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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Side 110
The Hindus , in their treatises on Algebra , indicated the ratio of two numbers , or
of two algebraical symbols , by placing ... This notation has been employed for
the expression of geometrical ratios by almost all writers on the Mathematics , on
...
The Hindus , in their treatises on Algebra , indicated the ratio of two numbers , or
of two algebraical symbols , by placing ... This notation has been employed for
the expression of geometrical ratios by almost all writers on the Mathematics , on
...
Side 204
Ratio is a mutual relation of two magnitudes of the same kind to one another , in
respect of quantity . " IV . Magnitudes are said to have a ratio to one another ,
when the less can be multiplied so as to exceed the other . v . The first of four ...
Ratio is a mutual relation of two magnitudes of the same kind to one another , in
respect of quantity . " IV . Magnitudes are said to have a ratio to one another ,
when the less can be multiplied so as to exceed the other . v . The first of four ...
Side 205
X . When three magnitudes are proportionals , the first is said to have to the third ,
the duplicate ratio of that which it has to the second . XI . When four magnitudes
are continual proportionals , the first is said to have to the fourth , the triplicate ...
X . When three magnitudes are proportionals , the first is said to have to the third ,
the duplicate ratio of that which it has to the second . XI . When four magnitudes
are continual proportionals , the first is said to have to the fourth , the triplicate ...
Side 210
the first and third shall have the same ratio to the second and fourth ; and in like
manner , the first and the third shall have the same ratio to any equimultiples
whatever of the second and fourth . Let A the first have to B the second the same
ratio ...
the first and third shall have the same ratio to the second and fourth ; and in like
manner , the first and the third shall have the same ratio to any equimultiples
whatever of the second and fourth . Let A the first have to B the second the same
ratio ...
Side 212
If the first of four magnitudes has the same ratio to the second , which the third
has to the fourth ; then , if the first be greater than the second , the third is also
greater than the fourth ; and if equal , equal ; if less , less . Take any equimultiples
of ...
If the first of four magnitudes has the same ratio to the second , which the third
has to the fourth ; then , if the first be greater than the second , the third is also
greater than the fourth ; and if equal , equal ; if less , less . Take any equimultiples
of ...
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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 |