The Elements of Euclid |
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Side 99
If the first of four magnitudes has the same ratio to the second which the third has
to the fourth, then any equimultiples whatever of the first and third shall have the
same ratio to any equimultiples of the second and fourth, viz. 'the equimultiple of
...
If the first of four magnitudes has the same ratio to the second which the third has
to the fourth, then any equimultiples whatever of the first and third shall have the
same ratio to any equimultiples of the second and fourth, viz. 'the equimultiple of
...
Side 100
fore, that K is the same multiple of A, that L is of C: and because A is to B, as C is
to D, and of A and C certain equimultiples have been taken, viz. K and L; and of B
and D certain equimultiples G, H; therefore if K be greater than G, L is greater ...
fore, that K is the same multiple of A, that L is of C: and because A is to B, as C is
to D, and of A and C certain equimultiples have been taken, viz. K and L; and of B
and D certain equimultiples G, H; therefore if K be greater than G, L is greater ...
Side 102
If the magnitude A be to B, as C is to D, then also inversely B is to A, as D, to C.
Take of B and D any equimultiples whatever E and F; and of A and C any
equimultiples whatever G and H. First, let E be greater than G, then G is less than
E; and ...
If the magnitude A be to B, as C is to D, then also inversely B is to A, as D, to C.
Take of B and D any equimultiples whatever E and F; and of A and C any
equimultiples whatever G and H. First, let E be greater than G, then G is less than
E; and ...
Side 107
be taken, and let D, E be equimultiples of A, B, and F a multiple of C such, that D
is greater than F, but E is not greater than F: therefore D is greater than E: and,
because D and D E are equimultiples of A and B, and D is greater than E;
therefore ...
be taken, and let D, E be equimultiples of A, B, and F a multiple of C such, that D
is greater than F, but E is not greater than F: therefore D is greater than E: and,
because D and D E are equimultiples of A and B, and D is greater than E;
therefore ...
Side 108
Take of A, C, E any equimultiples whatever G, H, K ; and of B, G H K A. C E B D F
— L M N D, F any equimultiples whatever, L, M, N : then because A is to B, as C
is to D, and E to F; and that G, H, K are equimultiples of A, C, E, and L, M, ...
Take of A, C, E any equimultiples whatever G, H, K ; and of B, G H K A. C E B D F
— L M N D, F any equimultiples whatever, L, M, N : then because A is to B, as C
is to D, and E to F; and that G, H, K are equimultiples of A, C, E, and L, M, ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Euclid,Robert Simson Uten tilgangsbegrensning - 1834 |
The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Robert Simson Ingen forhåndsvisning tilgjengelig - 2017 |
The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Robert Simson Ingen forhåndsvisning tilgjengelig - 2017 |
Vanlige uttrykk og setninger
altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given point given ratio given straight line gles gnomon join less Let ABC meet multiple parallel parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third three plane angles triangle ABC triplicate ratio vertex wherefore
Populære avsnitt
Side 45 - Ir a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Side 41 - 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 54 - Ir any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle. Let ABC be a circle, and A, B any two points in the circumference ; the straight line drawn from A to B shall fall within the circle.
Side 18 - ABD, the less to the greater, which is impossible ; therefore BE is not in the same straight line with BC.
Side 10 - From a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line: it is required to draw from the point A a straight line equal to BC.
Side 8 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 256 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Side 129 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 23 - At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle. Let AB be the given straight line, and A...
Side 20 - ANY two angles of a triangle are together less than two right angles.
Bibliografisk informasjon
| Tittel | The Elements of Euclid |
| Forfatter | Euclid |
| Redaktør | Robert Simson |
| Utgiver | Desilver, Thomas & Company, 1838 |
| Original fra | University of Michigan |
| Digitalisert | 20. sep 2007 |
| Lengde | 416 sider |
| Eksporter sitat | BiBTeX EndNote RefMan |