The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; the Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored ; Also the Book of Euclid's Data, in Like Manner Corrected |
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Resultat 1-5 av 6
Side 41
to the triangle EBC , because it is upon the same base BC , and between the
same A D parallels BC , AE : but the triangle ... In the same manner , it can be
demonstrated B that no other line but AD is parallel to BC ; AD is therefore
parallel to it .
to the triangle EBC , because it is upon the same base BC , and between the
same A D parallels BC , AE : but the triangle ... In the same manner , it can be
demonstrated B that no other line but AD is parallel to BC ; AD is therefore
parallel to it .
Side 203
Two straight lines which are each of them parallel to the same straight line , and
not in the same plane with it , are parallel to one another . H Let AB , CD be each
of them parallel to EF , and not in the same plane with it ; AB shall be parallel to ...
Two straight lines which are each of them parallel to the same straight line , and
not in the same plane with it , are parallel to one another . H Let AB , CD be each
of them parallel to EF , and not in the same plane with it ; AB shall be parallel to ...
Side 207
If two straight lines meeting one another , be parallel to two straight lines which
meet one another , but are not in the same plane with the first two , the plane
which passes through these is parallel to the plane passing the others . * Let AB ,
BC ...
If two straight lines meeting one another , be parallel to two straight lines which
meet one another , but are not in the same plane with the first two , the plane
which passes through these is parallel to the plane passing the others . * Let AB ,
BC ...
Side 208
If two parallel planes be cut by another plane , their common sections with it are
parallels . * Let the parallel planes , AB , CD be cut by the plane EFHG , and let
their common sections with it be EF , GH ; EF is parallel to GH . For , if it be not ,
EF ...
If two parallel planes be cut by another plane , their common sections with it are
parallels . * Let the parallel planes , AB , CD be cut by the plane EFHG , and let
their common sections with it be EF , GH ; EF is parallel to GH . For , if it be not ,
EF ...
Side 248
X parallel to DC , and not in the same plane with it , KL is parallel ( 9. 11. ) to BA :
and because KL , MN are each of them parallel to BA , and not in the same plane
with it , KL is parallel ( 9 . 11. ) to MN ; wherefore KL , MN are in one plane .
X parallel to DC , and not in the same plane with it , KL is parallel ( 9. 11. ) to BA :
and because KL , MN are each of them parallel to BA , and not in the same plane
with it , KL is parallel ( 9 . 11. ) to MN ; wherefore KL , MN are in one plane .
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid,Robert Simson Uten tilgangsbegrensning - 1825 |
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Euclid,Robert Simson Uten tilgangsbegrensning - 1838 |
Vanlige uttrykk og setninger
added altitude angle ABC angle BAC base centre circle circle ABCD circumference common cone cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples Euclid excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise magnitude manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid Q. E. D. PROP radius reason rectangle rectangle contained rectilineal figure remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole
Populære avsnitt
Side 9 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 81 - The angles in the same segment of a circle are equal to one another.
Side 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Side 33 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Side 49 - 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 96 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Side 155 - 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 22 - ANY two angles of a triangle are together less than two right angles.
Side 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.
Side 24 - Any two sides of a triangle are together greater than the third side.
Bibliografisk informasjon
| Tittel | The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; the Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored ; Also the Book of Euclid's Data, in Like Manner Corrected |
| Forfattere | Euclid, Robert Simson |
| Utgiver | Desilver, 1829 |
| Original fra | University of Michigan |
| Digitalisert | 11. jun 2007 |
| Lengde | 516 sider |
| Eksporter sitat | BiBTeX EndNote RefMan |