The Elements of Euclid |
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Side 55
the centre, bisect any straight line AB, which does not pass through the centre, in
the point F: it cuts it also at right angles. Take (1.3.) E the centre of the circle, and
join EA, EB. Then, because AF is equal to FB, and FE common to the two ...
the centre, bisect any straight line AB, which does not pass through the centre, in
the point F: it cuts it also at right angles. Take (1.3.) E the centre of the circle, and
join EA, EB. Then, because AF is equal to FB, and FE common to the two ...
Side 56
If two circles cut one another, they shall not have the same Centre. Let the two
circles ABC, CDG cut one another in the points B, C; they have not the same
centre. For, if it be possible, let E be their centre: join EC, and draw any straight
line ...
If two circles cut one another, they shall not have the same Centre. Let the two
circles ABC, CDG cut one another in the points B, C; they have not the same
centre. For, if it be possible, let E be their centre: join EC, and draw any straight
line ...
Side 59
THEOR. lf a point be taken within a circle, from which there fall more than two
equal straight lines to the circumference, that point is the centre of the circle. Let
the point D be taken within the circle ABC, from which to the circumference there
fall ...
THEOR. lf a point be taken within a circle, from which there fall more than two
equal straight lines to the circumference, that point is the centre of the circle. Let
the point D be taken within the circle ABC, from which to the circumference there
fall ...
Side 62
Let the straight lines AB, CD, in the circle ABDC, be equal to one another: they
are equally distant from the centre. Take E the centre of the circle ABDC, and
from it draw EF, EG perpendiculars to AB, CD; then, because the straight line EF,
...
Let the straight lines AB, CD, in the circle ABDC, be equal to one another: they
are equally distant from the centre. Take E the centre of the circle ABDC, and
from it draw EF, EG perpendiculars to AB, CD; then, because the straight line EF,
...
Side 66
If a straight line touch a circle, and from the point of contact a straight line be
drawn at right angles to the touching line, the centre of the circle shall be in that
line. Let the straight line DE touch the circle ABC in C, and from C let CA be
drawn at ...
If a straight line touch a circle, and from the point of contact a straight line be
drawn at right angles to the touching line, the centre of the circle shall be in that
line. Let the straight line DE touch the circle ABC in C, and from C let CA be
drawn at ...
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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 |