The Elements of Euclid |
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Side 249
Analogy is the similitude of ratios, is of the same kind, and can serve for no
purpose in mathematics, but only to give beginners some general, though gross
and confused notions of analogy: but the whole of the doctrine of ratios, and the
whole ...
Analogy is the similitude of ratios, is of the same kind, and can serve for no
purpose in mathematics, but only to give beginners some general, though gross
and confused notions of analogy: but the whole of the doctrine of ratios, and the
whole ...
Side 257
... we have given a legitimate demonstration of this proposition instead of that in
the Greek and other editions, which very ... I say the ratio of the third C to the
fourth D, is either equal to, or greater, or less than the ratio of the first A to the
second ...
... we have given a legitimate demonstration of this proposition instead of that in
the Greek and other editions, which very ... I say the ratio of the third C to the
fourth D, is either equal to, or greater, or less than the ratio of the first A to the
second ...
Side 265
pression by which the ratio of the first A to the third C is signified, and by which, at
the same time, is shown that there are ... demonstration is not Euclid's: these
superfluous things are now left out, and a more simple demonstration is given
from ...
pression by which the ratio of the first A to the third C is signified, and by which, at
the same time, is shown that there are ... demonstration is not Euclid's: these
superfluous things are now left out, and a more simple demonstration is given
from ...
Side 297
found to the sum of the two magnitudes by which the given ratio is exhibited, one
of them, and the given magnitude; each of the parts is given.” Let the given
magnitude AB be divided into the parts AC, CB. which have a given ratio to one ...
found to the sum of the two magnitudes by which the given ratio is exhibited, one
of them, and the given magnitude; each of the parts is given.” Let the given
magnitude AB be divided into the parts AC, CB. which have a given ratio to one ...
Side 301
If the excess of a magnitude, above a given magnitude, has a given ratio to
another magnitude; the excess of both together above a given magnitude shall
have to that other a given ratio: and if the excess of two magnitudes together
above a ...
If the excess of a magnitude, above a given magnitude, has a given ratio to
another magnitude; the excess of both together above a given magnitude shall
have to that other a given ratio: and if the excess of two magnitudes together
above a ...
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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 |