The Elements of Euclid |
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Side 214
Let a cone have the same base with a cylinder, viz. the circle ABCD, and the
same altitude. The cone is the third part of the cylinder; that is, the cylinder is
triple of the cone. If the cylinder be not triple of the cone, it must either be greater
than the ...
Let a cone have the same base with a cylinder, viz. the circle ABCD, and the
same altitude. The cone is the third part of the cylinder; that is, the cylinder is
triple of the cone. If the cylinder be not triple of the cone, it must either be greater
than the ...
Side 222
the cylinder to the cylinder; for every cone is the third part of the cylinder upon the
same base, and of the same altitude: therefore also the cylinder has to the
cylinder the triplicate ratio of that which AC has to EG. Wherefore similar cones,
&c.
the cylinder to the cylinder; for every cone is the third part of the cylinder upon the
same base, and of the same altitude: therefore also the cylinder has to the
cylinder the triplicate ratio of that which AC has to EG. Wherefore similar cones,
&c.
Side 223
it is to be shown, that the cylinder AH is to the cylinder HC, as the axis EK to the
axis KF. Produce the axis EF both ways; and take any number of straight lines EN
, NL, each equal to EK; and any number FX, XM each equal to FK; and let planes
...
it is to be shown, that the cylinder AH is to the cylinder HC, as the axis EK to the
axis KF. Produce the axis EF both ways; and take any number of straight lines EN
, NL, each equal to EK; and any number FX, XM each equal to FK; and let planes
...
Side 224
therefore also the cylinders EB, CM are equal. And because the cylinder FM is
cut by the plane CD parallel to its opposite planes, as the F cylinder CM to the
cylinder FD, so is (13. 12.) the axis LN to the axis KL. But the cylinder CM is equal
to ...
therefore also the cylinders EB, CM are equal. And because the cylinder FM is
cut by the plane CD parallel to its opposite planes, as the F cylinder CM to the
cylinder FD, so is (13. 12.) the axis LN to the axis KL. But the cylinder CM is equal
to ...
Side 225
consequently ES is a cylinder, the base of which is the circle EFHG, and altitude
MP: and because the cylinder AX is equal to ... is the base ABCD to the base
EFGH; for the cylinders AX, ES are of the same altitude; and as the cylinder EO to
the ...
consequently ES is a cylinder, the base of which is the circle EFHG, and altitude
MP: and because the cylinder AX is equal to ... is the base ABCD to the base
EFGH; for the cylinders AX, ES are of the same altitude; and as the cylinder EO to
the ...
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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 |