle AGB , also the remaining angles of
the one are equal to the remaining angles of ... to which the equal sides are
opposite ; viz . the angle ACF to the angle ABG , and the angle AFC to the angle
AGB .
and the triangle AFC is equal to the triangle AGB , also the remaining angles of
the one are equal to the remaining angles of ... to which the equal sides are
opposite ; viz . the angle ACF to the angle ABG , and the angle AFC to the angle
AGB .
Side 12
Then because AC is equal to AD in the triangle ACD , therefore the angles ECD ,
FDC upon the other side of the base CD , are equal to one another ; ( 1 . 5 . ) but
the angle ECD is greater than the angle BCD ; ( ax . 9 . ) therefore also the angle
...
Then because AC is equal to AD in the triangle ACD , therefore the angles ECD ,
FDC upon the other side of the base CD , are equal to one another ; ( 1 . 5 . ) but
the angle ECD is greater than the angle BCD ; ( ax . 9 . ) therefore also the angle
...
Side 13
PROPOSITION IX . PROBLEM . 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 D ; from AC cut off AE equal to
AD , ( 1 .
PROPOSITION IX . PROBLEM . 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 D ; from AC cut off AE equal to
AD , ( 1 .
Side 16
And because the angle CBE is equal to the angles CBA , ABE , add the angle
EBD to each of these equals ; therefore the angles CBE , EBD are equal to the
three angles CBA , ABE , EBD . ( ax . 2 . ) Again , because the angle DBA is equal
to ...
And because the angle CBE is equal to the angles CBA , ABE , add the angle
EBD to each of these equals ; therefore the angles CBE , EBD are equal to the
three angles CBA , ABE , EBD . ( ax . 2 . ) Again , because the angle DBA is equal
to ...
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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 |