The Elements of Euclid |
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Side 84
It is also rect- N // angular; for the straight line BD, being N 2^ / the diameter of the
circle ABCD, BAD is a N / / semicircle; wherefore the angle BAD is a N}^ - right (
31. 3.) angle; for the same reason C each of the angles ABC, BCD, CDA is a right
...
It is also rect- N // angular; for the straight line BD, being N 2^ / the diameter of the
circle ABCD, BAD is a N / / semicircle; wherefore the angle BAD is a N}^ - right (
31. 3.) angle; for the same reason C each of the angles ABC, BCD, CDA is a right
...
Side 86
... and be described about the square ABCD. Which was to be done. ... the
straight line BD is equal to AC, which is not greater than the diameter of the circle
BDE; join DA, DC, and about the triangle ADC describe (5. 4.) the circle ACD; the
...
... and be described about the square ABCD. Which was to be done. ... the
straight line BD is equal to AC, which is not greater than the diameter of the circle
BDE; join DA, DC, and about the triangle ADC describe (5. 4.) the circle ACD; the
...
Side 154
Describe (5.4) the circle ACB about the triangle, and draw its diameter AE, and
join EC; because the right angle BDA is ... Let ABCD be any quadrilateral
inscribed in a circle, and join AC, BD; the rectangle contained by AC, BD is equal
to the ...
Describe (5.4) the circle ACB about the triangle, and draw its diameter AE, and
join EC; because the right angle BDA is ... Let ABCD be any quadrilateral
inscribed in a circle, and join AC, BD; the rectangle contained by AC, BD is equal
to the ...
Side 202
CIRCLEs are to one another as the squares of their diameters.” Let ABCD, EFGH
be two circles, and BD, FH their diameters: as the square of BD to the square of
FH, so is the circle ABCD, to the circle EFGH. - For, if it be not so, the square of ...
CIRCLEs are to one another as the squares of their diameters.” Let ABCD, EFGH
be two circles, and BD, FH their diameters: as the square of BD to the square of
FH, so is the circle ABCD, to the circle EFGH. - For, if it be not so, the square of ...
Side 203
excess of the circle EFGH above the space S : because, by the preceding lemma,
if from the greater of two unequal ... the polygon AXBOCPDR to the polygon
EKFLGMHN: but the circle ABCD is greater than the polygon contained in it: ...
excess of the circle EFGH above the space S : because, by the preceding lemma,
if from the greater of two unequal ... the polygon AXBOCPDR to the polygon
EKFLGMHN: but the circle ABCD is greater than the polygon contained in it: ...
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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 |