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 47
... the same aggregate of units ; and two concrete numbers are equal , when they
contain the same number of units of the ... magnitudes are not admissible in
Euclid ' s criterion of Geometrical Equality , as he has not fixed the unit of
magnitude ...
... the same aggregate of units ; and two concrete numbers are equal , when they
contain the same number of units of the ... magnitudes are not admissible in
Euclid ' s criterion of Geometrical Equality , as he has not fixed the unit of
magnitude ...
Side 57
The square being considered as an equilateral rectangle , its area or surface may
be expressed numerically if the number of lineal units in a side of the square be
given , as is shewn in the note on Prop . 1 . , Book 11 . The student will not fail to ...
The square being considered as an equilateral rectangle , its area or surface may
be expressed numerically if the number of lineal units in a side of the square be
given , as is shewn in the note on Prop . 1 . , Book 11 . The student will not fail to ...
Side 58
For example , if the area of a square contain 9 square units , then the square root
of 9 or 3 , indicates the number of lineal units in the side of that square . Again , if
the area of a square contain 12 square units , the side of the square is greater ...
For example , if the area of a square contain 9 square units , then the square root
of 9 or 3 , indicates the number of lineal units in the side of that square . Again , if
the area of a square contain 12 square units , the side of the square is greater ...
Side 61
Is it possible to form a triangle with three lines whose lengths are 1 , 2 , 3 units : or
one with three lines whose lengths are 1 , V2 , V3 ? 53 . Is it possible to construct
a triangle whose angles shall be as the numbers 1 , 2 , 3 : Prove or disprove ...
Is it possible to form a triangle with three lines whose lengths are 1 , 2 , 3 units : or
one with three lines whose lengths are 1 , V2 , V3 ? 53 . Is it possible to construct
a triangle whose angles shall be as the numbers 1 , 2 , 3 : Prove or disprove ...
Side 99
Some one line of definite length is arbitrarily assumed as the linear unit , and the
length of every other line is represented by the number of linear units , contained
in it . The square is the figure assumed for the measure of surfaces . The square ...
Some one line of definite length is arbitrarily assumed as the linear unit , and the
length of every other line is represented by the number of linear units , contained
in it . The square is the figure assumed for the measure of surfaces . The square ...
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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 |