The Elements of Euclid |
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Resultat 1-5 av 12
Side 25
Let ABC, DEF be two triangles which have the angles ABC, BCA equal to the
angles DEF, EFD, viz. ABC to DEF, and BCA to EFD; also one side equal to one
side; and first let those sides be equal which are adjacent to the A D angles that
are ...
Let ABC, DEF be two triangles which have the angles ABC, BCA equal to the
angles DEF, EFD, viz. ABC to DEF, and BCA to EFD; also one side equal to one
side; and first let those sides be equal which are adjacent to the A D angles that
are ...
Side 86
Join AC, BD cutting one another in E; and because DA is equal to AB, and AC
common to the triangles DAC, BAC, the two ... it may be demonstrated that the
angles ABC, BCD, CDA are severally bisected by the straight lines BD, AC;
therefore, ...
Join AC, BD cutting one another in E; and because DA is equal to AB, and AC
common to the triangles DAC, BAC, the two ... it may be demonstrated that the
angles ABC, BCD, CDA are severally bisected by the straight lines BD, AC;
therefore, ...
Side 124
therefore, whatever multiple the base HC is of the base BC, the same multiple is
the triangle AHC of the triangle ABC; for the same reason, whatever multiple the
base LC is of the base CD, the E A F same multiple is the triangle ------ so ...
therefore, whatever multiple the base HC is of the base BC, the same multiple is
the triangle AHC of the triangle ABC; for the same reason, whatever multiple the
base LC is of the base CD, the E A F same multiple is the triangle ------ so ...
Side 209
Therefore the base ABC is not to the base DEF, as the pyramid ABCG to any
solid which is less than the pyramid DEFH. ... Divide the base ABCDE into the
triangles ABC, ACD, ADE; and the base FGHKL into the triangles FGH, FHK, FKL:
and ...
Therefore the base ABC is not to the base DEF, as the pyramid ABCG to any
solid which is less than the pyramid DEFH. ... Divide the base ABCDE into the
triangles ABC, ACD, ADE; and the base FGHKL into the triangles FGH, FHK, FKL:
and ...
Side 319
Let the sides AB, BC about the acute angle ABC of the triangle ABC, which has a
right angle at A, have a given ratio to one another; the triangle ABC is given in
species. Take a straight line DE given in position and magnitude; and because
the ...
Let the sides AB, BC about the acute angle ABC of the triangle ABC, which has a
right angle at A, have a given ratio to one another; the triangle ABC is given in
species. Take a straight line DE given in position and magnitude; and because
the ...
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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 |